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2013 26 Cristina Sáenz de Pipaón Soba Contributions to Molecular Magnetism: Chiral Magnets and Networked SMMs Departamento Director/es Física de la Materia Condensada Palacio Parada, Fernando Campo Ruiz, Jesús Javier Director/es Tesis Doctoral Autor Repositorio de la Universidad de Zaragoza – Zaguan http://zaguan.unizar.es UNIVERSIDAD DE ZARAGOZA Departamento Director/es Cristina Sáenz de Pipaón Soba CONTRIBUTIONS TO MOLECULAR MAGNETISM: CHIRAL MAGNETS AND NETWORKED SMMS Director/es Física de la Materia Condensada Palacio Parada, Fernando Campo Ruiz, Jesús Javier Tesis Doctoral Autor 2013 Repositorio de la Universidad de Zaragoza – Zaguan http://zaguan.unizar.es UNIVERSIDAD DE ZARAGOZA Departamento Director/es Director/es Tesis Doctoral Autor Repositorio de la Universidad de Zaragoza – Zaguan http://zaguan.unizar.es UNIVERSIDAD DE ZARAGOZA Contributions to Molecular Magnetism: Chiral Magnets and Networked SMMs. Cristina Sáenz de Pipaón Soba Zaragoza, Enero 2013 THESIS SUPERVISORS: Javier Campo Ruiz Fernando Palacio Parada A mis padres, Juani y Jesús. A mis hermanos, Ana y Miguel. Aprender sin pensar es inútil. Pensar sin aprender es peligroso. Resumen xiii como GN, [Cr(CN)6][Mn(S)pnH(H2O)]·2H2O [8], ya estudiado previamente por este grupo de investigación. Para poder vericar la existencia de quiralidad magnética en las muestras anteriormente citadas, es necesario determinar su estructura magnética. Por esta razón, se han realizado experimentos de difracción de neutrones en el Institute Laue Langvenin (ILL), empleando el difractómetro de cuatro círculos D15 y el difractómetro Laue VIVALDI. A partir de los datos de difracción de neutrones obtenidos, con la ayuda de la teoría de representaciones irreducibles y el programa FULLPROF [9], se han resuelto las estructuras magnéticas de los tres compuestos. Basándonos en la denición de quiralidad magnética propuesta y desarrollada en el capítulo 2 de esta tesis, se ha encontrado que en las muestras GN-MnMn y GN-DMF(R) coexisten quiralidad nuclear y magn tica. Este hecho convierte estos compuestos en excelentes candidatos para realizar experimentos de dicroismo magnetoquiral y observar si existe alguna diferencia entre la señal en fase paramagnética y en fase ordenada. El compuesto GN-DMF(rac) no presenta quiralidad magnética debido a la simetría de la estructura. Línea B Estudios anteriores han observado que algunos cubanos de Co(II) presentan un comportamiento de SMM en torno a 5K [10]. Pequeñas diferencias en la estructura nuclear del cluster generan variaciones en las interacciones magnéticas entre iones Co(II), provocando cambios en la barrera energética o en el estado fundamental, inuyendo por tanto en su magnetismo. Incluso pueden encontrarse situaciones en las que existe orden magnético a largo alcance por interacciones de canje [11, 12] o dipolares [13]. Nuestro objetivo en esta parte de la tesis es doble, por un lado queremos caracterizar cómo ligeras modicaciones en la simetría del cubano de Co(II) inuyen en sus propiedades magnéticas. Por otro lado, se quiere estudiar si estos SMMs cuando están ordenados en redes, conservan sus características puntuales de clústeres discretos y cómo el entorno puede inuir en su magnetismo, pudiendo darse el caso de la existencia de orden magnético de largo alcance. Para llevar a cabo estas investigaciones, se han caracterizado magnéticamente cubanos de Cobalto (II) aislados o dispuestos en redes de diferente dimensionalidad, sintetizados por miembros del grupo consolidado M4 y que forman parte de la tesis de la Lcda. Elena Forcén. Entre ellos se dispone de un compuesto Co 4 (citr) 4 [Co(H 2 O) 4 ] 4 (donde citr=citrato) que presenta tres fases cristalinas interconvertibles en estado sólido, en las que los clusters se encuentran aislados, formando una estructura nuclear modulada o constituyendo un polímero lineal. También se han estudiado redes bidimensionales cuadradas del tipo A4[Co4cit4{Co(OHCH2CH2OH)(H2O)2}2]·nH20 (A=K, Rb, Cs) [14, 15] y rómbicas Cs4[Co4cit4{Co(H2O)4}2]·11H2O formadas por xiv Resumen cubanos de Co(II) en su nodos y cobaltos que actúan como nexos entre ellos. Incrementando la dimensionalidad de la red, se ha estudiado en esta tesis una red tridimensional de tipo diamante (K4Co4(cit[µ−Co(H2O)4]2·8H2O)n con cubanos en los nodos que presenta una estructura MOF (Metal Organic Framework), lo que puede dar lugar a interesantes aplicaciones. El estudio magnético y calorimétrico de estos compuestos se ha realizado en varios equipos comerciales de Quantum Design (PPMS y MPMS). También se ha empleado, gracias a la colaboración con el Dr. F. Luis del ICMA, un refrigerador de dilución dotado con un SQUID para los estudios magnéticos a muy baja temperatura. La caracterización magnética de estos compuestos ha permitido observar la coexistencia de diferentes procesos de bloqueo y orden magnético en la misma muestra. Asimismo se ha observado como modicaciones estructurales inuyen en la respuesta magnética. Acronyms CsCo 4 /R Cs4{[Co(C6H4O7)]4µ(Co(H2O)4)2]·16H2O CsCo 4 /S ( C28H36Co6O36Cs4)n·4.5nH2O·2.5n(C2H6O2 ) CsCo 4 +1 Cs2[Co(H2O)6][Co6(C6H4O7)4(H2O)8]·12H2On DM Dzyaloshinskii-Moriya DMF Dimethylformamide ETG Ethylene glicol FT Fourier Transform GN [Cr(CN)6][Mn(S)−pnH(H2O)]·2H2O GN-MnMn [Mn(CN)6][Mn(S)−pnH(H2O)] ·2H2O GN-DMF(R) [Cr(CN)6][Mn(R)−pnH(DMF)]·H2O GN-DMF(rac) [Cr(CN)6][Mn(rac)−pnH(DMF )]·H2O ILL Institute Laue Langvenin IR Irreducible representation KCo 4 /S (C28H36Co6O36K4)n·XH2O·Y n(C2H6O2) RbCo 4 /S (C28H36Co6O36Rb4)n·9.5·n(H2O)·2n(C2H6O2) SSM Single Molecular Magnets YN K0.4[Cr(CN)6][Mn(S)−pn](S)−pnH0.6 Introduction Magnetism is a really broad branch of physics, and magnetic compounds are used for a wide variety of technical applications. Reducing the size of the magnetic units until a molecular level, we reach the area of molecular magnetism, where magnetism is combined with some of the intrinsic properties of molecular solids (nanoscopic size, low density, synthetic versatility, optical transparency, and so on). An interested reader could easily nd excellent books devoted to it ( i. e. see references [16, 17]). A smart synthesis chooses the molecular blocks (only organic molecules or organic molecules combined with inorganic fragments) and their connectivity (clusters, chains, plains or three-dimensional structures) to exert some control in the magnetic properties of the material. Moreover, multifunctional molecular magnetic materials combine magnetism and one or more physical properties (fotomagnetism, magnetooptic, magnetoconductivity, etc.). Due to the limited amount of magnetic atoms of molecular materials, they are excellent systems to study fundamental concepts of physic as magnetic exchange, tunnel eect of magnetization, electronic transfer, magnetic anisotropy, coexistence of nuclear and magnetic chirality, etc. Molecular magnetism has achieved important goals in the past two decades providing examples of novel phenomena and potential applications. It went under a revolution when the rst molecular ferromagnet of organic-metalorganic nature was synthesized in 1985, the salt [FeIII(Cp)∗2]+[TCNE]− that present spontaneous magnetization and magnetic order below 4.5K [18]. Since then, other molecular materials of dierent nature: purely organic, inorganic or metalorganic, have been discover to order magnetically at dierent temperatures. Through the development of new Prussian Blue Analogues (PBA) [19], a very important step was reached when molecule-based long-range magnetically ordered (LRMO) materials with Curie temperatures above room temperature (RT) were obtained. One paradigmatic example of the continuous evolution of molecular magnetism can be found in the organic magnets: the rst organic ferromagnet, p−NPNN , appeared in 1991 and has an order temperature of 0.67K [20]. From there, in just ve years, the ordering temperature reached 36K at normal pressure and 76K at 20Kbar, which is in the tem- 4 Introduction perature region of the liquid nitrogen, for the phase β of the organic radical p−NC −C6F4−CNSSN [21, 22]. It has been a synergy between a rational approach of the exchange interaction and coordination chemistry which has allowed molecule-based magnets to reach high ordering temperatures. But there have been others milestones in the development of molecular magnetism, like the magnetic hysteresis at molecular level, the discover of photoswichtable magnetic materials, and materials combining conduction and bulk ferromagnetism [23, 24]. This thesis is devoted to multifunctional molecular materials where nuclear and magnetic chirality coexist and Single Molecule Magnets (SMM). Historically, chirality was mainly studied in biology due to the important role that it plays in life, i. e. biological molecules use only left-handed amino acids and only right-handed sugars. But chirality can confer unique properties to compounds, arising interest progressively into much elds of chemistry, as organometallic and coordination compounds, metal nanoparticles and molecular materials [25]. A chiral nuclear structure may confer to the compound piezoelectricity, Natural Optical Activity (NOA), Pyroelectricity or Second Harmonic Generation [26], properties that can be relevant in the design of new molecular devices. Especially, because molecule-based materials are transparent for the light, their optical properties have attracted much attention. Moreover, if magnetic chirality coexists with nuclear chirality, spatial and temporal symmetries are simultaneously broken, and a new eect called magnetochiral anisotropy (MChA) will appear. This eect was observed in 1997 by Rikken and Raupach [27] for a paramagnetic enantiopure system. The phenomenon is enhanced in enantiopure chiral ferromagnets and the bistability of a magnetically ordered state open the possibility to employ such materials for data storage with a detections based in MChD instead of magnetic circular dichroism [28]. Moreover, ferromagnetic chiral media are magneto-electric, so it is possible electrical reading/writing of the magnetic state of the medium [29] [30]. Materials of this category are very interesting for their potential applications, and in addition, they allow to explore new elds for physics. The rst compound where the coexistence of nuclear and magnetic chirality has been demostrated is [Cr(CN)6][Mn(S)pnH(H2O)]·2H2O [8]. It orders magnetically and the resultant magnetic structure, determined by our working group [31], is chiral according to the denition given in section 2.5. The existence of a soliton at the magnetic phase transition temperature for this compound was rst postulated [32] and then demonstrated [33]. The experiments performed with this compound reveal the role that magnetic chirality plays in dynamical properties, the chirality can strongly inuence the generation, mobility and relaxation of spin-wave excitations. Very similar to GN are two chiral nuclear compounds studied in this thesis [Mn(CN)6][Mn(S)pnH(H2O)] ·2H2O [6], denoted as 1.2. Chirality 11 1.2.1 Non-magnetic chirality The term chirality, in a nuclear sense, refers to the symmetry restriction of the absence of improper symmetry operations in a molecule or a crystal. There is a punctual denition, called chemical, which is used referred to molecules and another denition more general, which is applied to whole crystal structures. This last one takes into account also the way the molecules are distributed in the crystal structure. Molecular chirality In chemistry, chirality usually refers to molecules, being a local concept. According to IUPAC (The International Union of Pure and Applied Chemistry) [38], chirality is the geometric property of a rigid object (or spatial arrangement of points or atoms) of being non-superposable on its mirror image; such an object has no symmetry elements of the second kind, i. e, improper elements (a mirror plane, a center of inversion, a rotoreection axes). A molecule non-superposable on its mirror image is called a chiral molecule, and its two mirror images are called enantiomers or optical isomers. In a racemic compound the molecules are chiral, but a mix of both chiralities makes the compound achiral. The word "racemic" is derived from the Latin word "racemus" for "bunch of grapes"; the term having its origins in the work of Louis Pasteur who isolated racemic tartaric acid from wine [39] There are several nomenclatures to refer to a pair of enantiomers. The more general one designate them as "right-" (R) and "left-handed" (S). Each chiral center is labeled R or S according to a system that assigns a priority to the ligands of the chiral center according to the Cahn-Ingold-Prelog priority rules (CIP) based on atomic numbers [40, 41]. If the center is oriented so that the lowest-priority of the ligands is pointed away from a viewer, the viewer see two possibilities: if the priority of the remaining substituents decreases in clockwise direction, it is labeled R, if it decreases in counterclockwise direction, it is S. This system labels each chiral center in a molecule (and also has an extension to chiral molecules not involving chiral centers) and can label, for example, an (R,R) isomer versus an (R,S), so it is useful for naming molecules with more than one stereocenter or chiral center. Pairs of enantiomers can also be named according to their optical activity. If it rotates the light clockwise (as seen by a viewer towards whom the light is traveling), the enantiomer is labeled dextrorotatory (+); it mirror imagine rotates light anticlockwise and is labeled levorotatory (-). 12 Chapter 1. Introduction and objectives In biology, there are a great number of chiral molecules and they are designated L or D relating the spatial conguration of the molecule atoms to glyceraldehyde, which is chiral itself . Most aminoacids are L and sugars are D. Proteins are named left-handed or right-handed depending on which aminoacid they proceed from. Enzymes are also chiral and distinguish between two enantiomers of a chiral substrate. The (+) or (-) and L or D nomenclatures are confusing if we have more than one chiral center, the only nomenclature useful in this case is the R or S classication. Most commonly, chiral molecules have point chirality, centered around a single atom, which has dierent substituent ligands and it is chiral. However in rare cases, two of the ligands dier from each other by being mirror images of each other. When this happens, the mirror image of the molecule is identical to the original, and the molecule is achiral. This is called pseudochirality. A molecule can have multiple chiral centers without being chiral overall if there is a symmetry between the two (or more) chiral centers themselves. Such a molecule is called a meso-compound (see example in gure 1.2a). It is also possible for a molecule to be chiral without having actual point chirality. Common examples include 1,1'-bi-2-naphthol (BINOL) (gure 1.2c), 1,3-dichloro-allene, and BINAP, which have axial chirality; (E)-cyclooctene (gure 1.2b) which has planar chirality; and certain calixarenes and fullerenes which have inherent chirality. As molecules have considerable exibility, they can adopt a variety of dierent conformations. These various conformations can be chiral, so it is also possible for a molecule to be chiral without having actual point chirality. When assessing chirality, a time-averaged structure is considered and for routine compounds, one should refer to the most symmetric possible conformation. Nuclear chirality In order to understand chirality in a physical context, we use the concept of congruence. Two objects, A and B, are said to be congruent if to each point of A corresponds a point of B; and the distance between two points of A is equal to the distance between the corresponding points in B. Consequently, the angles will be equal in A and B in absolute value. Such correspondence is an isomerism. The congruence can be direct or opposite (positive or negative), according to whether the corresponding angles have the same or opposite angles. An object will be said enantiomorphous or enantiomer with respect to another if they are congruent and the congruence is opposite [42]. 1.2. Chirality 13 Figure 1.2: a) Schematic drawing of an example for a mesocompound. b)(E)- cyclooctene, which shows planar chirality. c)1,1'-bi-2-naphthol (BINOL), which presents axial chirality 14 Chapter 1. Introduction and objectives If the congruence is direct, the objects can be bought to coincidence by symmetry operations whose determinant is equal to +1, called proper operations, which are translations, rotations and screws axis. If the congruence is opposite, one object will be said to be enantiomorphous with respect to the other one and the two objects can be bought to coincidence by symmetry operations whose determinant is equal to -1. This symmetry operations, called improper operations, are reections, inversions, glide planes, rotoinversions and rotoreections. Screws, glide planes, rotoinversions and rotoreections can be decomposed as a product of symmetry operations. Crystals can present dierent symmetry operations. When translations and symmetry operations involving them are not taking into account, 32 point groups can be constructed by combining symmetry operations in a threedimensional space. These crystal point groups, also called crystal classes, can be seen in table 1.1. The 32 point groups can be split in 21 non-centrosymmetric point groups and 11 centrosymmetric point groups. In a centrosymmetric group for every point (x, y, x) there is an indistinguishable point (-x, -y,-z). The 21 non-centrosymmetric groups can be divided in 10 polar groups and 11 enantiomorphic groups. Polar groups presents a polar direction which is not symmetry equivalent to its opposite direction. Enantiomorphic groups only allow proper symmetry operations. The compatibility of the crystal structure with rotation or inversion axes of order 1, 2, 3, 4, 6 impose some restrictions on the geometry of the lattice. Seven crystal systems can be distinguished: triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal and cubic. These crystal systems can also be combined with one of the following lattice centering: primitive centering (P), body centered (I), face centered (F) and centered on a single face (A, B, C). There are 14 possible combinations of lattice centering and crystal systems, which are the 14 Bravais lattices. If we combine the 14 Bravais lattices with the 32 point groups, we obtained 73 symmorphic groups. In a symmorphic group, all generating symmetry operations leave one common point xed. If we introduce translations, 230 space groups are found. In the 230 space groups [26], there are 65 enantiomorphic or chiral groups, which arise from the 11 enantiomorphic point groups where only proper symmetry operations are allowed and the congruence between their objects is direct. Thus, a chiral space group contains only pure rotations, pure translations and screw rotations, which are proper symmetry elements with determinant +1. Some chiral space groups are also polar. Enantiomorphic crystals can be build by chiral or achiral molecules or atom groups. In the last cases, the achiral molecules or atom groups form chiral congurations in the structure. 1.2. Chirality 15 Table 1.1: Laue Classes, centrosymmetric/non-centrosymmetric crystal classes (CS/NCS), enantiomorphic or polar group (E/P), and the occurrence ( X ) or not of natural optical activity (N), pyroelectricity and piezoelectricity (Pe) and Second Harmonic Generation (S) Crystal System Laue Class CS NCS E N Pe S Triclinic -1 1 E XXX -1 Monoclinic 2/m 2 E XXX m P XXX 2/m Orthorhombic 2/m 2/m 2/m 222 E X X mm2 P XXX 2/m 2/m 2/m Tetragonal 4/m 4 E XXX -4 P X X 4/m 4/m 2/m 2/m 422 E X X 4mm P X X -42m P X X 4/m 2/m 2/m Trigonal -3 3 E XXX -3 -3 2/m 32 E X X 3m P X X -3 2/m Hexagonal 6/m 6 E XXX -6 P X 6/m 6/m 2/m 2/m 622 E X X 6mm P X X -62m P X 6/m 2/m 2/m Cubic 2/m -3 23 E X X 2/m -3 -4/m -3 2/m 432 E X -43m P X -4/m -3 2/m 16 Chapter 1. Introduction and objectives 1.2.2 Previous denitions of magnetic chirality The concept of magnetic chirality has been widely discussed and several local denitions have been given, but there is not an universal and global denition for magnetic chirality as it varies from one author to another [4347]. It does not seem to be very clear, and it is often mixed with the concept of nuclear or crystallographic chirality. Nuclear and magnetic chirality are separated concepts: a chiral nuclear structure may be magnetically chiral or not, and a chiral magnetic structure may be chiral nuclear or not. Part of the confusion in the denition of magnetic chirality also arises from the dierent phenomena related to it. Most part of the studies about magnetic chirality are done to describe magnetic phase diagrams, new critical exponents, chiral critical uctuations, etc. We are interested in magnetic chirality referred to magnetic structures. Blume [48] and Malayev [49] were the rst authors interested in describing a magnetically chiral structure. Blume tried to explain that the magnetization density in dierent regions of the unit cell may not be collinear with the net magnetization. In this section, we give a brief glimpse of the dierent denitions for magnetic chirality that have been employed more or less frequently, and remark the need of a global denition. In the chapter 2, in the section 2.5, we explain the denition we propose and adopt for magnetic chirality. The magnetic chirality may arise due to the antisymmetric magnetic interactions and/or the single-ion anisotropy through the spin-orbital interactions. The most important antisymmetric magnetic interaction in this context is the Dzyaloshinskii-Moriya (DM) interaction that violates the inversion symmetry in the spin space. DM interaction is explained in this section. Local denitions for magnetic chirality When the rst studies of canted or non-collinear magnets appeared, with the discovery of rare-earth helimagnets such as Ho, Dy and Tb, several studies where performed to described the geometry of the arrangement of the spins. Villain [43] tried to describe the behavior of a frustrated lattice, which is a lattice in which all interactions between pair of spins can not be simultaneously satised. He focused on sets of four classical, two dimensional spins and stated two types of ground states that can be seen in gure 1.3: • If there is an even number (0, 2 or 4) of antiferromagnetic bonds, all spins are in the same direction, and the set of four spins is a non-frustrated plaquette. • If there is an odd number (1 or 3) of antiferromagnetic bonds, the ground state is canted, and the plaquette is frustrated. The system has an extra 1.2. Chirality 17 a) b) c) Figure 1.3: Plaquette where black bonds are ferromagnetic and red bonds are antiferromagnetic. a) Non-frustrated plaquette; b) Frustrated plaquette, spins rotate clockwise; c) Frustrated spins rotate counterclockwise degeneracy, characterized by τ , that indicates whether the spins rotate clockwise ( τ= 1 ) or counter-clockwise ( τ=−1 ) during a clockwise trip around the plaquette. Both states have the same energy. Villain gave a local denition of chirality based in the sign of τ , which only involved the atoms in a close trip around the plaquette. Another example of frustration is the organization of spins in antiferromagnetic materials when the spins are located at the vertices of a triangular lattice. Miyashita and Shiba [44] applied Villain's discovery to the case of a triangular lattice where frustration led to the non-collinear or canted ordered state. They introduced a scalar quantity, chirality, dened by equation 1.1. In this equation the summation runs over the three directed bonds surrounding a plaquette and kp gives ±1 for the two degenerated spin congurations depicted in gure 1.4. In this case, chirality is a pseudoscalar which is invariant under global spin rotation but it changes sign under global spin reection. kp=2 3 √3 p ∑ <ij> [Si×Sj]z (1.1) Kawamura and Miyashita [45] extended this denition of chirality to a twodimensional Heisenberg antiferromagnet on a triangular lattice, for which they redened chirality as a vector given in equation 1.2. kp=S1×S2+S2×S3+S3×S1 (1.2) Similar chiral degeneracy is also found in other types of canted magnets, such as helimagnets (spiral magnets, see gure 1.5 ) in which rightand left- 18 Chapter 1. Introduction and objectives a) b) Figure 1.4: Plaquette where bonds are antiferromagnetic. a) (+) chirality b) (-) chirality handed helices are energetically degenerated [46][50]. Another kind of chirality can be observed in many antiferromagnetic pyrochlores [51], where a high degree of geometrical frustration exists. Theoretical studies predict that the magnetic ground state is continuously disordered and susceptibility measurements show that they often behave as conventional spin glasses. As a consequence of frustration, non coplanar ordered phases, are stabilized and the anomalous Hall eect (AHE) can appear due to spin chirality. Three non-coplanar spins S1 , S1 , and S1 contribute to the AHE with a term which is proportional to the so-dened scalar chirality [52] shown in equation 1.3. Of course, in disordered congurations chirality is locally non-zero, but its average generally vanishes and this contribution can only be observed in systems with long range chiral ordering. χ123 =S1·(S2×S3) (1.3) All this denitions are local, and we are looking for more general denition of magnetic chirality or chirality of a magnetic structure. Blume-Malayev equation Blume [48] and Maleyev [49] formulated that the scattered intensity of a polarized neutron beam can be written as in equation 1.4: I=C(|FN|2+FM⊥·(FM⊥)∗+P·FM⊥F∗ N+P·(FM⊥)∗FN+P·(FM⊥×(FM⊥)∗) (1.4) In equation 1.4, I is the scattered intensity, FN is the nuclear structure factor, FM⊥ is the component of the magnetic structure factor which is perpendicular to the scattering vector q and P is the polarization of the neutron beam. In 1.2. Chirality 19 a) b) Figure 1.5: Chiral degeneracy in the ordered state of a XY helimagnet. the cases we have studied, P is zero as the neutron beam was not polarized. FM⊥ is also called the magnetic interaction vector and is dened as FM⊥(q) = e×FM(q)×e , where e is a unitary vector in the direction of q . Both the magnetic structure factor and the interaction vector are in general complex vectors. The neutron scattering theory is briey explained in appendix A. The term FM⊥×FM⊥∗ is the so-called chiral term. Dra. Clara González adopted in her thesis [31] a denition for chirality based on this term. We will modify this denition in section 2.5 to adopt a global denition for magnetic chirality. The DM interaction. A general spin Hamiltonian including the Zeeman term and describing the low-lying states for any pair of interacting magnetic centers A and B, may be written as follows (i. e. see ref. [53]): H =JSA·SB+SA¯ DSB+d·(SA×SB) + β(SA·gA+SB·gB)H (1.5) In equation 1.5, there are several terms: • The rst term refers to the isotropic exchange interaction, which lines up the spins of the magnetic atoms. This term is characterized by the exchange constant J , which gives the strength of the magnetic interaction, and can be either positive or negative depending on the nature of the interaction. If the interaction is ferromagnetic J is positive, while for antiferromagnetic couplings J will take negative values. 20 Chapter 1. Introduction and objectives Figure 1.6: a) Example of a ferromagnetic interaction b) Example of DM interaction • The second term describes both the dipolar and the anisotropic interaction, characterized by the tensor ¯ D . The dipolar interaction arises from the inuence of the magnetic eld created by one of the magnetic ions on the magnetic moment due to the other. The anisotropic interaction results from the combined eects of the local spin-orbit coupling and the interaction between the magnetic center. • The third term refers to the antisymmetric interaction called the Dzyaloshinski-Moriya interaction (DM) that will be further explained in this section. • The last term refers to the Zeeman term, which describes the splitting of the spectral lines of an atom in the presence of a strong magnetic eld. This eect is due to the distortion of the electron orbitals in the presence of a magnetic eld. We are specially interested in the term referred to the DM interaction. This interaction results from the anisotropic exchange interaction which is a combined eect of the spin-orbit coupling and the exchange interaction. It was rst proposed by Dzyaloshinsky [54] using symmetry arguments, and then analyzed by Moriya [55, 56]. According to the DM term in equation 1.5, the energy due to this term is minimized when the cross product of spins is as big as possible and its sign is opposite to d . This can be reached by spins 90 o apart and lying in a plane perpendicular to d . To minimize the DM interaction, spins tend to form non collinear spin structures. Therefore, as can be seen in gure 1.6, DM compete with the isotropic exchange interaction that tends to form collinear magnetic structures. DM interaction is responsible for weak ferromagnetism, as it favors a canted spin arrangement instead of a collinear one. In a crystal, the DM interaction depends on the sites in which the magnetic atoms are, i.e. it depends on the crystal symmetries. The vector d is determined by the fact that the energy of the system must remain invariant to the 1.3. Chiral Molecular Magnets 27 change term, whereas non-orthogonal magnetic orbitals will contribute to the antiferromagnetic term. The net interaction is simply the sum of all the ferromagnetic and antiferromagnetic contributions. One of the most important characteristics of the cyanide compounds is that their magnetic behavior can be predicted. It is therefore possible to tune the material changing the metal ion, its oxidation state and therefore the number of unpaired electrons per site. This is explained by the Goodeneough-Kanamori rules [76]. According to these rules, the exchange interaction between an M and a M' metal sites through a linear M−NC −M′ fragment can present three situations[75]: 1. If the unpaired electrons of M occupy eg orbitals, all the exchange interactions with the t2g magnetic orbitals present on [M′(CN)6] will be ferromagnetic. Thus, if a Prussian Blue is prepared by adding a d8 or d9 M cation to a paramagnetic [M′(CN)6] anion, a ferromagnet should result. 2. If all the unpaired electrons of M occupy t2g type orbitals, all the exchange interactions with the t2g magnetic orbitals present on [M′(CN)6] will be antiferromagnetic. In this case, if the Prussian Blue is prepared by adding a d2 or d3 cation to a paramagnetic [M′(CN)6] anion, a ferrimagnet should result. 3. If the unpaired electrons of M lie in both t2g and eg orbitals, ferromagnetic and antiferromagnetic interactions with the t2g magnetic orbitals on [M′(CN)6] coexist and compete. Here, the overall nature of the interaction is not so simple to predict. Usually, the antiferromagnetic interactions dominate and the solid orders ferrimagnetically. The compounds belonging to this family are extensively used as pigments and as electrochromic and electrocatalyst materials, and they have shown the capability to exhibit photo-induced properties. All these characteristics of cyanide-bridged Prussian-blue systems, make them excellent candidates for a smart design of nuclear and magnetic chiral compounds. To assure the presence of magnetic chirality in these compounds, the group of Prof. K. Inoue from the Hiroshima University has developed two synthetic strategies. The simplest one is to make use of a geometric approach using a chiral crystallographic skeleton, like a spiral, where paramagnetic blocks with high magnetic anisotropy, are joined. This skeleton would by itself allow antisymmetric magnetic interactions of DM type. This strategy has been used in the 3D networks [Cr(CN)6][Mn(S)−pn]{(S)−pnH}0.6K0.4 (Yellow Needle, YN) [77] and [Cr(CN)6][Mn(NH2−(ala)]3·H2O (Similar to Yellow Needle, SYN) [78], where (S)-pn=(S)-1,2-diaminopropane and 28 Chapter 1. Introduction and objectives Figure 1.10: A) View of the YN structure along the c axis. Some atoms are omitted for clarity. Color scheme: Cr: brown, Mn: red, C: gray, N: blue B) View of the bonding and coordination octahedra of YN. Figure taken from [31] ala=alanine. The nuclear and magnetic structure for the YN compound can be seen in gures 1.10 and 1.11. Other possibility used is based on DM interactions along a crystallographic axis in a non-centrosymmetric material, without the need of a chiral skeleton. This second strategy has been followed to form 2D networks as [Cr(CN)6][Mn( S )−pnH] (denoted as Green Needle, GN, for its shape and colour) [8] and [W(CN)8]4[Cu(S)−pnH2O]4[Cu(S)−pn]2·2.5H2O (WCu) [79]. The two chiral compounds studied in this thesis are the result of two modications in the GN synthesis, [Mn(CN)6][Mn(S)pnH(H2O)]·2H2O (GNMnMn) [6] and [Cr(CN)6][Mn(R)−pnH(DMF)]·2H2O (GN-DMF) [7], where DMF stands for N,N-dimethylformamide= (CH3)2N−CHO . For example, the WCu compound crystallizes in the space group P 21 , being the 21 axis parallel to the b axis. It is logical to think that the canting of the spins is due to DM vectors induced along the b axis. Both strategies can give rise to materials very dierent in nature, since in the rst one, magnetic chirality arises from the crystallographic geometry, whereas in the second, magnetic chirality is due to the lack of an inversion centre in the material. The nuclear and magnetic structure of some of this compounds (GN, YN and SYN) have been presented and discussed in Dra. 1.3. Chiral Molecular Magnets 29 Figure 1.11: A) View along the c axis of YN magnetic structure with Cr atoms in blue and Mn atoms in pink. B) Another view of the structure, with the c axis in vertical to easily see the helixes both types of atoms are displaying. Figure taken from [31] Clara Gonzalez's thesis [31]. Due to the likeness between GN and the compounds studied in this thesis, a brief summary about the GN nuclear and magnetic structure and properties is provided in the next subsection. GN The GN compound has been widely studied [8, 32, 33, 8083]. It was synthesized in 2003 by Inoue and coworkers [8]. In gure 1.12, an ORTEP drawing of the asymmetric unit of the compound can be seen. Four cyanide groups in the [Cr(CN)6]3− ion are linked to MnII ions to form a bimetallic network, which is arranged almost perpendicular to the c axis. The compound crystallizes in the space group P212121 and shows two sublattices, one of CrIII and another of MnII . It presents three dierent phases which are interconvertible (a scheme can be seen in gure 1.13). Each phase is magnetic at low temperature, with critical temperatures of Tc =38K, 39K and 73K for the Phases I, II and III, respectively. All the critical temperatures are remarkably high for a metal-organic molecular magnet. The three phases can be transformed into one another, diering mainly in the position of the chiral carbon and also in the water content. Magnetization measurements reveal a ferrimagnetic ordering. Chirality in the magnetic structure was at rst suggested by the enhanced magnetic circular dichroism near TC . AC susceptibility measurements show an unusual behavior between 34K and 38K, as can be seen in gure 1.14 [84]. In Dra. Clara Gonzalez thesis [31], the three phases were studied by single crystal neutron diraction experiments performed in VIVALDI and D10 at 30 Chapter 1. Introduction and objectives Figure 1.12: ORTEP drawing of the asymmetric unit of the GN compound. Hydrogen atoms are omitted for simplicity. Figure 1.13: Scheme of the transformation of the phases in GN compound. The lattice parameters and the interlayer distance between Cr and Mn are shown. Figure taken from [31] 1.3. Chiral Molecular Magnets 31 Figure 1.14: Ac susceptibility measurements of GN at frequencies between 1 Hz and 1 kHz and zero applied dc eld. Figure taken from [84] the ILL. The nuclear phases were rened, and the magnetic structures were determined. Phases I and II consist of planes containing CrIII and MnII octahedra linked by CN groups, where the MnII ion is also attached to a water molecule. In contrast, in Phase III there are no water molecules, and the MnII ion is linked to six CN groups, one of which is also linked to the diaminopropane moiety. As a consequence of the loss of water, the distances between magnetic atoms in the same plane and from one plane to the neighboring plane, which are similar for Phases I and II, they are much smaller for Phase III. Among the three phases, Phase I presents a more similar structure to GN-MnMn and GN-DMF. For this reason, some of its features are described in this section. As the distortion of the environments of magnetic atoms may be important in order to compare the magnetism of GN with the magnetic behavior of GnMnMn and GN-DMF, the distances and angles for CrIII and MnII octahedra can be found in table 1.2. Another factor that could be important, is the distance between magnetic atoms in the same plane and from one plane to the neighboring one. For Phase I, the distances are listed in table 1.3. A propagation vector equal to zero was found for the three phases and the magnetic structures agree with the previous magnetic measurements performed in single crystals. The structures for the three magnetic phases all correspond to two sublattices, one of chromium and the other one of manganese disposed ferrimagnetically with respect to each other. For Phases I and II the magnetic structure can be described by the Irreducible Representation Γ4 , which allows 32 Chapter 1. Introduction and objectives Table 1.2: Bond lengths and angles for CrIII and MnII octahedra at 43K. Data obtained in D10. A-X-B dA−X Å dB−X Å \ AXB C1-Cr-C6 2.126(8) 2.023(8) 177.8(5) C2-Cr-C5 2.006(7) 2.084(7) 177.0(4) C3-Cr-C4 2.009(7) 2.033(7) 173.2(4) N1-Mn-N5 2.125(7) 2.186(7) 178.1(3) N2-Mn-N6 2.163(7) 2.224(7) 177.2(3) N7-Mn-O1 2.327(7) 2.239(7) 177.8(4) A-X-B \ AMnB A-Mn-B \ AMnB C4-Cr-C5 90.69 O1-Mn-N2 86.13 C4-Cr-C1 87.08 O1-Mn-N5 95.85 C4-Cr-C2 86.48 O1-Mn-N6 92.56 C4-Cr-C6 90.80 O1-Mn-N1 82.23 C3-Cr-C6 95.34 N7-Mn-N3 93.38 C3-Cr-C5 90.83 N7-Mn-N5 86.29 C3-Cr-C1 86.76 N7-Mn-N6 88.02 C3-Cr-C2 91.88 N7-Mn-N1 95.64 C6-Cr-C5 92.23 N1-Mn-N2 90.02 C5-Cr-C1 88.50 N3-Mn-N5 90.11 C1-Cr-C2 90.37 N5-Mn-N6 87.54 C2-Cr-C3 91.88 N6-Mn-N1 92.28 Table 1.3: Shortest distances between magnetic atoms in the same layer (intra) and from dierent layers (inter). Data obtained in D10 at 43K. Atoms d Å Cr-Mn(Intra) 5.268(2) Cr-Cr(Inter) 8.041(2) Mn-Mn(Inter) 8.279(3) Cr-Mn(Inter) 7.285(2) a ferromagnetic component along the a axis, whereas for magnetic Phase III it is Γ2 , which allows a ferromagnetic component along the b axis. In table 1.4 the values of the moments found for each magnetic phase are given. The magnetic structure for Phase I is shown in gure 1.15. The magnetic moments for MnII and CrIII are nearly along the easy axis a and they are almost contained in the basal plane of their octahedra. The 1.3. Chiral Molecular Magnets 33 magnetic moment of the MnII is directed almost in the bisectrix between the bonding directions in the basal planes. The magnetic moment of the CrIII cation is directed almost in the bonding direction C1-Cr-C6, being C1-Cr the largest distance between the Cr and their ligand atoms (2.13Å). The net magnetic moment along the a axis of dierent layers is directed towards the same sense of the a axis. The magnetic moments of Cr and Mn atoms are not collinear, they are tilted as can be seen in gure 1.15. This may be due to several factors. Among them the DM interaction, as there is not a symmetry element rules it out. But it could be also explained because of the tilting of the octahedra and the anisotropy of the ions. Table 1.4: Magnetic moments for Cr and Mn along each axis and the total magnetic moment for the GN compound. Cation MxµBMyµBMzµB M µB CrIII 2.6(5) -1.7(9) -1.5(8) 3.4(7) MnII 4.8(5) -1.5(9) -0.8(8) 5(1) According to the denition of magnetic chirality adopted in Dra. Clara Gonzalez thesis, the compound was found to be magnetically chiral. Our more general denition explained in 2.5, has corroborated that GN is the rst molecular magnet where nuclear chirality and magnetic chirality coexist Several studies about the GN reveal a dynamical anomaly between 37K and 35K [8, 33, 82, 83]. A transition from a commensurate to an incommensurate magnetic phase has been postulated at the magnetic order temperature, which implies the formation of a chiral spin soliton in the lattice [32]. With the aim to observe if the neutron diraction experiments could corroborate the existence of this reorientation phase, we performed neutron diraction experiments in D15 at the ILL. We scanned the reciprocal space near the critical temperature region searching for any anomaly. In appendix B more details about this experiment can be found. Due to the estimated relation between the DM interaction and the symmetric exchange: | D| ∼ 0.01J , the length per turn of the spin helix is on the order of 100 lattice parameters. Unfortunately, the resolution needed to separate the main Bragg peaks and satellite peaks in a magnetic structure with a period of ∼100 ·15 Å is out of the experimental possibilities for actual neutron diractometers. 34 Chapter 1. Introduction and objectives Figure 1.15: Magnetic structure of GN-Phase 1. Views along the a, b and c axes. MnII atoms are in blue and CrIII atoms are in pink 1.4 Objectives The general objective of this part of the thesis is to study the coexistence of nuclear and magnetic chirality in new molecular magnets. In particular, we are interested in GN, GN-MnMn and GN-DMF compounds and how structural modications can inuence the magnetic structure, and hence, the magnetic chirality. The main structural dierence between GN and GN-MnMn is the substitution of the CrIII cation for the MnIII . We expect that this modi- cation has some inuence in the anisotropy and hence in the DM interaction. The substitution of H2O by a DMF molecule as a ligand of MnII is the main structural dierence between GN and GN-DMF. This modication increases the distance between layers due to the higher volume occupied by the DMF molecule. The separation between layers is expected to have an inuence in the magnetic order. The GN-MnMn and GN-DMF compounds are studied in chapters 2 and 3 respectively. Moreover, the racemic form of GN-DMF has been also studied in chapter 3 in order to check if the nuclear chirality may 1.4. Objectives 35 inuence the magnetic chirality. As it has been said in the previous section, some doubts about the existence of a magnetic reorientation phase for the GN were risen from dynamical features. We have also studied the critical temperature region in GN and scaned the reciprocal space searching for an evidence of a magnetic structure with a propagation vector dierent from zero. The results can be found in appendix B. In order to perform the magnetic analysis, neutron diraction experiments have been performed in D15 and VIVALDI at the ILL. From the data acquired the nuclear structures have been rened and, with the help or IR theory, the magnetic structures have been determined. Moreover, due to the lack of a general denition for magnetic chirality, we propose a global denition for chirality and studied in which cases a magnetic structure can present magnetic chirality. 2.3. Neutron Measurements 43 Table 2.1: Experimental details for GN-MnMn GN-MnMn VIVALDI Chemical Formula [Mn III (CN) 6 ][Mn II (S)pnH(H 2 O)] · 2H 2 O Lattice, Space Orthorhombic, P212121 a, b, c Å 7.662 14.633 15.003 Z 4 Temperature 290K 25K 2K N o of patterns 7 10 8 λrange Å 0.92-2.10 0.92-2.10 0.92-2.10 dmin Å 0.84 0.62 0.62 Measured reections 7814 18286 14106 Unique Reections 1330 2875 2914 (sinθ/λ)max−1 0.6054 0.8067 0.8235 Resolution Å 0.83 0.62 0.61 θmax 33.8 47.9 49.25 RLaue1 0.218 0.228 0.219 RLaue2 0.204 0.209 0.200 RLaue3 0.157 0.158 0.171 Rσ 0.083 0.104 0.137 0<h<9 0<h<11 0<h<11 hkl range 0<l<17 0<l<22 0<l<22 0<k<17 0<k<24 0<k<24 no evidence of twining. The pattern at 2K is indexed, as is shown in the top of gure, with the same lattice parameters as the pattern at 25K, without the presence of any extra peaks or magnetic satellites. This evidences that the magnetic phase has a propagation vector equal to zero. For the patterns collected at 290K, the exposure time was increased to three hours, due to the thermal motion, which decreases the intensity of the reections. For this data set, the curve normalization obtained at 25K was used, which allows us to increase the number of accepted reections to about 600 more. Still, the number of reections at high temperature, is lower than that at low temperature, which is not due to the number of patterns, because at 2K only one more pattern was recorder, but to a necessary increased in the dmin (the minimum distance that can observed, see section A.4.2). In gure 2.6 the normalization curve for 25K is shown. It is easy to see the good quality of the renement, as the normalization curve is smooth and the number of points where the observed and calculated values coincide on this scale is high, 44 Chapter 2. Neutron study of [Mn(CN) 6 ][Mn(S)-pnH(H 2 O)] · 2H 2 O Figure 2.5: Laue patterns for GN-MnMn at T=2K (top) and 25K (bottom) at ϕ= −5 o . On the top, the pattern at 2K has been indexed with the same lattice parameters as in the paramagnetic phase 2.4. Results 45 and those which do not coincide have close values. Figure 2.6: Empirical wavelenght normalisation curve for 25K data in VIVALDI. The experimental and theoretical values are shown: E is the extrapolated point on the graph, X the observed point for the curve tting, + the calculated point from the tted curve and * are points where the observed and calculated values coincide 2.4 Results 2.4.1 Nuclear phase The nuclear structure has been rened at 290K and 25K from data collected in VIVALDI. The structure solved at 290K by X-ray measurement [6] was used as starting point for the nuclear renement. The hydrogen positions were not determined by X-ray and hydrogen atoms were placed in calculated positions. Also, the number of water molecules were not determined. With neutrons, all the atoms have been positioned and thermal parameters rened anisotropically by full-matrix least-squares technique based on F2 using the programm SHELXL97 [88]. Experimental and rened data from the structural renements are summarized in table 2.1, and the fractional coordinates and thermal parameters are listed in Appendix C (table C.1 and table C.2). 46 Chapter 2. Neutron study of [Mn(CN) 6 ][Mn(S)-pnH(H 2 O)] · 2H 2 O Figure 2.7: View of the nuclear structure of the compound [Mn(CN) 6 ][Mn(S)pnH(H 2 O)] · 2H 2 O rened at 25K along the a axis (left) and the c axis (right) The agreement factors obtained at 290K with SHELX are R=0.0707 for 1103 reections whose intensity is bigger than 4σ and 0.1009 for all data. At 25K, the agreement factors are R=0.0979 for reections whose intensity is bigger than 4σ , and 0.1294 for all data. The same factors at 2K for the reections at θ > 30 o are R=0.1076 for reections whose intensity is bigger than 4σ , and 0.1461 for all data. Due to the high-quality of the sample, there is only one restriction in the renements: the distance between H and O atoms of the water molecule at 290K. The rened nuclear structure of the compound consists in two bimetallic planes containing MnIII and MnII atoms in a octahedral environments and linked by cyanide groups. The MnII atom is also linked to a water molecule. There is one water molecule of crystallization per unit formula, and four per unit cell. The two dimensional networks are arranged almost perpendicularly to the c axis. The nuclear structure rened at 25K can be seen in gure 2.7 At 290K, the reported structure contains and uncertain number of water molecules [6]. Our data analysis shows unambiguously that there is one water molecule per unit formula and four per unit cell. However, the magnitude of the thermal parameters for the water molecule (see table C.2) are indicative of some disorder. We tried to split the atomic positions of the water O and H atoms, but localizations with minimal energy could not be found. The thermal ellipsoids do not present irregular shapes such as cigar or plate shapes. We 2.4. Results 47 conclude that disorder is a dynamical disorder because the water molecule has enough space available for motion. There exist several hydrogen bonds between the water molecule and the network (see table 2.2) that justify the water molecule orientation. At high temperature, the dynamical disorder of the water molecule breaks the hydrogen bond O2···H2B···N3 , due to the increase in distance between atoms and the misalignment. At 25K, the thermal parameters of the atoms of the water molecule precludes disorder. All atoms have been rened with anisotropic thermal parameters except MnIII , whose thermal parameter was too low. The hydrogen bonds are also shown in table 2.2. Table 2.2: Hydrogen bonds for GN-MnMn at 290K, and 25K. The water molecule is constituted by H2A, O2 and H2B atoms. The hydrogen bond O2···H2B···N3 at 290K is broken. A···H···B T dA···H Å dH···B Å \ AHB N7···H1···O2 295K 1.013(18) 2.13(2) 165.9(15) 25K 1.047(8) 2.130(9) 162.8(7) N8···H10 ···O1 295K 1.03(3) 1.95(2) 170.4(14) 25K 1.054(10) 1.902(11) 172.1(8) N8···H11 ···O2 295K 1.03(3) 1.88(3) 170.4(19) 25K 1.063(10) 1.813(11) 174.2(10) O1···H12 ···N3 295K 0.93(2) 1.790(16) 173.2(17) 25K 1.003(11) 1.816(10) 175.4(9) O1···H13 ···N4 295K 0.96(2) 1.858(18) 169.8(17) 25K 1.001(10) 1.844(9) 168.2(9) O2···H2A···N3 295K 0.89(3) 2.37(2) 152(3) 25K 0.971(12) 2.299(12) 150.4(11) O2···H2B···N3 290K 0.918(2) 3.31(4) 127.3(9) 25K 0.960(13) 2.141(12) 166.1(9) The MnIII and MnII are in an octahedral environment. The distortion of their octahedra may be relevant for the magnetic behavior of the compound, so it can be seen in table 2.4. The distance and angles are similar to what has been found in another compounds. We can calculate the distortion of each octahedra by using the equation 2.1. The values obtained are shown in table 2.4. ∆d=1 6· 6 ∑ i=1 di−¯ d2 ¯ d2 (2.1) 48 Chapter 2. Neutron study of [Mn(CN) 6 ][Mn(S)-pnH(H 2 O)] · 2H 2 O Table 2.3: Bond lengths and angles for MnIII and MnII at 25K. A-Mn-B dA−Mn Å dB−Mn Å \ AMnB C1MnIII -C6 2.021(7) 2.014(7) 178.4(4) C2MnIII -C5 2.013(7) 2.024(7) 178.2(4) C3MnIII -C4 2.018(7) 2.043(7) 177.1(4) N1MnII -N5 2.238(7) 2.241(7) 177.1(3) N2MnII -N6 2.234(7) 2.250(7) 177.2(3) N7MnII -O1 2.347(7) 2.291(7) 177.8(4) A-Mn-B \ AMnB A-Mn-B \ AMnB C4MnIII -C5 88.87(4) O1MnII -N2 94.78(4) C4MnIII -C6 87.87(4) O1MnII -N5 91.76(4) C4MnIII -C2 92.93(4) O1MnII -N6 82.53(4) C4MnIII -C1 93.66(4) O1MnII -N1 85.31(4) C3MnIII -C6 89.48(4) N7MnII -N2 87.16(4) C3MnIII -C5 89.97(4) N7MnII -N5 89.45(4) C3MnIII -C1 88.98(4) N7MnII -N6 95.54(4) C3MnIII -C2 88.23(4) N7MnII -N1 93.49(4) C6MnIII -C5 88.90(4) N1MnII -N2 92.21(4) C5MnIII -C1 90.55(4) N2MnII -N5 87.73(4) C1MnIII -C2 89.47(4) N5MnII -N6 91.64(4) C2MnIII -C6 91.04(4) N6MnII -N1 88.28(4) Table 2.4: Distortion calculated of the octahedral environment for GN and GN-MnMn magnetic atoms at 43K for GN and 25K for GN-MnMn. Cation ∆d GN CrIII 4.6·10−4 GN MnII 8.4·10−4 GN-MnMn MnIII 2.5·10−5 GN-MnMn MnII 3.2·10−4 If the octahedral environment of CrIII in GN and MnIII in GN-MnMn are compared, we found that the distortion of the CrIII octahedra is one order of magnitude higher. The CMIII -C angles for no opposite C atoms, are in the range 95.3 o -86.5 o for the GN and 93.7-87.9 o for the GN-MnMn. The CMIII - C angles for opposite C atoms are in the range 173.2 o -178.1 o for the GN and 177.1 o -178.4 for the GN-MnMn. The explanation of this dierence can not be related to the Jahn-Teller eect. In the case of octahedral coordination, 2.4. Results 49 the Jahn-Teller eect is more pronounced when an odd number of electrons occupies the eg orbitals, as in complexes with the congurations d9 , low-spin d7 or high-spin d4 complexes, all of which have doubly degenerate ground states [76]. In such compounds, the eg orbitals involved in the degeneracy point directly at the ligands, so distortion can result in a large energetic stabilization. Strictly speaking, the eect also occurs when there is a degeneracy due to the electrons in the t2g orbitals (i.e. congurations as d1 or d2 , both of which are triply degenerate). However, the eect is less noticeable in the last cases, because the t2g orbitals do not point directly at the ligands. The CrIII has a d3 electronic conguration and Jahn-Teller eect is not present. The MnIII has a d4 electronic conguration in a low-spin conguration in this compound, so the expected Jahn-Teller eect is small [89]. As the ligands of CrIII and MnIII are the same in both compounds, this dierence may be attributed to some eect related with the cation substitution. In addition to distortions in the octahedral environment, the distances between magnetic atoms in the same plane or from dierent planes are very relevant, because they can inuence on the magnetic ordering. They can be seen at table 2.5 for the nuclear structure of Gn-MnMn rened at 25K. If we compare them with the distances found for the GN compound at 43K shown in table 1.3, we nd that the intralayer MnIII - MnII distance in GN-MnMn (5.25Å) is similar to the equivalent Cr-Mn (5.27Å) distance in GN compound. The interlayer distances between magnetic atoms are also similar tin both compounds. Table 2.5: Shortest distances between magnetic atoms in the same layer (intra) and from dierents layers (inter). Atoms d (Å) MnIII - MnII (Intra) 5.2528(5) MnIII - MnIII (Inter) 8.098(1) MnII - MnII (Inter) 8.359(1) MnIII - MnII (Inter) 7.358(1) 2.4.2 Magnetic phase This subsection is devoted to the analysis of the magnetic structure of GNMnMn. Due to the small size of crystals of GN-MnMn obtained ( ∼1mm3 ), we have performed our experiments in VIVALDI, where samples up to ∼1mm3 can be measured. However, VIVALDI is not the best neutron diractometer to solve magnetic structures, specially if the propagation vector is equal to zero 50 Chapter 2. Neutron study of [Mn(CN) 6 ][Mn(S)-pnH(H 2 O)] · 2H 2 O (see chapter A.4.2). This limitation is inherent to VIVALDI. Due to its geometry and λ range, VIVALDI does not allow to observe reections at very low angle because they are very close of the beam. In addition to this geometrical limitation, the reections that we can detect at low angle, present the problem of the chromatic overlap. As the magnetic contribution to the reections intensity decreases with high θ , solving magnetic structures in VIVALDI is not immediate. In spite of this diculty, we have solved the magnetic structure with a procedure described in the next paragraphs. In order to solve the magnetic structure is advisable to rene accurately the nuclear structure. To rene the nuclear structure at 2K, we have sorted our data two groups: high θ reections ( θ >30 o ) and low θ reections ( θ <20 o ), and use the hight θ reections for the nuclear renement . Such distinction is due to the fact that the magnetic form factor decreases for high q , therefore, the magnetic contribution to the diracted intensity becomes negligible at high values of θ . The choice of the θ limits has been done according to our own experience in neutron diraction and after comparing the intensity of reections at 25K and 2K. We have considered that the magnetic contribution to the diracted intensity is negligible for reections above θ >30 o . With these considerations and starting from the nuclear structure at 25K, we have used the reections at θ >30 o to rene the atomic positions and thermal parameters of all atoms in SHELX (see tables C.1 and C.2 in appendix C). The agreement factor for the nuclear renement at 2K is R=0.1076 for reections whose intensity is bigger than 4σ . Once that the nuclear structure at 2K has been rened using the high θ reections, we can determine the magnetic structure. The renement of the magnetic data was guided by the irreducible representation (IR) theory (for more information, see section A.5). According to this, the rst step is the identication of the propagation vector k . For this compound, we have determined that k=0 because the patterns at 2K have been indexed with the same cell parameters as the paramagnetic phase. The second step is the determination of the little group of vector k=0 and its IRs with the help of BASIREPs code. This method is based in the procedure of ZAK provided within the program KAREP [90] and has been adapted by Juan Rodriguez-Carvajal and included in the FULLPROF suite. For the GN-MnMn, four dierent one-dimensional IRs were obtained, called Γ1 , Γ2 , Γ3 and Γ4 in the notation of Kovalev. Each of them is included three times in the reducible magnetic representation Γ . The basis vectors for these irreducible representations are listed in table 2.6 As SHELX can not rened magnetic structures, we have used the FULLPROF programm to determine which IR describes the magnetic symmetry of Gn-MnMn and to rene the magnetic moments of the atoms. For this purpose, 2.4. Results 51 Table 2.6: Irreducible Representations for GN-MnMn and their basis vectors. m1 , m2 , m3 and m3 represent the magnetic atoms of each magnetic specie. Atom Position Γ1Γ2Γ3Γ4 m1 (x,y,z) (u, v, w) (u, v, w) (u, v, w) (u, v, w) m2 (-x+1/2,-y,z+1/2) ( u , v , w) ( u , v , w) (u, v, w ) (u, v, w ) m3 (-x,y+1/2,-z+1/2) ( u , v, w ) (u, v , w) ( u , v, w ) (u, v , w) m4 ( x+1/2,-y+1/2,-z) (u, v , w ) ( u , v, w) ( u , v, w) (u, v , w ) we have used the reections measured at θ <30 o , and it has been possible to determine and rene the magnetic structure. The two magnetic sites, MnIII and MnII , order in the same IR Γ4 , that is the same IR that we found for the Phase I of GN. The magnetic moments for MnII and MnIII along each axis and the total magnetic moment obtained are shown in table 2.7. The magnetic agreement factor for the reections at θ <20 o is RMag =7.24. The magnetic structure consist in two sublattices, one of MnII and one of MnIII as it is shown in the gure 2.8. According to the GoodeneoughKanamori rules [76] explained in section 1.3.2, the two sublattices order antiferromagnetically one respect to the other. It is due to the fact that the unpaired electrons of MnII lie in t2g and eg orbitals, so the MnII - MnIII interaction is antiferromagnetic. The IR Γ4 allows a ferromagnetic component parallel to the a axis, which is the easy axis. As v and w are of the same order and due to the symmetry imposed by Γ4 , the magnetic structure can be seen as spins along the a axis describing a spiral and turning around 90 o as can be seen in gure 2.9. As in the GN compound, the magnetic moments of Cr and Mn atoms are not collinear, which may be caused by the DM interaction, because there is not a symmetry element that can discard it, or by the anisotropy of the ions. The net magnetic moments along the a axis of dierent layers are directed in the same sense. Table 2.7: Magnetic moments for MnII and MnIII atoms placed in (x, y, z) Atom u v w mµB MnII -4.5(2) -1.1(5) -0.8(9) 4.7(3) MnIII 2.2(2) 1.0(3) 0.7(8) 2.5(3) In order to discuss the validity of the magnetic moments found, we revise the magnetochemistry of both magnetic ions, MnIII ( d4 ) and MnII ( d5 ) in an octahedral environment. In an octahedral symmetry the d-orbitals split in the energy levels as shown in gure 1.8. MnII in a low ligand eld octahedral 52 Chapter 2. Neutron study of [Mn(CN) 6 ][Mn(S)-pnH(H 2 O)] · 2H 2 O Figure 2.8: Magnetic structure of GN-MnMn. Views along the a, b and c axes. MnII atoms are in blue and MnIII atoms are in pink Figure 2.9: Orientation of each sublattice magnetic moments. a) Octahedral environment of MnIII : C1 (deep blue), C2 (red), C3 (light blue), C4 (yellow), C5 (green) and C6 (white). b) Octahedral environment of MnII : N1 (deep blue), N2 (red), N7 (light blue), O1 (yellow), N5 (green) and N6 (white). 2.6. Conclusions 59 ence in the direction of the magnetic moments and may have inuenced to the ordering temperature. As we are interested in nuclear and magnetic chirality and one of the objectives of our research is to nd the coexistence of both chiralities, a new denition has been adopted and discussed for magnetic chirality. This is not a local denition, this is a general denition which considerer the magnetic structure as a whole, and consider that magnetic chiral compounds obey that CM=FM×F∗ M= 0) . With this denition, the magnetic phase of GN-MnMn is magnetically chiral. Therefore, we have found nuclear and magnetic chirality in a molecular magnet. Chapter 3 Neutron study of the [Cr(CN)6][Mn(R/rac)−pnH(DMF)] ·2H2O compounds 3.1 Introduction As it has been said in the introductory chapter, several chiral compounds of the same family are studied in this part of the thesis. Our objective is to conrm the coexistence of nuclear and magnetic chirality in them and study how modications in the nuclear structure can aect to the magnetic structure. This chapter is devoted to the chiral compound similar to GN [Cr(CN) 6 ][Mn(R)-pnH (DMF)] ·2H2O , and its racemic compound [Cr(CN) 6 ][Mn(rac)-pnH(DMF)] · 2H 2 O, where DMF stands for N,N-dimethylformamide and (R/rac)-pn is (R/rac)-1,2-diaminopropane. Due to the similitude between the chiral compound and GN, these compounds are denoted as GN-DMF(R) and GN-DMF(rac). The nuclear structure of [Cr(CN) 6 ][Mn(R)-pnH(DMF)] ·2H2O determined by X-ray measurements at 290K is very similar to GN, the main dierence is the substitution of the H2O molecule linked to the MnII atom in the GN compound by a DMF molecule. This substitution implies an increasing in the interlayer distance and modies the corrugation of the layers. The GN-DMF(R) compound is a candidate to present coexistence of nuclear and magnetic chirality due to its resemblance to GN. It also represents a good opportunity to observe how a ligand substitution or the interlayer distance can inuence in the magnetism. 62 Chapter 3. Neutron study of [Cr(CN)6][Mn(R/rac)−pnH(DMF)] ·2H2O The GN-DMF(rac) compound crystallizes in a centrosymmetric space group, so nuclear chirality is absent. If we compare the GN-DMF(R) and GN-DMF(rac) compounds, we can see how the ligand (R)-pn transfers the nuclear chirality to GN-DMF(R) crystal. The knowledge of the magnetic structures of both compounds can allow us to see if the magnetic chirality is also related to the chirality of the ligand. In order to rene the nuclear structures and to solve the magnetic ones, single-crystal neutron diraction experiments have been performed at the ILL, in the diractometers VIVALDI and D15 (see A.3.2 and A.4.2 in appendix A for more information). The synthesis, the structure previously solved by X-ray measurements and the magnetization measurements of GN-DMF(R) and GN-DMF(rac) are described in 3.2. Then, the neutron diraction experiments carried on are explained in section 3.3 and results for the nuclear and magnetic structure are presented in 3.4. Our denition of chirality is applied to the samples at section 3.5 and some conclusions can be found at 3.6. 3.2 Synthesis, X-ray structure and magnetic characterization The GN-DMF(R) and GN-DMF(rac) compounds were synthesized by Prof. Inoue Katsuya and coworkers at the University of Hiroshima (Japan) [7]. Both compounds are synthesized by the same reaction but an enantiomeric or racemic precursor is employed. Green block-like crystals were obtained by slow diusion of MnCl2·4H2O (5.1 mmol), (rac)-1,2-diaminopropane-dihydrochloride ((rac)-pn · 2HCl, 6.8 mmol), and KOH (6.8 mmol) in a H 2 O/N,N-dimethylformamide mixture (1:1) into K 3 [Cr(CN) 6 ] (1.5 mmol) in a H 2 O/EtOH (1:1) mixture for several weeks. The synthesis were carried out under argon atmosphere, because manganese ion is air sensitive in the KOH solution. The unit cell for both compounds is orthorhombic, with cell parameters and space groups a=7.662(2)Å, b=14.581(4)Å, c=19.747(6)Å and P2 1 2 1 2 1 for GN-DMF(R); and a=14.5459(8)Å, b=7.6509(8)Å, c=19.723(2) Å and Pnma for GN-DMF(rac). In the unit cell of the GN-DMF(rac) compound there has been a changed of the a and b axis respect to the denition of the unit cell in GN-DMF(R). As in other compounds studied in this thesis, each [Cr(CN) 6 ] 3− ion utilizes four cyanide moieties in order to form bridges to four adjacent Mn II ions within the ab plane, building bimetallic sheets piled up along the c axis. In addition to Mn II and [Cr(CN) 6 ] 3− ions, an asymmetric unit contains a single molecule of (R/rac)-pnH, a DMF molecule and two water molecules. 3.2. Synthesis, X-ray structure and magnetic characterization 63 The octahedron around the Mn II ion is completed by coordination of the primary amino group of (R/rac)-pnH and the DMF molecules as can be seen in gure 3.1 for GN-DMF(R). The two water molecules occupy gaps between the sheets. The shortest and the second shortest inter-sheet metal separations are observed between the homo-metallic atoms, in contrast with GN, where the shortest inter-sheet metal separations are observed between MnII and CrIII atoms. This dierence may inuence on the magnetism. Figure 3.1: ORTEP drawing of [Cr(CN)6][Mn(R)−pnH(DMF)] ·2H2O , hydrogen atoms are omitted for simplicity. Adapted from [7] The crystal structures were solved by X-ray measurements on single crystals at room temperature and can be obtained at www.ccdc.cam.a-c.uk/ with the codes CCDC 223745 and CCDC 239941 [7]. All non-hydrogen atoms were rened anisotropically. Hydrogen atoms were placed in calculated positions but not rened, except for the water hydrogen atoms in both compounds which could not been placed. In addition, the hydrogen atoms of the terminal amino group of pn in GN-DMF(rac) were not placed due to some disorder of the nitrogen atom (see the thermal ellipsoid of N9 in gure 3.2). Among others, the impossibility of placing and rening the hydrogen atoms positions by Xray measurements is one of the reasons that motivated our neutron diraction 64 Chapter 3. Neutron study of [Cr(CN)6][Mn(R/rac)−pnH(DMF)] ·2H2O studies. Figure 3.2: ORTEP drawing of [Cr(CN)6][Mn(rac)−pnH(DMF )]·2H2O , hydrogen atoms are omitted for simplicity. The magnetic characterization of the compounds has been performed in polycrystalline samples [7] and in oriented single crystals [92]. The magnetic behavior of polycrystalline samples of the chiral compound shows a χmolT value of 4.92 cm3K/mol (6.28 µB ) at room temperature, which decreases while cooling down to a minimum value of 3.53 cm3K/mol (5.31 µB ) at 82 K. Upon further cooling, the χmolT value increases to a maximum value of 36.19 cm3K/mol (17.02 µB ) at 27 K and decreases below 27 K. The susceptibility obeys a Curie-Weiss law from 300-120K with a Weiss temperature θ =73.5 K, which is an indicator of the antiferromagnetic interaction between nearest neighbor CrIII and MnII ions through cyanide bridges. The behavior for the racemic sample is very similar. To conrm the long reach magnetic order around 30K, low eld measurements in single crystal have been performed. As can be seen in gure 3.3 for the chiral sample and gure 3.4 for the racemic one, both, the zero eld-cooled magnetization (ZFCM) and the eld-cooled magnetization (FCM) curves display abrupt increases in the magnetization below 40 K, which reach a maximum at TN =28.8 K. The magnetic behavior of the two samples below this temperature is dierent. In gures 3.5 and 3.6, the magnetization versus magnetic eld curves at 3.3. Neutron scattering experiments 65 Figure 3.3: Magnetization versus temperature for GN-DMF(R). Taken from [92]. Figure 3.4: Magnetization versus temperature for GN-DMF(rac). Taken from [92]. 2K can be seen for the two compounds; the saturation magnetization value per unit formula at 5T is around 2 µB , which corresponds to the value of S=2/2 expected for antiferromagnetically coupled MnII (S=5/2) and CrIII (S=3/2). For the chiral sample, spins are canted and in the bc plane and presents a spin- ip transition. While the chiral sample is a a metamagnet with TN of 28.5 K, the racemic one is a ferrimagnet with TN of 28 K. 3.3 Neutron scattering experiments Neutron scattering techniques are used in this thesis as a powerful tool to determine the nuclear and magnetic structure of the studied compounds. As it is said in appendix A, they allow us to rene nuclear structures including the atomic position of light elements, which are more dicult to place with 66 Chapter 3. Neutron study of [Cr(CN)6][Mn(R/rac)−pnH(DMF)] ·2H2O Figure 3.5: Magnetization versus eld for GN-DMF(R). The low eld region can be seen in the insert Figure 3.6: Magnetization versus eld for GN-DMF(rac). Histeresis cycles are shown in the insert photons. In addition, as neutrons interact with the magnetic moments of the atoms via the dipolar magnetic interaction and nuclear and magnetic interaction are of the same order of magnitude, neutron diraction also allow us to determine magnetic structures. As for the compounds described in previous chapters, neutron diraction have been used to rene the nuclear structure and to determine the magnetic structure of the compounds GN-DMF(R/rac). The diraction experiments have been done at the instruments D15 and VIVALDI, placed at the ILL (see A.3.2 and A.4.2 in appendix A). VIVALDI oers an almost complete sight of the reciprocal space in a short time, which can be very useful for detecting propagation vectors dierent from zero, but it is not the best instrument to determine magnetic structures. On the contrary, D15 only allows to collect reections one by one, which consumes a lot of time in measuring a great number of reections, but it does not have the problem of 3.3. Neutron scattering experiments 67 chromatic overlap of VIVALDI and can be very useful to determine magnetic structures. The instrument D15 was operated in four-circle conguration with a wavelength of 1.17Å and reections were measured through ω scans. The set-up was completed by a displex that allowed us to set temperatures between 2K and 300K for the GN-DMF(R) compound and between 10K and 200K for the GN-DMF(rac) sample. The crystals were glued in aluminium pins with kwikll , a two-part polymer glue suitable for measurements down 200K. The experimental procedure for a typical experiment in D15 in described in section A.3.2. In order to summarize it, some lines are given here. The rst step in an experiment is to orientate the crystal and obtain an orientation matrix. The orientation matrix allow us to link the real and reciprocal spaces. For orientating the crystals, we simulated the intensities of some lines at low θ using the X-ray structure with FULLPROF, and localized the most intense reections in the real space. Their positions in the angles of the instrument were noted and use to build the orientation matrix. After that, some reections at a temperature above TN were measured to rene the nuclear structure. In order to determine the magnetic structure, we cooled down the crystal down TN . As D15 does not allow us to observe all the reciprocal space, we can not determine a priori the propagation vector. The typical procedure implies to look for satellite peaks in some selected directions and to check if the magnetic intensity overlaps with the nuclear intensity. For this reason, several q-scans were performer below TN in smart directions scanning the reciprocal space to discard a propagation vector dierent from zero. Once the propagation vector was known, the crystals were cooled down, at 2K or 10K for the GN-DMF(R) and GN-DMF(rac) compounds respectively, to collect magnetic reections which allow us to determine the magnetic structure. For D15 data, all the reections were integrated and corrected by the Lorentz factor using the programm COLLD15, which is a modication of COLL5 [93]. The absorption correction was performed with the help of the programm DATAP [94]. In order to complete the neutron measurements performed in D15, monocrystals of the same batches as the crystals used in D15 experiments have been measured in VIVALDI. The crystals were wrapped in aluminium and attached with vacuum grease to a 1mm of diameter Vanadium pin. A standard He-ow ILL "Orange" cryostat was used to reach temperatures from 1.5K to 325K. In order to minimize the ratio of background scattering with respect to the scattering from the crystals, the nal aperture of the neutron incoming beam was chosen to be 3mm in diameter. As it is said in appendix A, and with the same procedure that we followed with the sample Gn-MnMn, all the Laue patterns were indexed using the programm LAUEGEN [85]. The reections were integrated following a two-dimensional version of the σ(I)/I algorithm [86] 68 Chapter 3. Neutron study of [Cr(CN)6][Mn(R/rac)−pnH(DMF)] ·2H2O implemented in the ARGONNE_BOXES program and corrected by absorption with the help of the programm LADIABS. The wavelength normalization was obtained using a curve derived by comparing equivalent reections and multiple observations, via the programm LAUENORM [87]. Nuclear structure renement and magnetic structure determination were done with SHELX [88] and Fullprof [9] programs. The experimental procedures to collect and analyze data are described in this section. 3.3.1 GN-DMF(R) In this subsection, details of the neutron diraction experiments performed for GN-DMF(R) in D15 and VIVALDI are given. D15. Experimental procedure for GN-DMF(R) For the measurements in D15 experiment, a 4x2x1mm 3 crystal was employed. The long dimension was identied with the a axis, which is the shortest cell parameter, and placed vertical in the pin, therefore along the ϕ axes of the Eulerian cradle. The slits used to optimize the ratio background/signal were 8mmx8mm at the font and 8mmx6mm at the detector. After aligning the crystal, it was cooled down to 35K, where 779 lines were acquired to rene the nuclear structure. To determine the magnetic propagation vector, the crystal was cooled down to 2K and a total of 27 qscans were performed. No evidence of a propagation dierent from zero was found. In order to check if the propagation vector was zero and to nd out the magnetic structure, 39 lines at low angle were measured at 35K and 2K. Several of these lines have a magnetic contribution to their intensity at 2K, which is another sign of a propagation vector equal to zero. The reections with the most signicant magnetic intensity contribution were measured as a function of the temperature near the transition region, which can be used to determine the critical exponent β of the transition. All relevant experiment details (temperature, number of reections, wavelength,etc...) are summarized in (table 3.1). In Figure as 3.7 a typical ω -scan can be observed. VIVALDI. Experimental procedure for GN-DMF(R) The dimensions of the crystal used in this experiment were 1.65x3.0x0.8 mm 3 . The crystal was aligned, its diraction quality was checked and presence of twining was discarded before cooling down or acquiring any data. To rene the nuclear structure at room temperature 8 Laue patterns at 290K were recorded 3.4. Results 75 to solve troublesome crystal structures [95], we checked the space group, the unit cell and the atom types and discarded any error. The R value for the adjustment is R=0.0984 for reections whose intensity is bigger than 4σ and 0.1075 for all data. the fractional coordinates and isotropic thermal parameters are listed in Appendix D (table E.1). The fuzzy structure and the unnatural size and shape of the thermal ellipsoids could be explained by two phenomena. An early stage of a degradation process and the loss os crystallinity may be the responsible of this anomalous ellipsoids. A visual inspection conrms that the crystals start to degrade after some time exposed to the air, they change their color from an emerald green to a greenish yellow and become porous. In addition, a lack of crystallinity has been observed in other Prussian Blue Analogues [75], specially if there are synthesized using a organic solvent as in the GN-DMF(R) compound. The other explanation is related to the disorder and the possibility of a interchange between the positions of the pnH and the DMF ligands. Due to the likeness between the (R)-pnH and DMF ligands, some disorder may be present and, in some small percentage, they positions may be interchanged. This last hypothesis is supported, for example, by the fact that eliminating the hydrogens H7A-H7B of the structure, one unexpected Q-peak appears in the renement, which may be related to the interchange and the position of H10 (see gure 3.8). Improvements have not been observe after trying to solve a disorder situation with dierent occupancies for (R)-pnH and DMF ligands. Solving the structure at 290K with VIVALDI data presents the same problems and challenges as for 33K, with and R=0.0939 for reections whose intensity is bigger than 4σ and 0.1175 for all data. The positions and thermal parameters for the renements of the nuclear structure can be seen in Appendix D (table E.1). In spite of these problems, we accept the main features of the nuclear structure of the compound, which can be seen in gure 3.9. It consist of bimetallic planes containing Cr III and Mn II atoms in a octahedral environments and linked by cyanide groups, where the Mn II is also linked to a DMF molecule and a (R/rac)-pnH group. There are two water molecule per f.u. of crystallization. The two dimensional networks are arranged almost perpendicularly to the c axis. Due to the precarious nuclear structure determination, we are not focusing in hydrogen bonds. If we compare the nuclear structure of GN and GN-DMF(R) we can observe that, the substitution of the H2O ligand of MnII for a DMF changes the piling of the layers, as can be seen in gure 3.10. In this gure, it can be seen as the upper layer in the unit cell of GN-DMF(R) is displaced b/2 along the b axis. This displacement may be due a stereo eect related to the higher volume 76 Chapter 3. Neutron study of [Cr(CN)6][Mn(R/rac)−pnH(DMF)] ·2H2O Figure 3.8: Structural unit of [Cr(CN)6][Mn(R)−pnH(DMF)] ·2H2O rened at 33K. The orange atom stands for the phantom peak obtained. of DMF ligand. As a consequence, the interlayer distances are increased (see table 3.6) and the valleys of dierent layers are not in-phase. In addition, the shortest interlayer distances are dierent, while in GN the shortest distance between atoms is heterometallic (Mn-Cr 7.285(2)Å), in GN-DMF(R) the shortest distance is homometallic (Mn1-Mn2 8.776(2)Å). All this modications in the nuclear structure may have some inuence in the magnetic behavior of the compound. The intralayer distance Mn-Cr is the same within an experimental error for GN and GN-DMF(R) (5.319(11)Å at 35K for GN-DMF(R)). Table 3.6: Interlayer distances between equal atoms and the shortest and largest heterometallic distances in GN-DMF(R) at 35K and GN at 43K. Atoms d (Å) GN-DMF(R) d (Å) GN Mn1-Mn2 8.776(2) 8.279(3) Mn3-Mn4 12.466(3) 8.279(3) Cr1-Cr2 10.551(3) 8.041(3) Cr3-Cr4 10.551(3) 8.592(2) Mn1-Cr2 9.246(2) 7.285(2) Mn4-Cr1 11.683(3) 9.043(2) 3.4. Results 77 Figure 3.9: Nuclear structure of GN-DMF(R) rene with VIVALDI data at 33K. The CrIII and MnII are in an octahedral environment. The distances and angles of these octahedra can be seen in table 3.7 and are similar to what has been found in another compounds. The distortion of CrIII and MnII octahedra in GN and GN-DMF(R) can be seen in table 3.8. If we compare the octahedral environment of CrIII and MnII in GN and 78 Chapter 3. Neutron study of [Cr(CN)6][Mn(R/rac)−pnH(DMF)] ·2H2O Figure 3.10: a)Interlayer separation in GN-DMF(R). b)Interlayer separation in GN GN-DMF(R), we found that the distortion has the same order of magnitude for MnII in both compounds, but for CrIII the distortion is one order of magnitude higher in the GN compound. The CCrIII -C angles for no opposite C atoms, are in the range 95.3 o -86.5 o for the GN and 91.0-89.2 o for the GNDMF(R). The CCrIII -C angles for opposite C atoms are in the range 173.2 o - 178.1 o for the GN and 179.3 o -179.9 for the GN-DMF(R). The higher distortion 3.4. Results 79 in the CrIII in the GN compound, can be relevant in order to compare the magnetic behavior of both compounds. Another important feature that we want to remark is the angles in the MnII octahedra. Although the distortion of the MnII octahedra is similar in GN and GN-DMF(R) compounds, there is a remarkable dierence in the N7MnII -O1 angle, whose value is 177.8 o in GN and 172.7 o in GN-DMF(R). The increase of the deviation of the theoretical 180 o value for the GN-DMF(R) compound is due to the higher volume of the DMF molecule, the DMF ligand is tilted and the value of the angle is dierent from 180 o in order to avoid the spatial proximity of another DMF molecule. Table 3.7: Bond lengths and angles for CrIII and MnII at 25K. A-Mn-B dA−X (Å) dB−X (Å) \ AXB C1Cr -C6 2.07(1) 2.08(1) 179.9(7) C2Cr -C5 2.06(1) 2.05(1) 179.3(7) C3Cr -C4 2.06(1) 2.08(1) 179.3(7) N1Mn -N5 2.22(1) 2.21(1) 176.4(5) N2Mn -N6 2.16(1) 2.26(1) 176.3(6) N7Mn -O1 2.34(1) 2.19(1) 172.7(5) A-Cr-B \ ACrB A-Mn-B \ AMnB C4Cr -C5 90.0(5) O1Mn -N2 94.6(4) C4Cr -C6 89.0(5) O1Mn -N5 90.1(4) C4Cr -C2 90.0(5) O1Mn -N6 89.1(4) C4Cr -C1 91.0(5) O1Mn -N1 92.7(4) C3Cr -C6 90.8(6) N7Mn -N2 92.6(4) C3Cr -C5 90.7(6) N7Mn -N5 90.8(4) C3Cr -C1 89.2(6) N7Mn -N6 83.7(4) C3Cr -C2 89.3(6) N7Mn -N1 86.1(4) C6Cr -C5 89.3(5) N1Mn -N2 89.7(4) C5Cr -C1 90.6(5) N2Mn -N5 92.3(4) C1Cr -C2 90.1(5) N5Mn -N6 87.8(4) C2Cr -C6 90.0(5) N6Mn -N1 90.1(4) Magnetic phase The next paragraphs are devoted to the analysis of the magnetic structure of GN-DMF(R). We have two data set to determine the magnetic structure. As it has been said before, during the analysis of GN-MnMn, VIVALDI is not the best neutron diractometer to solve magnetic structures, specially if the propagation vector is equal to zero due to the overlap of reections at low angle 80 Chapter 3. Neutron study of [Cr(CN)6][Mn(R/rac)−pnH(DMF)] ·2H2O Table 3.8: Distortion calculated of the octahedral environment for GN and GNDMF(R) magnetic atoms at 43K for GN and 33K for GN-DMF(R). Cation ∆d GN Cr 4.6·10−4 GN Mn 8.4·10−4 GN-DMF(R) Cr 2.8·10−5 GN-DMF(R) Mn 6.7·10−4 (see A.4.2). In spite of this inconvenience, we were forced to measured in it due to the small size of the available crystals at the time the rst neutron diraction experiments were performed. In addition, it allow us to rene the nuclear structure at 2K. To analyze VIVALDI data, we had the same consideration as for GN-MnMn. The proceeding followed to determine the magnetic structure in described in the next paragraphs. To obtain the nuclear structure at 2K we used in SHELX the high angle reections ( θ >30 o ) to rene the atomic positions and thermal parameters found at 33K (see tables E.1 and E.2 in appendix D). The agreement factor for the nuclear renement at 2K is R=0.1052 for reections whose intensity is bigger than 4σ . Once that the nuclear structure at 2K has been rened, we can determine the magnetic structure. The renement of the magnetic data was guided by the irreducible representation (IR) theory (for more information, see section A.5). The rst step it to determine the propagation vector. For this compound we have concluded that k=0 at 2K, because the patterns collected in VIVALDI at 2K have been indexed with the cell parameters of the paramagnetic phase. In gure 3.11 a pattern collected at 25K for ϕ=−45 o is shown together with the same pattern at 2K indexed with the nuclear cell parameters. In addition, twenty-seven q-scans at 2K were done in D15. The directions of the q-scans were selected to look for propagation vectors as (1/2,0,0), (0, 1/2, 0)... No extra peaks that evidence the existence of a propagation vector dierent from zero have been found (for example, see gure 3.12). This absence of satellite peaks, together with the fact that we observe magnetic intensity superimpose to nuclear intensity in our reections at 2K, corroborated that k=0 . Once that the propagation vector has been identied, we have determined the little group of vector k=0 and its IRs with the help of BASIREPs code. There exists two magnetic sites corresponding to the Cr and the Mn sublattices. The little group of vector k=0 and its IRs are the same that for the GN and GN-MnMn compounds. Four dierent one-dimensional IRs were obtained for each magnetic specie, called Γ1 , Γ2 , Γ3 and Γ4 in the notation of Kovalev. 3.4. Results 81 Figure 3.11: Laue patterns for Gn-MnMn at T=25K and 2K at ϕ= 45 o for GNDMF(R). On the bottom, the pattern at 2K has been indexed with the same lattice parameters as in the paramagnetic phase. Each of them is included three times in the reducible magnetic representation Γ . The basis vectors for these irreducible representations are listed in table 3.9. In order to decide which representation correspond to magnetic structure of the GN-DMF(R), we compare the calculated values for each IR and the experimental values of the magnetic contribution to the intensity of the measured lines. In order to simplify the process, we can discard some IRs by symmetry arguments. The theoretical magnetic intensity depends on the perpendicular component to the scattering vector of the magnetic structure factor, which can be calculated for each sublattice as can be seen in equation 3.1. 82 Chapter 3. Neutron study of [Cr(CN)6][Mn(R/rac)−pnH(DMF)] ·2H2O 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0 30 60 90 120 150 180 210 240 270 300 I (a.u.) h Figure 3.12: q-scan performed at 2K in the direction h00 for the compound GNDMF(R) Table 3.9: Irreducible Representations for GN-DMF(R) and their basis vectors. m1 , m2 , m3 and m3 represent the magnetic atoms of each magnetic specie. Atom Position Γ1Γ2Γ3Γ4 m1 (x,y,z) (u, v, w) (u, v, w) (u, v, w) (u, v, w) m2 (-x+1/2,-y,z+1/2) ( u , v , w) ( u , v , w) (u, v, w ) (u, v, w ) m3 (-x,y+1/2,-z+1/2) ( u , v, w ) (u, v , w) ( u , v, w ) (u, v , w) m4 ( x+1/2,-y+1/2,-z) (u, v , w ) ( u , v, w) ( u , v, w) (u, v , w ) FM(q) = ∑ i miexp (i2πq·ri) = +m1exp [i2πq·(x, y, z)] +m2exp [i2πq·(−x+ 1/2,−y, z + 1/2)] +m3exp [i2πq·(−x, y + 1/2,−z+ 1/2)] +m4exp [i2πq·(x+ 1/2,−y+ 1/2,−z)] (3.1) The line q= (−1,0,0) has no nuclear contribution to the diracted intensity due to the reection conditions of the group P212121 ( (h,0,0) with h=2n). Hence, the experimental intensity of 1748 ± 32 counts at 2K is due to a magnetic contribution. The magnetic structure factor of one magnetic sublattice for this line can be seen in equation 3.2. 3.4. Results 83 FM(−1,0,0) = 2isin(2πx)(m1+m2−m3−m4) (3.2) The value of FM of each sublattice for the line q= (−1,0,0) is (0,0,4w) for Γ1 , (0,0,0) for Γ2 , (4u,0,0) for Γ3 and (0,4v,0) for Γ4 . As this line has an experimental magnetic intensity that depends on the perpendicular component to the scattering vector of FM , the IRs Γ2 and Γ3 can be discarded. The FULLPROF programm has been used to t the experimental magnetic intensities of Γ1 and Γ4 , determine which IR describes the magnetic structure of GN-DMF(R) and to rene the magnetic moments of the atoms. To rene the magnetic structure, the data collected in D15 can oer a more accurately results due to the characteristic of both instruments, but in order to check the validity of our results, we have rened the magnetic structure with both data sets. For D15, the short number of reections acquired at 2K does not allow to rene the nuclear structure at this temperature. In order to obtain the magnetic contribution to the intensity, the atomic positions and thermal parameters at 2K and 35K have been considered as equal and the intensities measured at 35K and 2K have been compared. This assumption is supported if we compare the the structural data obtained with VIVALDI at 2K and 33K. Another option could have been to use the nuclear structure rened with VIVALDI at 2K to simulate the intensity of the lines, but the lack of a scale between reections in both instruments, make us to discard this procedure. The reections with a signicant magnetic contribution and some reections measured accurately at low angle, independently of their magnetic contribution, have been used in FULLPROF to determine the magnetic structure. In addition, the reections acquired in VIVALDI at low θ have been examined carefully and the ones measured accurately (low dispersion in the value and low standard deviation), have been selected to perform a parallel renement. The magnetic structure corresponds to the irreducible representation Γ1 and the values obtained for the magnetic moment can be seen in table ?? for a magnetic agreement factor R=4.68 R=10.85 for VIVALDI and D14 respectively. The magnetic moment for the CrIII cation along the a axis could not be determined, there is a contribution that can not be estimated with our data. If we compare the magnetic structure obtained with VIVALDI and D15 data, we found that although the magnetic structure is the same, there is a small dierence in the magnetic moments. The magnetic moments for MnII and CrIII obtained in VIVALDI are 4.6(2) and 2.1(3) µB respectively, while the same moments obtained from D15 data are 5.6(3) and 2.7(1) µB . We need to compare these experimental values with the theoretical values given by the magnetochemistry of each cation. As it has been said for the GN-MnMn compound in 2.4.2 MnII ( d5 ) in a low ligand eld octahedral environment 84 Chapter 3. Neutron study of [Cr(CN)6][Mn(R/rac)−pnH(DMF)] ·2H2O Table 3.10: Magnetic moments for Mn and Cr along each axis and the total magnetic moment for GN-DMF(R) determined with VIVALDI and D15 data at 2K. Instrument Cation MxµBMyµBMzµB M µB VIVALDI MnII 1.3(6) 3.70(9) -2.5(3) 4.6(2) CrIII -0.5(9) 2.08(15) 0.2(2) 2.1(3) Cation MxµBMyµBMzµB M µB D15 MnII 1.2(5) 5.19(12) -1.7(9) 5.6(3) CrIII  2.64(12) 0.2(3) 2.7(1) present a ground term 6A1 ( t3 2ge2 g ) which is a high spin state with S=5/2. If the ligand eld is strong enough, a transition to a ground term 2T2 ( t5 2g ) occurs and the MnII has a spin S=1/2. In this compound, MnII is surrounded by nitrogen and oxygen atoms and the ligand eld is low enough to have a ground state 6A1 and a spin S=5/2. The CrIII ( d3 ) has a ground state 4A2 ( t3 2g ) and a spin state S=3/2. The theoretical spin-only magnetic moments for MnII and CrIII are 5 µB and 3 µB , according to S=g·S·µB with a Lande factor equal to g=2. For the CrIII cation, the spin-orbit coupling is small and only a slightly decreased in the value of the magnetic moment can be expected. No orbital contribution to the magnetic moment is expected for MnII ion, as the ground state present L=0 [89]. The dierence between the theoretical and the experimental values may be due to a problem with the scale, specially in D15. The net magnetic moment is higher for the results obtained from D15, which may be due to an underestimation of the nuclear intensity at 2K (therefore, a overestimation of the magnetic contribution) implicity when we assume that the thermal parameters at 2K are equal than the thermal parameters at 35K. The theoretical ratio between magnetic moments is 1.67, and the experimental is 2.2 and 2.0 for VIVALDI and D15 respectively. Although a problem with the scaling process make the dierence between experimental and theoretical value higher for D15 results, the ratio is nearer from the theoretical value. The major contribution to the deviation in the magnetic moments comes from the Cr magnetic moment along the a axis, which has not been determined with D15 data due to a low resolution in this direction. As there is not magnetic moment of Cr missed, we supposed that this contribution must be negligible. AS D15 is better prepared to solve magnetic structures than VIVALDI, we have in better consideration the D15 results for the magnetic moments. As it is logic, the magnetic structures obtained with the data acquired in VIVALDI and D15 are the same. It consists in two sublattices, one of MnII 3.4. Results 91 be seen in table 3.13. If we compare the distorstion of the octahedra in GNDMF(R) (see table 3.8) and GN-DMF(rac), we found that the distortions are of the same order of magnitude. The distance and angles inside the octahedra can be seen in table 3.13 and within the experimental error they are equal to the distance and angles found in the octahedra of GN-DMF(R), except for the angle N4-Mn-O whose value is 174.6(8) o in the GN-DMF(rac) and the equivalent angle in GN-DMF(R) is 172.7(5). The deviation of this angle from the theoretical 180 o value is due to a stereo eect due to the volume of the DMF molecule. Table 3.12: Distortion calculated of the octahedral environment for GN-DMF(rac) magnetic atoms at 35K. Cation ∆d GN-DMF(rac) CrIII 8.6·10−5 GN-DMF(rac) MnII 7.4·10−4 Table 3.13: Bond lengths and angles for CrIII and MnII in GN-DMF(rac) at 35K. A-Mn-B dA−X (Å) dB−X (Å) \ AXB C1CrIII -C2 2.09(2) 2.07(2) 179(1) C3CrIII -C4 2.07(3) 2.12(2) 178(1) N1MnII -N2 2.20(2) 2.27(2) 175.6(9) N4MnII -O1 2.36(2) 2.22(2) 174.6(8) A-Cr-B \ ACrB A-Mn-B \ AMnB C3CrIII -C1 89.7(9) O1MnII -N1 94.2(6) C3CrIII -C2 91.3(9) O1MnII -N2 89.6(6) C4CrIII -C1 89.1(9) N4MnII -N1 89.6(6) C4CrIII -C2 89.9(9) N4MnII -N2 86.5(6) C1CrIII -C1 89.1(8) N1MnII -N1 91.3(6) C2CrIII -C2 89.3(8) N2MnII -N2 91.3(6) C1CrIII -C2 90.8(8) N1MnII -N2 86.8(6) Magnetic phase In order to determine the magnetic phase of the GN-DMF(rac) compound we have the D15 data acquired at 10K. It would be advisable to rene the nuclear structure at this temperature before starting the magnetic analysis, but the shortage of reections at this temperature make us discard this option. Instead, 92 Chapter 3. Neutron study of [Cr(CN)6][Mn(R/rac)−pnH(DMF)] ·2H2O as a rst order of approximation, the atomic position and thermal parameters at 10K have been assumed to be equal than a 35K. As usual, the rst step is to determine the magnetic structure is to nd the propagation vector. With this objective, several lines at low q were measured at 10K and 35K and their intensities at both temperatures compared. The increase in the intensity at low temperature was observed, which indicates that the magnetic cell and the unit cell are the same, and hence the propagation vector is equal to zero. In order to conrm this hypothesis, we scanned the reciprocal space along strategic directions in a search for magnetic satellite peaks with (h,k,l) no integers. A total of forty-ve q-scans at 10K have been performed and no evidence of a propagation vector dierent from zero has been found. We accept that the propagation vector for the GN-DMF(rac) is ( k=0 . An example of a q-scan at dierent temperatures is shown in gure 3.17. In this case, we measured along the direction (h,0,0) and found a magnetic peak at (1,0,0). 0.6 0.8 1.0 1.2 1.4 0 1000 2000 3000 4000 I (a.u.) h Figure 3.17: Qscan performed in the direction h00 at 50K ( ⋆ ), 35K ( ◦ ) and 10K ( • ) As in the study of the previous compounds, the IR theory has been used to determine the magnetic structure. The IRs have been determined by BASIREPS code and the magnetic moments have been calculated by using FULLPROF. The space group of GN-DMF(rac) is Pnma and there are two magnetic sublattices in which the magnetic atoms are in special positions (x, 0.25, z) . Eight dierent one-dimensional IRs were obtained for this space group, and the reducible magnetic representation can be written as Γ = Γ1+ 2Γ2+ 2Γ3+ Γ4+ Γ5+ 2Γ6+ 2Γ7+ Γ8 . The basis vectors for these irreducible representations are listed in table 3.4.2. 3.4. Results 93 Table 3.14: Irreducible Representations for GN-DMF(rac) and their basis vectors. m1 , m2 , m3 and m4 represent the magnetic atoms of each magnetic specie. Atom Position Γ1Γ2Γ3Γ4 m1 (x,0.25,z) (0,v,0) (u,0,w) (u,0,w) (0,v,0) m2 (-x+1/2,-0.25,z+1/2) (0,-v,0) (-u,0,w) (-u,0,w) (0,-v,0) m3 (-x,0.75,-z) (0,v,0) (-u,0,-w) (u,0,w) (0,-v,0) m4 (x+1/2,0.25,-z+1/2) (0,-v,0) (u,0,-w) (-u,0,w) (0,v,0) Atom Position Γ5Γ6Γ7Γ8 m1 (x,0.25,z) (0,v,0) (u,0,w) (u,0,w) (0,v,0) m2 (-x+1/2,-0.25,z+1/2) (0,v,0) (u,0,-w) (u,0,-w) (0,v,0) m3 (-x,0.75,-z) (0,v,0) (-u,0,-w) (u,0,w) (0,-v,0) m4 (x+1/2,0.25,-z+1/2) (0,v,0) (-u,0,w) (u,0,-w) (0,-v,0) In order to decide which representation correspond to magnetic structure of the GN-DMF(rac), several attempts of tting have been performed using FULLPROF. In the ttings, the theoretical magnetic intensity and the experimental magnetic intensity are compares. The theoretical magnetic intensity depends on the perpendicular component to the scattering vector of the magnetic structure factor, which can be calculated for each sublattice as can be seen in equation 3.4. FM(q) = ∑ i miexp (i2πq·ri) = +m1exp [i2πq·(x, 0.25, z)] +m2exp [i2πq·(−x+ 1/2,−0.25, z + 1/2)] +m3exp [i2πq·(−x, 0.75,−z)] +m4exp [i2πq·(x+ 1/2,0.25,−z+ 1/2)] (3.4) The line q= (0,1,0) has no nuclear contribution to the diracted intensity due to the reection conditions of the group ( (0,k,0) with k=2n). Hence, the experimental intensity of 2176 ± 37 counts measured at 10K for this lines corresponds to the magnetic contribution. The magnetic structure factor of one magnetic sublattice for the line (0,1,0) can be seen in equation 3.5. FM(0,1,0) ∝[m1−m2−m3+m4] (3.5) The expression FM(0,1,0) becomes zero for all the IRs except for Γ2 and Γ6 , for which its value is (4u,0,0) and (0,0,4w). For this reason, the only IRs 94 Chapter 3. Neutron study of [Cr(CN)6][Mn(R/rac)−pnH(DMF)] ·2H2O that can correspond to our magnetic structure are Γ2 and Γ6 . Two ttings of the magnetic structure imposing the symmetry of Γ2 or Γ6 clarify that Γ2 describes the magnetic symmetry for both magnetic species as can be seen in table 3.15. The magnetic moments found with an agreement factor of R=11.2 are shown in table 3.16. Table 3.15: Experimental and calculated magnetic contribution to the intensity of several lines for the compound GN-DMF(rac). ( h, k, l) I35K−I2KIΓ2IΓ6 ( -1, 0, 0) 0 ± 25 4 0 ( 1, 0, -2) 292 ± 28 282 278 ( 0, 1, 0) 2120 ± 43 2444 1353 ( -2, 0, 1) 366 ± 55 277 1122 ( -1, 1, 1) 54 ± 49 78 499 ( 0, 1, 2) 1796 ± 48 1756 700 ( -1, 0, 3) 74 ± 42 73 6 ( 1, 1, 2) 69 ± 50 69 10 ( -2, 0, -3) 704 ± 59 645 403 ( -1, 1, -3) 472 ± 52 498 557 ( -1, 0, 4) 766 ± 55 750 302 ( -3, 0, -2) 59 ± 55 14 228 ( 0, 0, -5) 187 ± 50 193 0 ( -1, 2, -2) 270 ± 73 244 404 ( -3, 0, -4) 368 ± 62 258 407 ( -2, 2, -1) 1383 ± 71 1236 877 ( -1, 0, 6) 573 ± 69 603 232 ( -4, 1, -2) 300 ± 56 334 682 ( -3, 1, 5) 458 ± 72 407 111 ( 0, 0, -7) 578 ± 66 634 0 Table 3.16: Magnetic moments for Mn and Cr along each axis and the total magnetic moment for GN-DMF(rac). Cation MxµBMyµBMzµB M µB Mn -3.69(4) 0 -1.5(4) 4.0(4) Cr 1.97(5) 0 -0.3(1) 1.99(15) The magnetic moments for MnII and CrIII obtained are 4.0(4) and 1.99(15) µB respectively. As for the chiral compound GN-DMF(R), the theoretical values given by the magnetochemistry of each cation are 5 µB and 3 µB , according to 3.4. Results 95 S=g·S·µB and with a Lande factor equal to g=2. The dierence between the experimental values and the theoretical ones could be attributed to the fact that the data were acquired at 10K, so the saturation regimen may not be reached. The magnetic structure can be described as two sublattices, one of Mn and one of Cr , that order antiferromagnetically one respect to the other. The reason for the antiferromagnetic ordering has been already explained in the Chapter 1 and it is predicted by the Goodeneough-Kanamori rules [76]. The IR Γ2 does not allow a magnetic component along the b axis and hence the magnetic moments lie in the plane ac , which the major contribution along the a axis. The net magnetic moments along the a axis of dierent layers are directed in an opposite sense. The magnetic structure can be seen in gure 3.18. The magnetic moments are not collinear, which could be due to the anisotropy of the ions of the DM interaction. A inspection of the symmetry elements of the group Pnmma reveals and inversion center in the middle point of the lines that join m1−m3 and m2−m4 . According to the symmetry rules published by Moriya [55], this symmetry element discards the existence of a DM interaction between these atoms, but not between the other magnetic atoms. P212121 is a subgroup of Pnma and the symmetry operations of the space group Pnma of the GN-DMF(rac) compound are all the symmetry operations of the space group P212121 for the GN-DMF(R) compound plus the inversion. Attending to the symmetry of the magnetic structures, the magnetic structure of GN-DMF(R) is described by the IR Γ1 of the space group P212121 (see table 3.9) while the magnetic structure of GN-DMF(rac) is described by the IR Γ2 of the space group Pnma (see table ). Both IRs becomes the same one if we suppose a magnetic moment with no component along the b axis for Γ1 . For this reason, the magnetic structure of GN-DMF(rac) is equivalent to the magnetic structure of GN-DMF(R) except for the component along the b axis. As for the GN-DMF(R), the magnetic moment of the Cr atom in GN-DMF(rac) is almost in the basal plane along the bisectrix between basal plane bonds, and the magnetic moment of the Mn atom is directed towards the center of a face of the octahedra. This behavior may be explained by the same arguments given for GN-DMF(R). Comparing the direction of magnetic moments from dierent layers in GN-DMF(rac), an antiferromagnetic alignment can be seen as for the GN-DMF(R) compound. Due to the similitude between GN-DMF(R) and GNDMF(rac) and their exchange pathways, we considerer that the explanation for this alinement may be the same for both compound, already described in 3.4.1. Several reections with a signicant magnetic intensity contribution have 96 Chapter 3. Neutron study of [Cr(CN)6][Mn(R/rac)−pnH(DMF)] ·2H2O Figure 3.18: Magnetic structure GN-DMF(rac) been measured at dierent temperatures: (221) , (22-1) , (-102) , (223) , (-10-4) , as can be seen in gure 3.19. As the magnetic moments in the GN-DMF(rac) compound are in the plane xz , the best lines to estimate the critical exponent β are the lines (0,k,0), but unfortunately none of these lines has been measured. A tting with the data of the line (223) , gives a value of β= 0.32(3) . Within the experimental error, this value could correspond to a three dimensional Ising, XY or Heisenberg model (see [96] for a wide compilation of results for critical exponents). 3.5 Chiral term calculation The chiral compound GN-DMF(R) compound crystallizes in the space group P2 1 2 1 2 1 , which is chiral, so the compound presents nuclear chirality. The possibility of being magnetically chiral depends on the cross product FM× 3.5. Chiral term calculation 97 12 16 20 24 28 32 100 200 300 400 500 600 700 800 900 -102 223 -10-4 I (a.u.) T(K) Figure 3.19: Intensity of several lines as T was decreased. (FM)∗ as it has been explained in section 2.5. In the unit cell there are eight magnetic atoms, four Mn II and four Cr III , which must be present in the calculation of the magnetic structure factor. As for the GN-MnMn compound, the chiral product can be decomposed in a term due to the MnII cations, a term related to the CrIII sublattice and two mixed terms as can be seen in equation ?? . The terms corresponding to the two sublattices are dierent from zero, as they are canted magnetic structures, and the cross terms are also dierent from zero. We can conclude that nuclear and magnetic chirality coexist in the GN-DMF(R). FM×F∗ M={FCr M+FMn M}×{(FCr M)∗+ (FMn M)∗}= ={FMn M×(FMn M)∗}+{FCr M×(FCr M)∗} +{FCr M×(FMn M)∗}+{FMn M×(FCr M)∗} (3.6) The racemic compound GN-DMF(rac) crystallizes in an centrosymmetric space group, so it is not nuclear chiral. In section 2.5.1, it has been said that magnetic chirality can no exist in centrosymmetric space groups, so the GNDMF(rac) must be nuclear and magnetic achiral. Although the inversion is a symmetry operation of the space group Pnma, and the magnetic sites m1 - m3 and m2 - m4 are related by an inversion center, there are two sublattices that are not related by symmetry operations and whose magnetic moments 98 Chapter 3. Neutron study of [Cr(CN)6][Mn(R/rac)−pnH(DMF)] ·2H2O are not collinear. The no collinearity of this sublattices may create rise doubts about the magnetic achiral structure of this compound. The no chirality of the magnetic structure can be corroborate by an inspection of the magnetic structure factor for each sublattice, which can be written as in equation by taking into account that r1=−r3 , m1=−m3 , r2=−r4 , m2=−m4 . The structure factor and its conjugate are equal except by a phase, so the chiral term is zero and the magnetic structure is achiral, as it has been postulated. FM(q) = 2i(m1sin(2πq·r1) + m2sin(2πq·r2)) (3.7) 3.6 Conclusions In this chapter, the nuclear structures of the compounds GN-DMF(R) and GN-DMF(rac) have been rened using neutron diraction. In addition, we have determined the atomic positions of the hydrogen atoms, which were not determined previously [7].In the renement performed with neutron data, all the thermal parameters of the atoms have been set as anisotropic, except for Mn and Cr in GN-DMF(rac) at 35K. Is spite of acceptable agreement factors for the renements, we have found an anomalous size and shape of the thermal ellipsoids. This anomaly may be attributed to a lack of crystallinity or some structural disorder. If we compare the nuclear structure of GN-DMF(R) and GN-DMF(rac) with the nuclear structure of GN compound, we can see how the substitution of a H2O ligand in GN by a DMF molecule modies the corrugation of the layers and the shortest interlayer distances. In addition to the renement of the nuclear structure, the neutron data acquired have allowed us to solve the magnetic structures for both compounds. A propagation vector equal to zero k= 0 has been determined for GN-DMF(R) at 2K and GN-DMF(rac) at 10K, so the nuclear and the magnetic cells are the same. For the chiral compound, the magnetic phase can be described with the IR Γ1 of the space group P212121 . Below the critical temperature, the compound presents two interpenetrating magnetic sublattices, one of MnII and another one of CrIII which interact antiferromagnetically. The magnetic moments of the Cr atoms try to remain in the basal plane, while the magnetic moments of Mn are out of the plane. The magnetic moments try to follow the direction of the bisectrix between bonds. The lack of a center of symmetry between the magnetic atoms allows the existence of a DM interaction, which may be the responsible of the non-collinearity of magnetic moments. The interaction between layers in GN-DMF(R) compound is antiferromagnetic in contrast with GN and GN-MnMn where it is ferromagnetic. This could be justied by the 3.6. Conclusions 99 dierence in the interaction pathways between layers. Considering our the denition for a magnetically chiral compound CM=FM×(FM)∗= 0) , the magnetic phase of GN-DMF(R) is magnetically chiral, therefore, nuclear and magnetic chirality coexist in this compound. The symmetry of magnetic phase of the racemic compound GN-DMF(rac) can be described with the IR Γ2 of the space group Pnma. As for the chiral compound, the magnetic structure of GN-DMF(rac) can be described as two interpenetrating and antiferromagnetic layers, one of MnII and another one of CrIII . The inversion center between pairs of magnetic atoms in the GN-DMF(rac) is the main dierence between the GN-DMF(R) and the GNDMF(rac). As a consequence of the inversion center, the component of the magnetic moments along the b axis is set equal to zero and magnetic chirality no longer occurs. 4.2. Single Molecule Magnets (SMMs) 107 Figure 4.1: a). Schematic drawing of the ∆ created by a high anisotropy. b) Modi- cations in the energy levels due to an external magnetic eld. is shown in equation 4.2 and is known as a Arrhenius law. M(t) = M0·(1 −exp(−t/τ) (4.1) τ=τ0exp(∆/kT ) (4.2) An alternative to calculate the energy barrier and the relaxation time is based on an average magnetic relaxation time τav , that can be estimated with the relation given by equation 4.3. This equation is often used to analyze magnetic dynamics of spin glasses and other complex magnetic system [98]. This relation is specially useful when two superposed frequency-dependent signals coexist or the blocking phenomenon can be hardly observed and it is not easy to determine the peak position in the out-of-phase signal. τav = lim (ω→0)[χ”/ωχ′] (4.3) The origin of the energy barrier in a cluster lies in a high spin ground state in addition to an Ising magnetic anisotropy. Its magnitude is given by the dierence between energies of the lowest lying level and the top lying level as can be seen in gure 4.1a. It can be calculated as ∆ = |D|S2 if the spin of the cluster is an integer, or ∆ = |D|(S2−1/4) if the spin is a half integer, where D reects the axial anisotropy, selecting a preferred orientation of the magnetization along z (easy-axis anisotropy). If the D parameter is negative, major projections of the spin |mS>=±S lie lowest. A positive D term corresponds to easy-plane anisotropy with preferred orientation of the spins in the xy plane. In absence of an external eld and at very low temperature, if D is negative, the state levels |ms>= +S and |ms>=−S are degenerate, lie lowest and 108 Chapter 4. Introduction to SMMs. Concepts and objetives are the unique levels populated. Magnetization is zero. If a magnetic eld parallel to the anisotropy axis is applied, a sense of magnetization is favored as can be seen in gure 4.1b. If the external eld is high enough, only one level ( |ms>= +S or |ms>=−S ) is populated and the magnetization reaches its saturation value. When the eld is removed the system must go back to thermal equilibrium, so it "relaxes". Classically, this process is possible by the coupling of the spin system to the environment, i.e. spin-phonon interaction. In this situation, spins absorb energy from phonons to reach the higher level energy and then loss energy by exciting vibrational modes of the lattice, until equilibrium exists. As the energy barrier depends directly on the anisotropy and the net magnetic moment of the system, a smart rational design for SMMs will look for clusters with high magnetic anisotropy and a high spin ground state to increase the energy barrier and hence the blocking temperature of a SMM. With this objective, eorts to achieve a smart design have been performed in several directions: clusters containing larger numbers of metal centers to increase the spin, the use of metals with a large anisotropy to increase D , or by using a directed synthesis approach toward specic cluster geometries. For example, in homometallic compounds, a good strategy is to use brigding angles close to 90 o . Other consideration that have to be taken into account, is the fact that the exchange coupling should be as large as possible, so the resultant spin ground state that characterize the cluster is isolated from the excited states. A synthesis strategy based on increasing the D value or the spin cluster and to hope for the best for the other parameter has been followed for a long time. However, recent studies show that S and D are correlated [99, 100]. For the same compound, increasing S will generally result in enhancing the energy barrier, but not as S2 as it could be expected. The magnitude of the barrier is mainly determined by D , therefore, increasing the anisotropy of the cluster and the single-ion anisotropy of each magnetic site given by the local tensor Di , results a more promising strategy than increasing the number of metal ions and their spins. In this scenario, atoms with spin-orbit coupling are promising candidates to increase the energy barrier in cluster. For an ion with a ground state S , orbital contributions may be mixed into the ground state through spinorbit coupling H=λ·L·S , so the |mS> components of a given S state are split in zero eld, leading to a preferred orientation of the magnetization with respect to the anisotropic axis of the molecule. The magnitude of this splitting and therefore of the anisotropy is proportional to λ2 , the spin-orbit coupling constant. Transition metal ions which a large spin-orbit coupling show larger anisotropies and Co(II) complexes results very interesting due to the spin-orbit coupling which can generate an important zero-eld-splitting (ZFS). This phenomenon causes a single-ion anisotropy and as the main contribution to the 4.2. Single Molecule Magnets (SMMs) 109 cluster magnetic anisotropy is the sum of the single-ion anisotropies of the metal ion constituents, it enhances the energy barrier. Often, ZFS contributes to magnetic anisotropy of the cluster more than dipolar or exchange interactions. The size of D parameter depends upon the metal ions present and its coordination environment. A tendency to increase the nuclearity (and hence the maximum spin value) has lead to clusters up to 84 atoms [101], whose size is approximating the magnetic nanoparticles. However, a large number of metal centers do not guarantee a large total molecular spin. One approach is to have a cluster topology that provides ferromagnetic interactions such as a metal-oxo cubane structure that can promote ferromagnetic interactions via superexchange. The metal-oxo cubane structure is described in next section. The control of the magnetic properties of polynuclear complexes is in an early stage of development. The highest energy barrier described until the present is 86.4K with a blocking temperature of 4.5K for a [Mn6] cluster [102] 4.2.1 Relaxation pathways The magnetic moment reversal implies overcoming an energy barrier, which classically is a very slow process at temperatures much cooler than the blocking temperature. But SMMs are in the limit between classical and quantum physics, and beyond the thermally activated relaxation, they can also relax through quantum tunneling mechanisms [35]. The SMMs are the best superparamagnets to study these complex relaxation processes, because distribution of sizes and anisotropy axis that can dicult the study with nanoparticles are absent. At very low temperature only the degenerate |ms>=±S levels are populated. If only exits an axial anisotropy, the two states |ms>= +S and |ms>=−S are degenerate and orthogonal to each other, and there is no possibility of tunneling. However, with a suitable perturbation, the eigenstates of the full Hamiltonian are are linear combination of states with dierent sign of ms and the wavefunction is therefore partially delocalized on both wells. In these conditions, tunneling may be observed. As a consequence of the mix of states, the degenerate levels with dierent sign of ms are split in an energy quantity ∆T , the so-called tunnel splitting; one of the two levels is of lower energy than the degenerate levels, while the other is of higher energy. There exist dierent perturbations that allow the existence of quantum tunneling: dipolar forces between molecules, hyperne elds or an anisotropy in the perpendicular plane, E , called transverse anisotropy or rhombic anisotropy. A convenient form for the perturbational hamiltonian that takes into account the anisotropy 110 Chapter 4. Introduction to SMMs. Concepts and objetives in the perpendicular plane can be seen in equation 4.4 H=E(S2 x+S2 y) (4.4) Equation 4.4 directly couples states diering in mS by 2 in a rst order of approximation. Therefore, states |ms>= +S and |ms>=−S are mixed in a higher order in perturbational theory and their ∆T will be low. As the possibility of tunneling is related to the relative energies of the tunnel splitting and of the barrier, the smaller the ratio between the two the smaller the possibility of observing tunneling, it is very important the contribution to the higher levels in the tunneling. If the spin of the cluster is a half integer, the transverse term of the anisotropy does not admix the ground states and the tunnel splitting is zero. These states remain degenerate as predicted by the Kramers theorem, according to which the minimum possible degeneracy of the states of odd-integer spin systems is two. Therefore, in principle, no tunneling is possible for a system with half-integer spin in rigorously zero eld. Tunneling can occur also between dierent pairs of degenerate excited states, and it is called phonon-assisted or thermally activated tunneling mechanism. Phonons are absorbed in order to populate excited states involved in the tunneling process. As the tunneling frequency is expected to increase on decreasing the value of ms this mechanism is very important when these levels are populated. Molecules may not need to go over the maximum of the barrier even at relatively high temperatures, but may nd a shortcut and tunnel. The former quantum phenomenons occur in absence of a external magnetic eld. If a magnetic eld is applied parallel to the anisotropy axis, it modies the energy levels as can be seen in gure 4.1b, so it removes the degeneracy between pairs of levels with the same ms . However, the modication in the level structure, implies that for some values of the magnetic elds, levels at dierent sides of the energy barrier will meet, so the conditions for resonant tunneling are restored. If the eld is applied parallel to the hard axis, it generates an oscillating phenomenon that modulates the tunnel splitting making it even zero for certain values [103]. This phenomena generates the typical stepped hysteresis cycle for SMM as can be seen in gure 4.2. The steps are observed at the elds at which pairs of levels become degenerate. They correspond to relative minima in the relaxation times, because at these elds two mechanisms are operative: thermally activated and quantum tunneling. 4.2. Single Molecule Magnets (SMMs) 111 Figure 4.2: Magnetic hysteresis loop for a single crystal of Mn12ac with the eld parallel to the tetragonal axis at 2.1 K. [104] 4.2.2 Applications SMMs are materials that have important potential applications in several elds. Below the blocking temperature, a SMM behaves like a magnet, in the sense that if magnetized by an applied eld it retains the magnetization a time, rising to magnetic hysteresis. The ground state doublet is separate by the energy barrier, therefore stabilizing two eective spin states at low temperatures. After these discovers, it was suggested that the SMMs may be used as information storage units, being each molecule a bit with two binary states switched by an external magnetic eld . This goal is still out of reach, but some progresses are being done. In order to have the possibility to used the SMM as information storage units, it is necessary to increase the relaxation time to signicant values at accessible temperatures which implies to increase the energy barrier until very high limits. This future technological application helped to rise the interest in this eld. In a more broad horizon, SMM are not limited to data storage at incredible high limits. Other potential technological application of SMM, is the possibility to integrate them as building blocks in quantum computers [36] [105]. The physical laws governing these small devices are in the frame of quantum physics and classical Boolean logic may not be valid at this scale or there may exist other logics more appropriate at this case. This will imply a deep revolution, not only in the materials, but also in their functionalities and applications, as the nal objective is to store information in a molecule, process information in a molecule and communicate the result to a 112 Chapter 4. Introduction to SMMs. Concepts and objetives (supra-)molecular device. In a classical device, a bit can be only 0 or 1, but in a qubit, it can be coded as any linear superposition of the two states associated with the logical 1 and 0. Linear superpositions are very important during the dynamics, allowing quantum algorithms that performs computational tasks at inaccessible rates for classical computers. For the case of SMM, the physical magnitude to be manipulated is the spin state of the molecule, giving rise to the development of the spintronics [5] [37]. In addition, the nite number of atoms in SMMs made them excellent model systems to study the exchange interactions at the molecular scale, anisotropy eects. Due to the possibility to achieve an uniform size and distribution of SMM in a crystal, there are also excellent probes to study long range order (as produced purely by dipolar forces [13]), spin-glass-likedynamics or competition between single-particle blocking and collective blocking. Its unique properties in the frame of quantum physics made them unvaluable sceneries where new quantum theories can be tested. 4.3 Networked SMMs If one of the nal objectives of the work with SMM is to use them as devices for data storage, it is necessary to organize the molecules so they can be addressed. Some attempts have been done to organize them in Langmuir-Blodgett lms [106] or on polymeric thin lms [107], to network them by polymers [108], or to transfer SMMs onto various substrate materials [109], as the rst attempts performed on gold surfaces [110]. An alternative approximation may be the self-assembly of SMM, especially in regular 2D arrays of SMM [111]. Some of the compounds presented in this thesis are self-organized in bidimensional or tridimensional covalent networks, which makes the organization of SMMs trivial. Several studies in nanoparticles have been performed to study long range order, spin-glass-like-dynamics or competition between single-particle blocking and collective blocking [112], but due to the usual distribution of particle size and interparticle distance as well as the random localization of the particles, make this task very dicult. Therefore, SMM arranged on a regular lattice represent a more convenient scenery. Dierent collective behaviors can be observed when there is an aggregate of SMMs or networked SMMs, and they can provide an understanding of collective phenomena occurring in an interacting SMM system or among nanosized magnets. The rst evidence for the inuence of the environment in the behaviour of SMMs was given by W. Wernsdorfer et al. on dimers of Mn 4 [113] where anti- 4.3. Networked SMMs 113 ferromagnetic interactions through H bonds appear, the interactions between SMMs modify their energy levels leading to an exchange bias of the quantum resonances and may allow the control of their quantum properties. Therefore, organizing SMMs into supramolecular architectures became a very interesting eld. In addition, linking SMMs in networks can give rise to new magnetic materials whose properties lie in the boundary between classic and quantum eects. We would like to remark, that linking clusters in networks may present a wide variety of dierent behaviors, where relaxation process and magnetic order phenomenons can appear together. We are focusing ourselves in clusters that have shown a SMM behavior as isolated entities and have been bridged through dierent ligands to form nets. But also clusters dierent from SMM can be part of networks and show magnetic order and relaxation process of dierent nature [114]. Several regimens in temperature and eld frequency are expected in a network of SMM [115]. If we attend to the eld frequency regimen, the superparamagnetic behavior of SMM is revealed in presence of AC magnetic elds, therefore, this characteristic can be neglected in DC elds, where long magnetic order may appear. As the frequency of an AC eld is increased, the nature of the SMM manifests more signicantly until no conventional order can appear and SMM behaves as individual clusters. However, in the intermediate situation, there is a magnetic aggregation of SMM whose may shown a glassy response. Attending to the temperature regime, the blocking phenomenon tends to freeze the cluster spins in random directions, in contrast to interclusters interactions which favor magnetic order. If long magnetic order is presented by a compound, its origin can be purely from dipolar interaction, as it was seen for rst time in a crystal of Mn6 cluster [13], from magnetic superexchange interaction origin or a mix of both phenomenons [116]. Due to the dierent considerations that have to be taken for temperature and eld regimens, there are a wide variety of dierent behaviors at the moment and no prediction exists to anticipate the magnetic response of a compound. In our compounds studied in Chapters 6 and 7, SMMs are linked covalently through bridges with one Co(II) ion, so we expected that superexchange pathways exist and the dipolar interaction is negligible. Focusing our attention in SMMs linked covalently, the most part of them are based on Mn (see for example refs. [117120]) and among them, a family of related compounds based on a Mn4 SMM [121] that has been studied while it forms a 1D chain of SMM showing canted antiferromagnetic coupling[122], 2D networks exhibiting canted antiferromagnetic coupling [123] and a 3D structure with ferrimagnetic order at 4.1K [11, 12] and where no sign of SMM behavior is found, represents a 114 Chapter 4. Introduction to SMMs. Concepts and objetives very complete study. In the 2D structures, dierences in the orientation of the [Mn 4 ] unit, lead to dierent properties, from SMM behavior to a ordered magnetic phase at 4.2K without sign of magnetic relaxation, going through a state where canted ferromagnetic order below 2.1K coexist with a slow relaxation of the magnetization process. In contrast to Mn compounds, the number of Co(II) SMM networked is signicantly lower, for example ref. [124], where a relaxation phenomenon for a pentanuclear Co(II) cluster is found around 5K with a characteristic time two orders of magnitude higher than the expected, and although no peak in χ” appears below it, the existence of a divergence in the ZFC-FC magnetization around 3K is used to postulate a magnetic order. If we restrict our attention to networks of Co(II)-cubanes, only a few examples have been synthesized. Modifying the synthesis of the Co(II) citrate cubane reported in 2003 [125], a 3D network of cubane units linked by octahedral Co(II) centers crystallizes [126], where the SMM character of the cubane is present around 5K and ferromagnetic interactions between clusters appears at lower temperature. For this compound, a long magnetic order is suspected although not observed in the temperature range explored. In another 3D framework build up from Co(II) and dicyanamide bridges, the SMM behavior typical of Co(II)-cubanes has been lost and neither SMM blocking neither magnetic order are observed in the 3D structure [127] down to 2K. During all this chapter, we are overlooking a supramolecular structure of Co(II) cubanes arranged in a 3D network [128], but whose structure contents some features that makes us be cautious about it. Our working group is doing some progress in arranging Co-cubanes in different dimensionality networks with dierent cations, morphologies and Co(II) content. A 1D chain of cobalt(II) citrate cubanes with peripherical octahedral Co(II) centers which can be transformed into a 2D network by dehydration has been synthesized [129], but its magnetism can not be studied due to the impossibility to asses the purity of the phase. A series of 2D networks of cobalt(II) citrate cubanes with peripherical octahedral Co(II) centers were obtained and magnetically characterized, the results are partially published [14, 15] and the fully magnetic characterization can be found in chapter 6. A 3D structure studied in chapter 7 keeps on with the work increasing the dimensionality of the network. The study of these compounds, might provide clues on how to modulate the SMM properties. 4.4. The Co(II) ion and it magnetochemistry 115 4.4 The Co(II) ion and it magnetochemistry As it has been said in 4.2, a tendency to increase D dominates the eorts to achieve a smart design for SMM. Co(II) represents an excellent candidate for SMM due to its high spin-orbit coupling and anisotropy, but the diculty to treat analytically problems where Co(II) ions appear, has made Co(II) not very used for SMMs. Several Co(II)-cluster of dierent nuclearity and geometry show SMM behavior, as Co(II)-cubanes (see next section), Co 4 molecular squares [130], Co 5 square pyramids and higher nuclearity clusters. There exist also SMMs where dierent oxidation states are mixed and dierent atoms combined, even rare earths (for a more extended discussion, see the review of ref. [10]). There are even mononuclear compounds of Co(II)-organic radicals systems that exhibit slow magnetic relaxation [131]. In this section a brief revision about Co(II) magnetic behavior and its possibilities is exposed. The Co(II) ion is a d7 which can present a wide variety of magnetic behaviors and interesting magnetic phenomenon. Among all the opportunities and advantages that can be found in Co(II) complexes: variable coordination number (4-6), dierent lengths in coordination bonds, stability in air, dierent colors... we are interested in Co(II) due to the high spin that it presents in weak ligand elds (S=3/2), its spin-orbit coupling and its magneto-crystalline anisotropy. The Co(II) complexes can show large values of D that increases the energy barrier for the relaxation. In these compounds is very common a situation where the anisotropy is of the same order of magnitude or even larger than the exchange coupling [53]. Solving the Hamiltonian of a magnetic system leads to know its energy levels and to analyze theoretically its magnetic and spectroscopic properties. The origin of the magnetic exchange interaction between neighboring spins can be direct exchange between orbitals of interacting paramagnetic ions or superexchange through a diamagnetic bridge and the overall type of exchange interaction (ferroor antiferromagnetic) depends on the orbital overlap integrals, the interatomic distances and the bond angles. The exchange is modeled using eective exchange parameters J . Magnetic susceptibility, heat capacity, EPR, and INS [132] are some experimental methods used to determine J , where the rst two methods are adequate as long as one is dealing with relatively simple clusters. For more complex systems, having more than one or two J parameters, INS is the best technique, since it allows a direct, spectroscopic access to the energy levels and therefore the exchange interactions. In Co(II) clusters, solving the hamiltonian of the system can become an not easy task due to the spin-orbit coupling terms. Recently, a very complete review about exchange coupling in molecular magnets with unquenched orbital 116 Chapter 4. Introduction to SMMs. Concepts and objetives angular momenta performs a complete analysis of the dierent problems and approaches to this problem [133]. For a long time, the exchange interactions in these clusters have been modeled using the Heisenberg-Dirac-Van Vleck (HDVV) Hamiltonian, which is magnetically isotropic and expressed in terms of spin operators and therefore it is only applicable to clusters whose magnetic centers have isolated ground spin states. But the magnetic coupling in clusters with unquenched magnetic orbital momentum cannot be described in terms of spin operators only (with some exceptions), and orbital operators must be included in the Hamiltonian. The eect of the unquenched orbital angular momentum causes a strong magnetic anisotropy and anisotropic interactions between ions that can be of the same magnitude as the isotropic ones. If a general orbitally-dependent hamiltonian is build, it usually contains a pure orbital part, a mixed spin-orbital part and a third part which is of the same form as HDVV Hamiltonian. The description of the interactions in these clusters requires a great number of parameters, making necessary magnetic and spectroscopic characterizations to adjust them. Due to the diculty of elaborating accurate models for systems with unquenched orbital momentum and the existence of friendly-use computing programs to solve it (as MAGPACK [134]), the HDVV model is frequently used for cases where it is incorrect. As a result, the parameters obtained from tting the experimental data to the theoretical model are articial. For this reason, several models and approximations have been used in the study of theses clusters. The rst approximation for compounds with Co(II) appears in 1971 by Lines [135] and it is only valid for highly symmetric environments. For a free Co(II) ion, the lowest levels are 4F (L=3 and S=3/2) and 4P ((L=1 and S=3/2) and the energy dierence between them is 15000K, so we can take into consideration only the 4F level. In the presence of an octahedral crystalline eld, which is a very common feature, the 4F is splitted in 4A2g , 4T2g and 4T1g being this last one, the unique level populated for our purposes. If the octahedral eld is perfect, the spin-orbit coupling splits the 4T1g state in six Krammer's doublets. The population of this levels depends of the temperature, so the magnetic moment can be temperature dependent and not follow a Curie-behavior. Lines dened a pseudo-spin-1/2 hamiltonian to describe interactions between Co(II) in a prefect octahedral environment and the exchange interactions were simulated as HDVV hamiltonian for the lowest lying Krammers doublet. The result was a ctitious g factor that depends on the temperature and includes the eect of the spin-orbit and the excited levels. However, in real complexes, the Co(II) environment is usually distorted and the local geometry at each Co(II) plays a very important role in the magnetic properties. Distortions in octahedral eld remove the degeneracy of the 4T1g , i.e., a tetragonal distortion gives as a result a ground level 4A2g and a excited 4.7. Techniques 123 to characterize the samples. The PPMS has been used to wide the frequency range in AC measurements from 0.01 Hz to 10KHz and calibrate the data obtained with the dilution. It has also been used for heat capacity measurements between 1.4K and 120K to characterize possible magnetic transitions. The dilution allow us to increase the temperature range for the AC characterization down to 90mK and frequencies up to 13333Hz. To perform magnetic measurements in the MPMS and the PPMS, around 10 or 20 milligrams of polycrystalline sample were mixed with some vacuum grease to prevent torquing. The mixture was deposited in a gelatine capsule stuck in a straw. Diamagnetic corrections were made using Pascal's constants and the diamagnetic contribution of the sample gelatine capsule can be considered as negligible if it is compared with the magnetic signal of the samples. The diamagnetic contribution of the straw is considered negligible as it is as large as the space region seen by the SQUID sensor and its contribution can be due only to inhomogeneities. A special case is the compound Co 4 (citr) 4 [Co(H 2 O) 4 ] 4 , which is called Co 8 for simplicity and it is studied in chapter 5. It has three dierent phases, two of them interconvertible at room temperature by losing or absorbing water molecules through the surface of the crystals. It exits the possibility to go through a phase transition in a few minutes in the frame of the lab by absorbing water from the environment or losing it by heating a few degrees, creating vacuum, drying with a ow of nitrogen ... it was necessary to isolated each phase and sealed it. The gelatine capsules does not prevent the sample from losing water due to the purging operations in the equipments, so PIREX capsules were used instead. Phase 1 is stable at laboratory conditions, so around 20 milligrams of polycrystalline sample were deposited in a PIREX test tube of 3mm of diameter. The tube was sealed by applying heat at the 3cm from the sample extreme with a gas welding torch for less than one second, forming a PIREX capsule that sealed the sample. For isolating phase 2, some milligrams stayed in a dryer camera for two days and were introduced in a PIREX test tube. The capsule with the sample was sealed by heat as quickly as possible in order to avoid contamination. The PIREX capsules were introduced in a straw as usually in a commercial SQUID magnetometer. The contribution of the homemade PIREX capsules was measured separately. From 300 to 200 shows a diamagnetic contribution and paramagnetism appear below 80K. As can be seen in graphic 4.5, the signal of the Pirex capsule can be neglected due to the higher values for the samples. Several tries to measure monocrystals of Co8 were also done. The volume of samples was lees than 1 mm 3 . Each time, one monocrystal of Phase 1 (stable at normal conditions) was covered to prevent water exchange and glued 124 Chapter 4. Introduction to SMMs. Concepts and objetives 0 50 100 150 200 250 300 0 2 4 6 8 T(K) DC (emu)· 10 -4 DC (emu) LongMomentemu ### ### 0 50 100 150 200 250 0 100 200 300 400 Phase 1 21.9m g Phase 2 19.2m g Pirex DC (emu) LongMomentemu LongMomentemu LongMomentemu Figure 4.5: χ versus T plot measured at 500Oe for phase 1 (21.9mg), phase 2 (19.2mg) and a PIREX capsule on a plastic strip. Araldite, Superglue or transparent nail polish were used as coverture and glue. The crystal was manually oriented with the long dimension parallel to the strip and the strip was rotated to measured magnetization along the dierent axis. The magnetic contribution of a drop of Araldite, Superglue or transparent nail polish was measured separately as can be seen in gure 4.6. Superglue is the only material that only has a diamagnetic contribution and the magnetic signal of a monocrystal is at least ve times stronger than the drop used in the test experiment. In addition, the drop used nally to cover the crystal was less than a third part of the drop used in the test, so the superglue contribution can be neglected. For this reason, it was used as coverture. The possibility to observe a structural transition in situ motivates another experimental set up. Around 20mg of polycrystalline sample were introduced in a gelatine capsule stuck in a straw, the sample chamber purged as usual and the powder was cool down to 10K suddenly. After that, the capsule was holed, the sample was heated at 300K and the sample space was purged again before cooling down. To be sure of the loss of water, the same process was done but increasing the temperature before purging at 350K for 90 minutes and at 260K for 3 hours. To measured in the dilution, some milligrams of powder with vacuum grease were put in a plastic tube. The dilution equipment present the disadvantage of not being calibrate, so it was necessary to do it externally using the PPMS. Comparing the AC signals obtained from both instruments, and applying a multiplicative and additive factor to the signal from the dilution, it is possible 4.7. Techniques 125 0 10000 20000 30000 40000 50000 -0.5 0.0 0.5 1.0 1.5 2.0 (emu)·10 -4 H (Oe) Nail pol ish Araldite Superglue Figure 4.6: χ versus H plot measured at 1.8K for dierent covertures to relate the dilution data to the desired units. The heat capacity of the sample (K4{Co4(citr)4[µ−Co(H2O)4]2}·8H2O)n , denoted as Co 4 /3D, was measured in the PPMS. For this purpose, a small amount of powder was several times pressed in a hydraulic press until a pill of dimensions 3x3mm 2 and 0.74mg was obtained. It was glued to a sample holder with some grease and the contribution of the sample holder and the grease was subtracted. Chapter 5 Interconvertible Co(II)-cubanes 5.1 Introduction This chapter is devoted to the magnetic characterization of isolated Co 8 clusters based on Co(II)-citrate-cubane very similar to the ones that are arranged in layers presented in chapter 6 or the three dimensional structure studied in chapter 7. The objective is to understand the magnetic behavior of the isolated cluster and how distortions and symmetry can inuence its magnetism. For this purpose, polycrystalline samples of several phases of a compound were magnetically characterized. The cubane presents dierent symmetry in each phase. The synthesis and structure of the phases is described in section 5.2 and the magnetic properties presented in section 5.3. A discussion about the results and some conclusions can be found at the end of the chapter. 5.2 Synthesis and structure Starting from a water solution of citric acid and cobalt carbonate, pink single crystals of clusters Co 4 (citr) 4 [Co(H 2 O) 4 ] 4 (which is called Co 8 for simplicity) are obtained after a chemical process. Three interconvertible phases can be isolated due to two reversible solid-state reactions. Each phase is reached after a dehydration or hydration process, where crystallization water molecules are lost or absorbed through the surface of small monocrystals. In each phase cubane cores with four adjacent Co(II) ions are found, but they present dierent topologies. 128 Chapter 5. Interconvertible Co(II)-cubanes Phase 1. Modulated structure. This phase has space group C2/c , a=23.1494(9)Å, b=9.6555(2)Å, c=23.5036(8)Å, β =111.017 o (4) and V=4904.0(3)Å 3 . Phase 1 is the stable one at room temperature and normal conditions of humidity. It can be describe as a sub-periodic crystalline material with a modulated structure produced by a hopping of peripheral Co(II) ions between neighboring molecules as the ones existing in Phase 2. The rened modulated vector is (0 0.372 0) and the modulation aects to the direction of the hoping, but the clusters present in the structure are all of the same species an can be found in gure 5.1a. There are four clusters per unit cell. A two-fold axis parallel to b cell axis goes through the cubane, orthogonal to two faces, but the outer Co(II) centers broke a possible C 2 symmetry for the cluster. Inside the cubane, there are two pairs of M-M distances and other two dierent distances. We can not considered the cubane as an isolated cluster, because there are three Co(II) that are called peripheral, but whose distances to the Co(II)-cubanes are of the same magnitude that the intra-cubane distances and they are linked by two oxo-bridges, as can been in tables 5.1 and 5.2. The interaction with the outer Co(II) ions is expected to be of the same magnitude as the intra cubane interaction. Ab initio calculations show that the easy axis of anisotropy for the Co(II) centers of the cubanes are directed towards the center of the cubane. Looking in this direction, the metal atoms present a C3 environment, as can be seen in gure 5.2a, where the oxygen atoms of the cubane are represented in red and the oxygens from the citrate in green. The peripheral Co(II) atoms are in slightly distorted octahedral environments. Table 5.1: Characteristic distances and angles for the cubane in Phase 1 Distance Angle Co1-Co2 3.1736(1) Co2-O-Co2' 100.02 o (1) Co1-Co2' 3.1307(1) Co1-O-Co1' 100.77 o (1) Co2-Co2' 3.2325(1) Co1-O-Co2 98.74 o (1) / 96.66 o (1) Co1-Co1' 3.2383(2) Co1-O-Co2' 97.82 o (1) / 96.33 o (1) Table 5.2: Characteristic distances and angles for the outer Co(II) atoms to the cubane in Phase 1 Distance Angle Co1-Co3 3.2958(2) Co1-O-Co3 101.68 o (1) / 102.34 o (1) Co2-Co4 3.2880(1) Co2-O-Co4 100.48 o (1) / 103.24 o (1) 5.2. Synthesis and structure 129 Figure 5.1: a) Cluster for Phase 1, the outer Co(II) and O atoms are lighter. b) Cluster for Phase 2, the outer Co(II) and O atoms are lighter. c) Unit cell for phase 2, hydrogens are omitted for the shake of clarity. Phase 2. If a loss of water is produced as consequence of heating, drying with a nitrogen ux or creating vaccum, the modulation disappears and a new phase can be isolated. The structure has the same space group that the hydrated phase but the cell parameters change as a result of the lost water: a=22.8070(17)Å, b=9.6745(4)Å, c=23.3079(14)Å, β =111.643 o (8), Z=4, V=4780.23Å 3 . This phase has four high symmetric Co 8 clusters as the ones shown in gure 5.1b per unit cell, which can be seen as a cubane and four more Co(II), forming an 130 Chapter 5. Interconvertible Co(II)-cubanes octanuclear cluster with a cubane core. The cubane is distorted and a two-fold axis, parallel to b cell axis, is orthogonal to two faces. The distances and angles between Co(II) centers in the cubane are detailed in table 5.3. There are two pairs of M-M distances and other two dierent distances. As for phase 1, we can not considered the cubane as an isolated cluster, because distances from peripheral Co(II) ions to the Co(II)-cubanes are of the same magnitude that the intra-cubane distances and they are linked by two oxo-bridges, as can be seen in table 5.3. The interaction with the outer Co(II) ions is expected to be of the same magnitude as the intra cubane interaction. Ab initio calculations show that the easy axis of anisotropy for the Co(II) centers of the cubanes are directed towards the center of the cubane, and they present a C3 environment, as for phase 1. The peripheral Co(II) atoms are in slightly distorted octahedral environments. Figure 5.2: a) C 3 environment for the Co(II) centers in the cubane. Oxygen atoms of the cubane are represented in red and the oxygens from the citrate in green. b) C 2 symmetry for the cubane For Phase 1, the cluster is distorted as a consequence of the hoping of one Co(II) peripherical and the symmetry decreases. Although the cubane core keeps the C 2 symmetry, the angles and distances are dierent from Phase 2. 5.3. Magnetic properties 131 Table 5.3: Characteristic distances and angles for the cubane in Phase 2 Distance Angle Co1-Co2 3.1910(7) Co2-O-Co2' 100.4 o (1) Co1-Co2' 3.1337(7) Co1-O-Co1' 99.5 o (1) Co2-Co2' 3.2340(8) Co1-O-Co2 99.2 o (1) / 97.3 o (1) Co1-Co1' 3.2210(6) Co1-O-Co2' 97.3 o (1) / 95.6 o (1) Table 5.4: Characteristic distances and angles for the outer Co(II) atoms to the cubane in Phase 2 Distance Angle Co1-Co3 3.2833(6) Co1-O-Co3 100.0 o (1) / 102.3 o (1) Co2-Co4 3.2829(8) Co2-O-Co4 100.4 o (1) / 102.1 o (1) Phase 3. A third phase can be reached if we keep on dehydrating the compound but, unfortunately, the structure can not be isolated and measured. A polymerization process takes place and its nature is under study. 5.3 Magnetic properties The two phases were magnetically characterized as described in section 4.7. These samples were manipulated with special care due to a potential phase transition in the frame of the lab. To asses the purity of the phases, polycrystalline samples were isolated and sealed in PIREX capsules. For both samples, the magnetization at a eld of 500Oe has been measured from room temperature to 1.8K, as can be seen in gure 5.3. The χM·T ( χM is the magnetic susceptibility per mol) at 300K is 22.75 emu·mol−1·K for both compounds. This value is consistent with eight independent Co(II) ions with an eective magnetic moment of 4.77 µB , given by to S=3/2 and g ≥ 2.4 as it was expected [53]. The value of g dierent from 2 is due to the existence of a unquenched orbital moment. The χM·T value remains constant for both samples until 200K. Below 200K, the signal for Phase 1 increases slightly to 22.9 emu·mol−1·K and then star to decreases at 120K reaching 6.6 emu·mol−1·K at 1.8K; for Phase 2, the decrease begins at higher temperature (around 200K) but it is smoother until reaching 8.8 emu·mol−1·K at 1.8K. The only dierence between both signals is quantitative. 132 Chapter 5. Interconvertible Co(II)-cubanes The slight increase for phase 1 near 150K is predicted for a Co(II) ion [53]. The decreases of χM·T at low temperature may be due to an antiferromagnetic interaction between the Co(II) ions and/or the depopulation of the higher energy Kramers doublet. 0 50 100 150 200 250 300 0 3 6 9 12 15 18 21 24 0 10 20 30 40 50 60 6 9 12 15 18 21 Phase 1 Phase 2 M ·T (emu mol -1 K) T(K) Figure 5.3: χM·T versus T plot for phases 1 (full circles) and 2 (open circles). The inset shows in detail the low temperature region. 0 5000 10000 15000 20000 25000 30000 0 2 4 6 8 10 12 14 Phase 1 T=1.8K Phase 1 T=5K Phase 2 T=1.8K Phase 2 T=5K M ( B ) H/T (Oe K -1 ) Figure 5.4: Magnetization in Bohr magnetons per unit formula versus the ratio H/T for phases 1 (full gures) and 2 (open gures) at two temperatures No maximum of the magnetic susceptibility is observed in the χM versus T graphics and a Curie-Weiss adjust to a eight independent Co(II) ions give as parameters: g=2.758(2), θ =4.7(3)K (ferromagnetic interaction) and g=2.850(1), θ =-0.3(2)K for phase 1 and phase 2 respectively. Due to the depopulation for Appendix E [Cr(CN)6][Mn(rac)−pnH(DMF)]·2H2O 236 Appendix A. Experimental techniques. Neutron Diraction Table E.1: Atomic positions X Y Z Uiso Mn1 290K 1.0000(13) 0.2584(4) 0.7006(4) 0.0218(16) 33K 0.9978(14) 0.2580(6) 0.6997(5) 0.005(2) 35K 1.003(6) 0.259(3) 0.6998(18) 0.000(10) 2K 0.9928(17) 0.2581(7) 0.6999(7) 0.009(2) Cr1 290K 1.4948(18) 0.5046(5) 0.7647(5) 0.0259(18) 33K 1.4985(19) 0.5056(6) 0.7631(6) 0.008(2) 35K 1.507(9) 0.505(3) 0.7652(19) 0.005(12) 2K 1.4988(2) 0.5057(1) 0.76294(9) 0.011(2) N1 290K 1.2046(6) 0.3617(3) 0.7163(3) 0.0429(14) 33K 1.2033(6) 0.3639(4) 0.7138(4) 0.0177(15) 35K 1.204(3) 0.363(2) 0.7137(12) 0.015(7) 2K 1.2031(2) 0.36396(10) 0.71349(9) 0.021(2) N2 290K 1.2049(6) 0.1491(3) 0.6915(3) 0.0373(13) 33K 1.2037(7) 0.1488(4) 0.6898(4) 0.0219(15) 35K 1.196(3) 0.1476(16) 0.6923(12) 0.001(6) 2K 1.2038(3) 0.14888(10) 0.68966(9) 0.023(2) N3 290K 0.7975(6) 0.1493(3) 0.6920(3) 0.0469(15) 33K 0.7996(7) 0.1482(4) 0.6917(3) 0.0159(14) 35K 0.798(3) 0.1493(18) 0.6907(14) 0.026(8) 2K 0.7997(2) 0.14842(10) 0.69156(9) 0.023(2) N4 290K 0.7978(6) 0.3618(3) 0.7184(3) 0.0410(14) 33K 0.8000(6) 0.3620(4) 0.7165(4) 0.0157(14) 35K 0.796(3) 0.3610(17) 0.7159(11) 0.003(7) 2K 0.8000(2) 0.36221(10) 0.71653(9) 0.019(2) N5 290K 1.4753(18) 0.4108(5) 0.9110(4) 0.118(4) 33K 1.494(3) 0.4070(5) 0.9088(4) 0.108(6) 35K 1.533(4) 0.4087(17) 0.9103(13) 0.055(9) 2K 1.4943(2) 0.40718(10) 0.90869(9) 0.118(10) N6 290K 1.4867(15) 0.5944(4) 0.6157(3) 0.088(2) 33K 1.4999(13) 0.5976(4) 0.6141(3) 0.0387(17) 35K 1.506(3) 0.5954(12) 0.6142(10) 0.020(6) 2K 1.5002(2) 0.59770(10) 0.61398(9) 0.045(2) C1 290K 1.3095(7) 0.4137(4) 0.7334(3) 0.0276(17) 33K 1.3088(9) 0.4133(5) 0.7314(5) 0.015(2) 35K 1.301(4) 0.413(2) 0.7292(16) 0.003(9) 2K 1.3088(2) 0.41353(10) 0.73130(9) 0.022(1) C2 290K 1.3070(7) 0.0961(4) 0.7053(4) 0.0297(17) 33K 1.3101(9) 0.0964(5) 0.7055(5) 0.015(2) 35K 1.302(4) 0.104(2) 0.7062(15) 2K 1.3101(2) 0.09661(10) 0.70519(9) 0.021(2) C3 290K 0.6869(7) 0.0984(5) 0.7070(4) 0.0327(18) 33K 0.6896(9) 0.0967(6) 0.7065(4) 0.0131(19) 35K 0.677(4) 0.090(2) 0.7045(16) 0.009(9) 2K 0.6895(2) 0.09664(10) 0.70644(9) 0.015(2) C4 290K 0.6907(9) 0.4135(4) 0.7343(4) 0.038(2) 33K 0.6900(9) 0.4147(5) 0.7330(5) 0.0130(19) 35K 0.680(4) 0.414(2) 0.7355(15) 2K 0.6899(3) 0.41482(10) 0.73283(9) 0.013(2) C5 290K 1.4951(13) 0.4458(4) 0.8585(3) 0.0525(16) 33K 1.4977(16) 0.4439(5) 0.8569(4) 0.031(2) 35K 1.482(4) 0.4431(18) 0.8557(13) 0.014(8) 2K 1.4980(3) 0.44404(10) 0.85673(9) 0.031(2) C6 290K 1.5019(13) 0.5634(4) 0.6688(3) 0.0482(15) 33K 1.5059(13) 0.5660(4) 0.6678(3) 0.0211(16) 35K 1.508(5) 0.5658(19) 0.6690(14) 0.023(8) Continued on next page 237 continued from previous page X Y Z Uiso 2K 1.5063(2) 0.56614(10) 0.66770(9) 0.024(2) O1 290K 0.9953(13) 0.2752(4) 0.5917(3) 0.0440(15) 33K 0.9962(11) 0.2742(5) 0.5899(3) 0.0131(15) 35K 1.098(4) 0.2775(18) 0.5916(12) 0.000(8) 2K 0.9962(2) 0.27424(10) 0.58968(9) 0.018(2) N7 290K 1.0219(16) 0.2286(4) 0.8162(3) 0.071(2) 33K 1.0290(9) 0.2293(4) 0.8160(3) 0.0207(14) 35K 1.017(2) 0.2282(10) 0.8158(8) 0.016(5) 2K 1.0290(2) 0.22959(10) 0.81585(9) 0.023(2) H7C 290K 1.137(4) 0.239(2) 0.8269(16) 0.133(13) 33K 1.146(4) 0.2441(16) 0.8241(12) 0.056(6) 35K 1.1497 0.2447 0.8329 0.019 2K 1.14652 0.24428 0.82389 0.062(8) H7D 290K 0.940(6) 0.2689(18) 0.8413(12) 0.20(3) 33K 0.956(3) 0.2752(13) 0.8403(11) 0.057(7) 35K 0.9280 0.2764 0.8413 0.019 2K 0.95631 0.27531 0.83982 0.083(16) C7 290K 1.001(2) 0.1328(8) 0.8381(5) 0.066(3) 33K 0.9852(13) 0.1367(5) 0.8393(4) 0.0243(18) 35K 0.975(4) 0.1377(3) 0.8398(8) 0.027(5) 2K 0.9854(3) 0.13685(10) 0.83919(9) 0.032(3) H7A 290K 1.055(5) 0.1018(19) 0.8152(16) 0.110(12) 33K 1.057(5) 0.0902(14) 0.8071(11) 0.071(8) 35K 1.0367 0.0886 0.8047 0.033 2K 1.05823 0.09040 0.80701 0.073(10) H7B 290K 0.858(3) 0.115(2) 0.8236(13) 0.118(8) 33K 0.853(3) 0.1251(19) 0.8274(14) 0.079(9) 35K 0.8339 0.1288 0.8353 0.033 2K 0.85386 0.12495 0.82722 0.088(13) C10 290K 0.9993(15) 0.2105(5) 0.5504(3) 0.0560(17) 33K 0.9955(17) 0.2070(5) 0.5520(4) 0.034(2) 35K 0.990(4) 0.2097(19) 0.5542(12) 0.008(7) 2K 0.9956(3) 0.20711(10) 0.55175(9) 0.041(3) H10 290K 1.002(5) 0.1433(14) 0.5700(11) 0.136(10) 33K 0.985(8) 0.1361(16) 0.5724(12) 0.14(2) 35K 0.964(10) 0.141(5) 0.577(3) 0.06(2) 2K 0.98466 0.13639 0.57225 0.110(14) N9 290K 1.0068(10) 0.2187(5) 0.4845(3) 0.0690(16) 33K 1.0055(8) 0.2098(3) 0.4842(3) 0.0201(12) 35K 0.997(2) 0.2092(11) 0.4843(7) 0.006(5) 2K 1.0060(3) 0.21000(10) 0.48405(9) 0.025(2) C8 290K 1.0363(11) 0.1151(6) 0.9138(5) 0.058(2) 33K 1.0280(9) 0.1114(5) 0.9113(4) 0.0163(18) 35K 1.027(3) 0.1091(16) 0.9114(12) 0.000(7) 2K 1.0279(2) 0.11144(10) 0.91118(9) 0.020(3) H8 290K 1.161(4) 0.1345(17) 0.9245(13) 0.115(8) 33K 1.163(2) 0.1330(16) 0.9213(10) 0.044(6) 35K 1.164(4) 0.129(5) 0.914(4) 0.06(2) 2K 1.16284 0.13318 0.92127 0.049(7) N8 290K 0.9031(19) 0.1584(8) 0.9554(5) 0.111(4) 33K 0.921(2) 0.1623(8) 0.9576(6) 0.103(6) 35K 0.917(4) 0.1585(19) 0.9617(13) 0.069(11) 2K 0.9198(3) 0.16206(10) 0.95729(9) 0.109(9) H8A 290K 0.905(4) 0.2284(16) 0.9610(10) 0.134(10) 33K 0.890(6) 0.223(2) 0.9587(12) 0.107(10) 35K 0.9212 0.2326 0.9512 0.103 Continued on next page 238 Appendix A. Experimental techniques. Neutron Diraction continued from previous page X Y Z Uiso 2K 0.88914 0.22327 0.95877 0.109(13) H8B 290K 0.918(5) 0.1369(19) 1.0075(12) 0.145(12) 33K 0.934(7) 0.139(2) 1.0060(12) 0.134(15) 35K 0.9666 0.1454 1.0130 0.103 2K 0.93118 0.13807 1.00596 0.102(15) H8C 290K 0.784(3) 0.1342(15) 0.9403(13) 0.084(7) 33K 0.764(4) 0.1324(17) 0.9357(14) 0.060(7) 35K 0.7814 0.1341 0.9579 0.103 2K 0.76642 0.13271 0.93560 0.070(10) C9 290K 1.008(4) 0.0112(9) 0.9230(9) 0.134(6) 33K 1.001(2) 0.0084(6) 0.9238(5) 0.043(3) 35K 0.988(3) 0.0088(18) 0.9242(10) 0.037(9) 2K 1.00070 0.00857 0.92366 0.054(5) H9A 290K 1.016(6) -0.0067(14) 0.9750(17) 0.145(10) 33K 1.028(4) -0.0073(13) 0.9787(12) 0.071(8) 35K 1.0138 -0.0075 0.9776 0.056 2K 1.02878 -0.00712 0.97842 0.079(12) H9B 290K 1.130(7) -0.022(3) 0.891(2) 0.21(2) 33K 1.107(4) -0.026(2) 0.8944(16) 0.095(12) 35K 1.0716 -0.0339 0.8917 0.056 2K 1.10725 -0.02623 0.89420 0.119(18) H9C 290K 0.905(5) -0.013(2) 0.919(2) 0.158(16) 33K 0.908(5) -0.012(2) 0.9109(18) 0.120(14) 35K 0.8501 -0.0051 0.9125 0.056 2K 0.90890 -0.01267 0.91064 0.114(16) C11 290K 0.999(4) 0.1392(13) 0.4405(9) 0.148(6) 33K 1.006(4) 0.1283(9) 0.4444(8) 0.095(6) 35K 0.030(3) 0.1297(17) 0.4422(10) 0.033(10) 2K 1.0057(2) 0.12832(10) 0.44435(9) 0.113(9) H11A 290K 1.087(6) 0.138(3) 0.4027(13) 0.185(19) 33K 1.120(6) 0.131(3) 0.4103(19) 0.116(15) 35K 1.1342 0.1458 0.4057 0.050 2K 1.11956 0.13093 0.40952 0.119(12) H11B 290K 0.867(5) 0.152(3) 0.413(2) 0.206(19) 33K 0.895(4) 0.117(3) 0.4123(19) 0.100(12) 35K 0.9106 0.1109 0.4148 0.050 2K 0.89557 0.11757 0.41254 0.116(12) H11C 290K 1.016(8) 0.0752(19) 0.472(2) 0.199(19) 33K 1.020(9) 0.068(3) 0.4754(14) 0.139(17) 35K 1.0717 0.0719 0.4743 0.050 2K 1.01893 0.06813 0.47525 0.128(12) C12 290K 0.989(3) 0.3056(12) 0.4519(7) 0.107(4) 33K 1.000(4) 0.2925(7) 0.4496(6) 0.082(6) 35K 1.034(2) 0.2897(15) 0.4483(9) 0.017(8) 2K 0.9998(2) 0.29265(10) 0.44947(9) 0.088(8) H12A 290K 1.088(5) 0.317(3) 0.4106(18) 0.174(12) 33K 1.088(7) 0.296(3) 0.4102(17) 0.147(19) 35K 1.1435 0.2772 0.4136 0.026 2K 1.09032 0.29625 0.41058 0.114(16) H12B 290K 0.930(7) 0.357(3) 0.480(2) 0.174(13) 33K 1.003(9) 0.350(2) 0.4868(15) 0.17(2) 35K 1.0690 0.3445 0.4841 0.026 2K 1.00534 0.34991 0.48651 0.135(16) H12C 290K 0.881(6) 0.293(3) 0.433(2) 0.164(13) 33K 0.869(4) 0.292(3) 0.426(2) 0.102(13) 35K 0.9182 0.3105 0.4191 0.026 Continued on next page 239 continued from previous page X Y Z Uiso 2K 0.86855 0.29062 0.42661 0.094(13) O2W 290K 0.999(3) 0.4610(14) 0.8786(14) 0.234(18) 33K 0.992(2) 0.4649(9) 0.8738(8) 0.072(6) 35K 1.015(5) 0.468(3) 0.877(2) 0.071(13) 2K 0.9926(3) 0.46505(10) 0.87382(9) 0.059(6) H2WA 290K 0.933(6) 0.490(3) 0.8480(15) 0.41(7) 33K 0.904(4) 0.489(3) 0.851(2) 0.110(16) 35K 0.942(9) 0.498(6) 0.851(4) 0.09(2) 2K 0.90426 0.48941 0.85154 0.18(5) H2WB 290K 1.106(5) 0.483(4) 0.867(3) 0.32(4) 33K 1.098(5) 0.478(3) 0.859(2) 0.138(19) 35K 1.127(6) 0.480(7) 0.866(5) 0.10(2) 2K 1.09958 0.47706 0.85878 0.13(3) O3W 290K 0.975(7) 0.3440(12) 0.9826(10) 0.29(3) 33K 1.030(7) 0.3485(15) 0.9800(9) 0.23(3) 35K 1.032(6) 0.346(3) 0.9769(14) 0.058(14) 2K 1.0242(3) 0.34811(10) 0.98007(9) 0.23(3) H3WA 290K 0.984(5) 0.3644(19) 1.0242(9) 0.131(12) 33K 1.020(4) 0.3684(15) 1.0214(11) 0.074(8) 35K 1.002(9) 0.365(4) 1.0188(16) 0.026(13) 2K 1.01996 0.36859 1.02140 0.095(16) H3WB 290K 0.956(6) 0.400(2) 0.9651(19) 0.37(6) 33K 0.982(6) 0.386(3) 0.9493(18) 0.132(17) 35K 1.040(7) 0.381(4) 0.951(3) 0.036(17) 2K 0.98094 0.38671 0.94934 0.095(2) 240 Appendix A. Experimental techniques. Neutron Diraction Table E.2: Anisotropic thermal parameters U11 U22 U33 U23 U13 U12 N1 290K 0.029(3) 0.045(3) 0.053(4) -0.006(2) -0.005(2) -0.019(2) N2 290K 0.032(2) 0.041(3) 0.037(3) 0.001(2) 0.003(2) 0.017(2) N3 290K 0.035(2) 0.033(3) 0.072(4) 0.014(3) 0.005(2) -0.010(2) N4 290K 0.032(3) 0.022(3) 0.068(4) -0.007(2) 0.007(2) 0.002(2) N5 290K 0.230(11) 0.078(4) 0.045(4) 0.019(3) 0.013(6) -0.013(6) N6 290K 0.140(6) 0.067(3) 0.056(4) 0.016(3) 0.002(5) -0.008(5) C1 290K 0.018(3) 0.022(3) 0.041(4) -0.001(3) 0.005(2) 0.004(2) C2 290K 0.027(3) 0.016(2) 0.045(4) 0.019(2) 0.000(2) 0.014(2) C3 290K 0.016(3) 0.037(3) 0.043(4) -0.012(3) -0.005(2) 0.004(2) C4 290K 0.031(3) 0.026(3) 0.057(5) -0.010(3) 0.004(2) 0.013(2) C5 290K 0.079(4) 0.047(3) 0.031(3) 0.004(2) -0.014(5) -0.010(4) C6 290K 0.067(3) 0.042(3) 0.034(3) 0.009(2) 0.022(4) 0.018(4) O1 290K 0.056(3) 0.040(3) 0.034(3) 0.000(2) -0.004(5) 0.004(4) N7 290K 0.126(6) 0.050(3) 0.036(3) 0.002(2) -0.007(5) 0.001(5) H7C 290K 0.13(2) 0.15(3) 0.10(2) 0.039(19) 0.02(2) -0.09(2) H7D 290K 0.44(7) 0.098(16) 0.052(12) 0.030(10) 0.09(2) 0.14(2) C7 290K 0.080(7) 0.073(7) 0.045(5) 0.022(4) -0.021(6) -0.030(7) H7A 290K 0.15(3) 0.078(16) 0.09(2) 0.051(13) 0.000(16) -0.00013) H7B 290K 0.072(11) 0.16(2) 0.111(16) 0.026(15) -0.033(11) -0.050(12) C10 290K 0.076(4) 0.059(4) 0.031(4) -0.012(3) 0.013(5) -0.004(5) H10 290K 0.25(3) 0.063(11) 0.093(15) -0.024(10) 0.03(2) 0.052(18) N9 290K 0.055(3) 0.105(5) 0.045(3) -0.021(3) -0.012(3) 0.001(4) C8 290K 0.055(5) 0.064(4) 0.054(5) 0.013(3) -0.003(4) 0.008(4) H8 290K 0.13(2) 0.111(19) 0.097(19) 0.017(15) 0.018(17) -0.019(15) N8 290K 0.195(11) 0.081(7) 0.057(6) 0.024(5) 0.053(6) 0.079(7) H8A 290K 0.28(3) 0.059(12) 0.057(13) 0.029(9) 0.042(15) 0.028(15) H8B 290K 0.26(3) 0.106(17) 0.067(15) 0.048(12) 0.092(16) 0.054(17) H8C 290K 0.101(14) 0.069(12) 0.081(17) 0.009(11) 0.003(12) 0.014(10) C9 290K 0.24(2) 0.064(7) 0.088(10) -0.022(7) -0.020(16) 0.040(13) H9A 290K 0.25(3) 0.062(12) 0.114(18) 0.006(12) 0.00(2) -0.022) H9B 290K 0.29(5) 0.14(3) 0.17(4) 0.01(2) 0.03(3) 0.12(3) H9C 290K 0.18(3) 0.105(19) 0.18(3) 0.052(19) -0.01(2) -0.10(2) C11 290K 0.209(17) 0.152(13) 0.081(11) -0.067(10) -0.047(15) 0.034(16) H11A 290K 0.31(5) 0.19(3) 0.038(15) -0.071(18) 0.03(2) 0.03(2) H11B 290K 0.17(3) 0.23(4) 0.20(3) -0.12(3) -0.08(2) -0.01(2) H11C 290K 0.33(5) 0.069(15) 0.19(2) -0.055(17) 0.08(3) -0.00(2) C12 290K 0.150(11) 0.126(10) 0.044(6) 0.030(6) 0.006(10) 0.005(12) H12A 290K 0.19(2) 0.22(3) 0.098(19) 0.03(2) 0.02(2) 0.00(2) H12B 290K 0.24(3) 0.12(2) 0.14(2) 0.013(19) 0.04(2) 0.06(2) H12C 290K 0.19(2) 0.18(2) 0.11(2) 0.02(2) -0.02(2) 0.02(2) O2W 290K 0.19(2) 0.128(16) 0.37(5) -0.06(2) -0.16(3) 0.102(17) H2WA 290K 0.82(16) 0.35(7) 0.053(19) 0.12(3) -0.09(4) -0.36(9) H2WB 290K 0.28(5) 0.17(3) 0.48(9) 0.01(4) 0.28(6) -0.09(3) O3W 290K 0.58(7) 0.058(10) 0.24(3) 0.038(16) -0.21(49 -0.04(2) H3WA 290K 0.20(2) 0.13(2) 0.046(12) -0.016(12) 0.021(18) 0.08(2) H3WB 290K 0.39(7) 0.54(10) 0.18(3) 0.26(5) -0.19(4) -0.36(2) Bibliography [1] A. 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