Chemical, magnetic and electronic properties of NaxCoO2 and related compounds

Universidad de Santiago de Compostela Departamento de Química Física Chemical, magnetic and electronic properties of NaxCoO2 and related compounds. Memoria presentada por D. Manuel Bañobre López Para optar al grado de Doctor en Química Universidad de Santiago de Compostela Abril, 2011 ISBN 978-84-9887-753-3 (Edición Digital PDF) D. Manuel Arturo López Quintela, catedrático del departamento de Química Física de la Universidad de Santiago de Compostela; D. José Francisco Rivadulla Fernández, profesor titular del departamento de Química Física de la Universidad de Santiago de Compostela y D. Carlos Vázquez Vázquez, contratado doctor del departamento de Química Física de la Universidad de Santiago de Compostela, Certifican: Que el trabajo descrito en la memoria titulada “Chemical, magnetic and electronic properties of NaxCoO2 and related compounds” ha sido realizado bajo nuestra dirección por D. Manuel Bañobre López y reúne todos los requisitos necesarios para ser presentado como Tesis Doctoral. Santiago de Compostela, 8 de Abril de 2011. Fdo.:Prof. D. M. Arturo Fdo.:Prof. D. J. Francisco Fdo.:Prof. D. Carlos López Quintela Rivadulla Fernández Vázquez Vázquez Fdo.: Manuel Bañobre López El doctorando Agradecimientos (Spanish readers) En primer lugar me gustaría agradecer a mi director, el Prof. M. Arturo López Quintela, por darme la oportunidad de trabajar en su grupo y confiar en mí durante todo este tiempo. De su parte siempre he recibido buenas ideas, consejos, libertad y toda la dirección que he necesitado. Mi más sincero agradecimiento también para mi co-director el Prof. Francisco Rivadulla. Lo que a continuación podréis leer es el resultado de un reto que ambos nos propusimos hace ya unos años, y que él tenía en su cabeza. De él destaco y agradezco su profesionalidad, su metodología, su dedicación, y esas charlas de café en las que consigue renovar tu motivación e ilusión, tantas veces decaídas. Con él comencé a familiarizarme con el mundo del estado sólido, y sin duda que el futuro confirmará que habrá sido el mejor maestro posible. Mis disculpas si no he estado a la altura y no he aprendido más. Pero además de un buen jefe es un mejor amigo, siempre accesible y dispuesto a ayudar cuando se le necesita, tanto en lo profesional como en lo personal; se me ocurren muchas cosas que agradecerte, pero bueno…mejor es que siga con esto. Gracias Fran. Gracias también a mi co-director el Prof. Carlos Vázquez, con el que empecé a trabajar en un laboratorio sintetizando nanopartículas de óxidos de cromo, y más tarde, lo que se puso por delante. Con él aprendí a fijarme en los detalles y no dar nada por perdido en el lab. Gracias Carlos por estar siempre disponible para echar esa mano que tantas veces hizo falta. Un gran amigo. Gracias también al Prof. José Rivas, que siempre que lo he necesitado me ha dado su tiempo y nunca me ha escatimado medios para avanzar y seguir adelante. Y por permitirme el pluriempleo!, e ir terminando esta escritura al tiempo que trabajamos en la hipertermia magnética de materiales híbridos y multifuncionales. Mi más sincero agradecimiento para el Prof. J. B. Goodenough, por aceptarme en su grupo para una estancia realizada en el Texas Materials Institute de la Universidad de Texas en Austin. Una ejemplar combinación de lucidez, responsabilidad y respeto. Su puerta siempre estuvo abierta para recibirme y responder mis preguntas, seguramente absurdas. Aunque ha sido poco tiempo, la experiencia de trabajar en su grupo y haberlo conocido ha sido inolvidable, y un honor. Gracias también a Román Caudillo, por su recibimiento y su colaboración en el estudio del NaxCoO2. Y al Dr. Huang, por enseñarme a fabricar baterías! Aquí de nuevo…Gracias a los X-men (y a la X-woman) de la unidad de difracción de rayos-X de la USC, especialmente al Dr. Bruno Dacuña, a quién recurría cuando algún ajuste se podía mejorar o cuando quería echarme unas risas. Y llega el turno del FEDER…hay una larga lista de amigos ahí dentro, ellos son los responsables de ese gran ambiente que consigue que uno trabaje agusto. Sois muchos, así que gracias a todos. Pero permitidme que destaque a los componentes del laboratorio de estado sólido, que han sido los verdaderos compañeros de batalla: a los que están, Bea (de inestimable ayuda en su etapa en Física, ¿cuántos transfers habremos hecho?), Camilo (el principal responsable del diseño de esta portada y de la síntesis industrial del CrN en el lab); y a los que ya no están, Marta, Santi, Pablito Botta…con quiénes solucionaba los problemas que surgían en el día a día. Y a Suelih, mi contrabandista de papers en Brasil! Gracias también a Alfonso Fondado, que tantas veces tuvo que arreglar el aparato de poder termoeléctrico por mi culpa. Pero, sobre todo, gracias a mis compis de despacho: Yolanda (la Mamma, los galones, cuantos consejos me habrá dado!), Ana (la mejor gestora del tiempo que conozco, la que siempre está para una caña (ejem…), la que poco a poco está descubriendo el perfeccionismo, jeje…ánimo!), Camilo otra vez (un erudito de las ciencias y las artes, respetuoso del orden y las proporciones y fiel seguidor de Diógenes, jeje), Cristina Hoppe (la bohemia marplatense que nos visita en cuanto puede)…Ellos son los que han sufrido más de cerca aquellos días en que uno se levantaba con mejor o peor pie, los que escuchaban las aventuras y desventuras cotididanas, las risas, los problemas, el silencio a veces, y los más dispuestos a arrimar el hombro cuando hacía falta. Sois ya amigos de una época, gracias!. Gracias también a todos los co-autores que han participado de una u otra forma en las publicaciones en las que aparece mi nombre, por su trabajo. Gracias ahora a los amigos que hacen que el tiempo de ocio sea, precisamente, eso, especialmente a los de la “aldea Gala”, a Jenaro en particular por esa capacidad de sacar GB libres de un disco duro repleto, cuántas veces me habrá salvado la vida...Mención especial para Myriam, que ha seguido de cerca esta tesis y a la que tengo mucho que agradecer, entre otras cosas su confianza y sus palabras de ánimo. A Arnold, el filósofo-psicólogo de la vida defensor de la agricultura orgánica y ahora también de las cervezas de triple fermentación, jeje. Y a Matt, por esas cañas con acento inglés! Y a los colegas emigrados, que a pesar de los kilómetros de distancia siempre hacen lo que sea por reunirse, Juan Carlos (un llanero solitario en el Sahara que convierte la arena en cemento; como te echo de menos, tío), David de Lires (un percebeiro da Costa da Morte reconvertido a “Texan driller engineer” en el Golfo de México) y Julito (un “bilingual teacher” que tiene la “tecnología para hacerlo”). Y a David Abeal, un amigo de siempre que lo relativiza todo, y eso ayuda. Gracias también a la financiación, parte crucial en estas labores. A la Xunta de Galicia y al Ministerio de Educación y Ciencia (en aquella época), por la estabilidad que me proporcionaron en mis inicios y en esos cuatro años de FPU, respectivamente. Claro, GRACIAS a Cristiana, por su sosiego, por decir siempre lo que uno necesita oír en los momentos difíciles y por ayudarme a encontrar un final feliz para esta historia. Y el último lugar lo reservo para quién más se lo merece, mi familia. GRACIAS. Especialmente a mis padres, a mi madrina (también abuela) y a mi padrino (también abuelo, también Manolo), de quiénes nunca se deja de aprender. Vuestra comprensión y vuestro sacrificio ha sido fundamental para llegar hasta aquí, de otra forma no habría sido posible. Gracias por compartir vuestra ilusión y por no cansaros nunca de preguntar “¿como va esa tesis?” Ahora os respondo: “Aquí está”. Es también vuestra. Table of Contents Prologue (Spanish readers)………………………………………………...1 Prologue (English readers)……………………………………………....... 13 Chapter 1: Synthesis, chemical and structural characterization of NaxCoO2……………………………………………………. 25 1.1 Polycrystalline Samples…………………………………………............ 25 1.1.1. Parent Compound: Na0.7CoO2………………………........... 25 1.1.2. NaxCoO2, 0.3x0.7........................................................... 31 1.1.2.1. Na+ deintercalation............................................. 31 1.1.2.2. Na+ intercalation................................................. 44 1.1.3. NaxCoO2, x>0.7…………………………….......................... 49 1.2 Single-crystal Samples....................................................................... 52 Chapter 2: Magnetic and transport properties of NaxCoO2………. 55 2.1. NaxCoO2 (0.30x0.7) ……………………………………………… 57 2.2. NaxCoO2 (x>0.7)……………………………………………………...75 Chapter 3: Proximity to a Quantum Phase Transition……………… 83 Chapter 4: The role of water in the development of Superconductivity…………………………………………… 107 Chapter 5: The special case of half-doping: Na0.5CoO2……………. 125 Chapter 6: Topotactic Cation exchange in NaxCoO2 Li+, Sr2+, Ca2+………………………………………………… 145 6.1 Monovalent cation exchange……………………………………………. 147 6.1.1 LixCoO2………………………………………………………… 147 6.2 Divalent cation exchange…………………………………………………161 6.2.1 SrxCoO2………………………………………………………… 161 6.2.2 CaxCoO2……………………………………………………….. 171 Conclusions………………………………………………………………… 185 Appendix A: Synthesis and Magnetic properties of Co3O4……….. 187 A.1. Synthesis of Co3O4 nanoparticles……………………………………… 188 A.2. Magnetic properties of Co3O4 powder………………………………….190 Post-graduate Publications......................................................... 194 Chemical, magnetic and electronic properties of NaxCoO2 and related compounds. 1 Prologue (Spanish readers) En el momento de escribir esta tesis acerca de las propiedades químicas y físicas del NaxCoO2, mi ambición principal fue la de presentársela al lector de una forma sencilla y amena. Con el objetivo de ofrecer una lectura comprensible, ligera y dinámica, esta tesis fue confeccionada como un ensamblaje de historias individuales en las que, a menudo, resultados, interpretaciones y referencias se intercalan casi sin pausa, más al estilo de un libro especializado en un sistema en particular que al de una tesis. Teniendo esto en cuenta, esta presentación se divide en seis capítulos, conclusiones y un apéndice. La común introducción teórica general utilizada normalmente en las disertaciones doctorales, ha sido sustituida aquí por una breve introducción específica al principio de cada capítulo. Por lo tanto, el lector dispondrá de una visión general del estado del arte de la materia que se desarrolla en cada capítulo en particular y apreciará mucho mejor la contribución de este trabajo a la comprensión de las propiedades químicas y físicas del sistema. Sin embargo, una introducción general a la fenomenología básica del sistema, así como la descripción de la motivación que nos ha llevado a la realización de esta tesis, sigue siendo necesaria, y será, por tanto, brevemente proporcionada en las páginas siguientes. Prologue 2 El NaxCoO2 no es un material nuevo; fue primeramente sintetizado en la década de 19701 y ha sido estudiado ampliamente desde entonces2,3,4. Sin embargo, el descubrimiento de nuevas propiedades y su posible relación con fenómenos similares en otros materiales, ha impulsado un renovado interés en este sistema. Si se hace una búsqueda bibliográfica en un explorador científico (Scifinder, por ejemplo) por la palabra clave "NaxCoO2", y se representan los resultados siguiendo un orden cronológico, podemos observar el gran número de artículos publicados en la última década acerca de este sistema (Figura P.1). 70's 80's 90's 00's 0 50 100 150 200 250 x0.25 NaxCoO2 Publicated articles number Decade Figure P.1: Evolución del número de artículos científicos publicados cada año durante la última década en el sistema NaxCoO2, de acuerdo con el buscador Scifinder. La flecha en cian indica cronológicamente el punto inicial de esta tesis. 1 C. Fouassier, G. Matejka, J.-M. Reau and P. Hagenmuller. J. Solid State Chem. 6, 532 (1973). 2 R. Berthelot, D. Carlier and C. Delmas. Nature Materials 10, 74 (2011). 3 S. Hébert and A. Maignan. Thermoelectric Oxides, in Functional Oxides (eds D. W. Bruce, D. O'Hare and R. I. Walton), John Wiley & Sons, Ltd, Chichester, UK. ISBN: 9780470997505 (2010). 4 Y. Ihara, K. Ishida, H. Sakurai and E. Takayama-Muromachi. Phase diagram for Nax(H3O)zCoO2yH2O, in New research on Superconductivity (ed. B. P. Martins), Nova Science Publishers, Inc, New York, USA. ISBN: 978-1-59454-197-1 (2007). & Motivation 3 El NaxCoO2 es excepcional en este sentido, ya que ha conseguido el interés de la comunidad científica durante las últimas tres décadas por diferentes razones. Así, en los años 80 se investigó debido a sus propiedades electroquímicas (alta movilidad iónica, alta conductividad eléctrica) 5,6,7,8,9 y su potencial aplicación como cátodo en baterías alcalinas reversibles, al igual que su análogo LixCoO2.10 En los 90, sus propiedades termoeléctricas fueron las que despertaron el interés de este material para la captación de energía a alta temperatura y la refrigeración11. El rendimiento termoeléctrico de un sistema particular se cuantifica a partir del valor proporcionado por la figura de mérito termoeléctrica (ecuación [P.1]), k S Z  .  eq. [P.1] donde S,  and  son el poder termoeléctrico, la resistividad eléctrica y la conductividad térmica, respectivamente. El poder termoeléctrico representa el voltaje creado por un gradiente térmico entre dos puntos de la muestra. La tabla P.1 muestra los valores del poder termoeléctrico expresados a partir de la figura de mérito de la ecuación [P.1] a diferentes temperaturas para monocristales y policristales de NaxCoO2, en comparación con un material termoeléctrico convencional tipo-p. Pero la verdadera revolución científica originada por este material llegaría en 2005, después de que Takada et a12l reportaran superconductividad (SC) a temperaturas por debajo de 5 K en una fase de bajo contenido de Na+ después de que moléculas de agua se intercalasen en su estructura, Na0.3CoO2•1.3H2O (Figura P.2). Después de esta 5 C. Delmas, J. J. Braconnier, C. Fouassier and P. Hagenmuller. Solid State Ionics 3-4, 165 (1981). 6 J. Molenda, C. Delmas and P. Hagenmuller. Solid State Ionics 9-10, 431 (1983). 7 S. Kikkawa, S. Miyazaki and M. Koizumi. J. of Power Sources, 14, 231 (1985). 8 S. Kikkawa, S. Miyazaki and M. Koizumi. J. Solid State Chem. 62, 35 (1986). 9 J. Molenda, C. Delmas, P. Dordor. Solid State Ionics 12, 473 (1989). 10 K. Mizushima, P.C. Jones, P.J. Wiseman and J.B. Goodenough. Mater. Res. Bull. 15, 6, 783 (1980). 11 I. Terasaki, Y.Sasago, K.Uchinokura. Phys. Rev. B 56, 12685 (1997). 12 K. Takada, H. Sakurai, E. Takayama-Muromachi, F. Izumi, R. A. Dilanian and T. Sasaki. Nature 422, 53 (2003). Prologue 4 publicación, las similitudes entre el NaxCoO2 y los cupratos superconductores surgieron de forma inminente. Particularmente, la proximidad a una fase aislante de Mott en x=0.5 incrementó las especulaciones de que la superconductividad en los óxidos de cobalto y de cobre podría estar gobernada por mecanismos similares. Table P.1: Valores de la figura de mérito adimensional, ZT, para monocristales y policristales de NaxCoO2 en comparación con un material termoeléctrico convencional. Figure P.2: Susceptibilidad magnética en función de la temperatura en NaxCoO2  H 2O reportada por Takada et al (Ref. 12) mostrando el estado SC por debajo de 5 K. 0.570.160.310.081.20.03ZT -- 800K300K800K300K800K300K Si 0.95 Ge 0.05 typical p-type Na x CoO 2-δ polycrystal Na x CoO 2-δ single crystal 0.570.160.310.081.20.03ZT -- 800K300K800K300K800K300K Si 0.95 Ge 0.05 typical p-type Na x CoO 2-δ polycrystal Na x CoO 2-δ single crystal & Motivation 5 Sin embargo, muchos puntos fundamentales en la química y física de este sistema permanecen sin ser clarificados para el entendimiento de la superconductividad en NaxCoO2. El más importante es el cuál es el papel que ejerce el agua en la aparición de la superconductividad en el sistema. Pero también la relación existente entre el contenido de Na+ y la concentración de portadores en los planos de CoO2, o el efecto de la dimensionalidad estructural y electrónica son aspectos clave que no han sido explicados todavía. Con el objetivo de comprender un poco mejor las propiedades químicas y físicas de este sistema, es esencial describir brevemente los aspectos estructurales y electrónicos del NaxCoO2. La estructura cristalina de este óxido consiste en capas bidimensionales de octaedros CoO6 que comparaten aristas y que se encuentran separadas entre sí por capas de iones Na+ (see Figure P.3). En esta estrucutura, los átomos de Co forman una red hexagonal con enlaces triangulares M-M. CoO6 Na+ CoO6 Figure P.3: Izquierda: Representación 3D de la estructura bidimensional de NaxCoO2. Las bolas grises (rojas) [naranjas] representan los átomos de cobalto (oxígeno) [sodium]. Derecha: (arriba) Disposición de los octaedros CoO6 a lo largo de las capas de CoO2 perpendiculares al eje c (abajo) Detalle de la coordinación alrededor de un átomo de Co. Prologue 6 Los iones Na+ ocupan dos posiciones cristalográficas diferentes en la estructura del NaxCoO2: octaédrica (O) o trigonal prismática (P), ambas situadas en el mismo plano y a la mitad de la distancia que separa las capas de CoO2. La celda unidad de NaxCoO2 está determinada por la orientación relativa de los planos de CoO2 y la geometría de los sitios de Na+ (Figure P.4). 13 Figure P.4: Representación de las diferentes celdas unidad para NaxCoO2: O3, P2 and P3. La letra indica la geometría del sitio de Na+, octaédrica (O) o trigonal prismática (P). El número 2 o 3 indica el número de capas de CoO2 presentes en la celda unidad (Ref. 13). De esta forma, fases y estructuras diferentes pueden aparecer en función del contenido de Na+ (Table P.2) 1432: 13 B. L. Cushing and J. B. Wiley. J. Solid State Chem. 141, 385 (1998). 14 L. Viciu, J. W. G. Bos, H. W. Zandbergen, Q. Huang, M. L. Foo, S. Ishiwata, A. P. Ramirez, M. Lee, N. P. Ong and R. J. Cava. Phys. Rev. B 73, 174104 (2006). 13 Prologue (English readers) At the time of writting this thesis, my main concern was to present the chemical and physical properties of NaxCoO2 in an amenable way to the reader. In order to offer an understable, lighter and dynamic reading of this thesis, the whole dissertation can be considered as an assembly of individual “stories”, where results, interpretations and references are intercalated continuously in an almost “non-stop” way, more in the style of a book or a scientific paper about a particular system, than in a thesis. Taking this into account, this presentation is divided into seven chapters and two appendixes. The common general theoretical introduction normally used in the PhD dissertations, has been replaced by a brief specific introduction at the beginning of each chapter. Therefore, the reader will have a specific overview of the state of the art in the topic developed in each particular chapter and will appreciate much better the contribution of this work to the understanding of the chemical and physical properties of the system. However, some general introduction to the basic phenomenology of the system, as well as to the motivation of the thesis is still needed, and provided in the following pages. Chapter 1 14 NaxCoO2 is not a novel material; it was first synthetized in the 1970’s20 and it has been extensively studied since then21,22,23. However, the discovery of novel properties and their possible relationship with similar phenomena found in other materials, boosted a renewed interest in this system. If we make a bibliographic search in a scientific browser (i. e. Scifinder) by the key_word “NaxCoO2”, and plot the results following a cronological order, we can observe the large number of articles published in the last decade (Figure P.1). 70's 80's 90's 00's 0 50 100 150 200 250 x0.25 NaxCoO2 Publicated articles number Decade Figure P.1: Evolution of the number of scientific articles published each year in the system NaxCoO2, according to the Scifinder. The cian arrow marks the starting point of this thesis. 20 C. Fouassier, G. Matejka, J.-M. Reau and P. Hagenmuller. J. Solid State Chem. 6, 532 (1973). 21 R. Berthelot, D. Carlier and C. Delmas. Nature Materials 10, 74 (2011). 22 S. Hébert and A. Maignan. Thermoelectric Oxides, in Functional Oxides (eds D. W. Bruce, D. O'Hare and R. I. Walton), John Wiley & Sons, Ltd, Chichester, UK. ISBN: 9780470997505 (2010). 23 Y. Ihara, K. Ishida, H. Sakurai and E. Takayama-Muromachi. Phase diagram for Nax(H3O)zCoO2yH2O, in New research on Superconductivity (ed. B. P. Martins), Nova Science Publishers, Inc, New York, USA. ISBN: 978-1-59454-197-1 (2007). & Motivation 15 NaxCoO2 is excepcional in this sense, as it raised the interest of the community by different reasons during the last three decades. In the 80´s, it was investigated due to its electrochemical properties (high ionic mobility, high electrical conduction)24,25,26,27,28 and tested as a cathod in reversible alkaline cells, as its analogous LixCoO229. In the 90’s, its thermoelectric properties raised the interest of this material for energy harvesting at high temperature and refrigeration30. The thermoelectric performance of a particular system is quantified by the thermoelectric figure of merit (equation [P.1]), k S Z  .  eq. [P.1] where S,  and  are the thermoelectric power, electrical resistivity and thermal conductivity, respectively. The thermoelectric power represents the voltage created by a thermal gradient between two points of the sample. Table P.1 shows the values of the thermoelectric performance expreseed by the figure of merit (equation [P.1]) at different temperatures for NaxCoO2 single- and polycrystals in comparison with a conventional p-type thermoelectric material. But the breakthrough come in 2005, after Takada et al31 reported superconductivity (SC) below 5 K after water intercalation in a phase with low Na+ content, Na0.3CoO21.3H2O (Figure P.2). Inmediately after this report the similarities of NaxCoO2 with the superconducting cuprates were raised. Particulary, the proximity to a Mott insulating phase at x=0.5 fuelled 24 C. Delmas, J. J. Braconnier, C. Fouassier and P. Hagenmuller. Solid State Ionics 3-4, 165 (1981). 25 J. Molenda, C. Delmas and P. Hagenmuller. Solid State Ionics 9-10, 431 (1983). 26 S. Kikkawa, S. Miyazaki and M. Koizumi. J. of Power Sources, 14, 231 (1985). 27 S. Kikkawa, S. Miyazaki and M. Koizumi. J. Solid State Chem. 62, 35 (1986). 28 J. Molenda, C. Delmas, P. Dordor. Solid State Ionics 12, 473 (1989). 29 K. Mizushima, P.C. Jones, P.J. Wiseman and J.B. Goodenough. Mater. Res. Bull. 15, 6, 783 (1980). 30 I. Terasaki, Y.Sasago, K.Uchinokura. Phys. Rev. B 56, 12685 (1997). 31 K. Takada, H. Sakurai, E. Takayama-Muromachi, F. Izumi, R. A. Dilanian and T. Sasaki. Nature 422, 53 (2003). Chapter 1 16 speculation that superconductivity in the cobalt and copper oxides could be governed by similar mechanisms. Table P.1: Values of the dimensionless figure of merit, ZT, for NaxCoO2 single- and polycrystals in comparison with a conventional thermoelectric material. Figure P.2: Temperature dependence of the magnetic susceptibility in NaxCoO2  H2O by Takada et al (Ref. 12) showing the SC state below 5K. However, many fundamental issues remain to be clarified for the understanding of SC in NaxCoO2. The more important is the role that water plays in the occurrence of superconductivity. Also the direct relationship between the Na+ content and the concentration of charge carriers in the 0.570.160.310.081.20.03ZT -- 800K300K800K300K800K300K Si 0.95 Ge 0.05 typical p-type Na x CoO 2-δ polycrystal Na x CoO 2-δ single crystal 0.570.160.310.081.20.03ZT -- 800K300K800K300K800K300K Si 0.95 Ge 0.05 typical p-type Na x CoO 2-δ polycrystal Na x CoO 2-δ single crystal & Motivation 17 CoO2 planes, or the effect of structural/electronic dimensionality are key aspects that have not been explained yet. In order to understand a little better the chemical and physical properties of this system, it is essential to describe shortly the basic structural and electronic aspects of NaxCoO2. The crystal structure of this oxide consists of two dimensional layers of edge-sharing CoO6 octahedra separated by Na+ layers (see Figure P.3). Co-atoms form an hexagonal lattice with triangular M-M bonding. CoO6 Na+ CoO6 Figure P.3: Left: 3D-representation of the layered structure of NaxCoO2. The grey (red) [orange] balls represent the cobalt (oxygen) [sodium] atoms. Right: (upper) Arrangement of the CoO6 octahedra in the CoO2 layers perpendicular to the c-axis. (lower) Detail of the coordination around a Co atom. Chapter 1 18 In NaxCoO2, Na+ ions can occupy two different crystallographic positions in the structure, octahedric (O) or trigonal prismatic (P), both of them in the same plane and a halfway between the CoO2 layers. The unit cell of NaxCoO2 is determined by the relative orientation of the CoO2 planes and the geometry of the Na+ sites (Figure P.4).32 Figure P.4: Representation of different unit cells for NaxCoO2: O3, P2 and P3. The letter indicates the geometry of the Na site, octahedral (O) or trigonal prismatic (P). The number 2 or 3 indicates the number of CoO2 layers in the unit cell (Ref. 13). In this way, different phases and structures can be distinguished depending on the Na+ content (Table P.2)3332: 32 B. L. Cushing and J. B. Wiley. J. Solid State Chem. 141, 385 (1998). 33 L. Viciu, J. W. G. Bos, H. W. Zandbergen, Q. Huang, M. L. Foo, S. Ishiwata, A. P. Ramirez, M. Lee, N. P. Ong and R. J. Cava. Phys. Rev. B 73, 174104 (2006). & Motivation 19 Table P.2: Symmetry of the unit cell for NaxCoO2 compounds (0.3<x<1) depending on the Na+ coordination and the number of layers per unit cell (Ref. 14). In the case of the superconducting phase, water intercalates between the Na+ and CoO2 layers to Na0.3CoO21.3H2O, increasing dramatically the c-axis lattice parameter from ~11.1 Å to ~19.5 Å, Figure P.5. It has been suggested that the influence of water in reducing dimensionality of the structure is essential to superconductivity (Ref. 10). This is supported by the observation of the absence of SC in Na0.3CoO20.6H2O with the same Chapter 1 20 oxidation state but substantially less separation between the CoO2 layers than the SC samples.34 Figure P.5: Schematic representation of the increase of the unit cell of NaxCoO2 in the c-direction as water is intercalated into the structure (from Ref. 9). Once water intercalates into the lattice, new structural details arise that should be analyzed. Solving the crystal structure of the superconducting phase has been one of the most important tasks for the last years. It constitutes a crucial point for the understanding of the pairing mechanism that originates superconductivity in this system. However, different structural models of water-intercalated NaxCoO2yH2O have been proposed and no agreement has been reached between them to date. What is clear is that many compositions with different amounts of intercalated H2O coexist in hydrated samples, complicating the analysis even further. Now, let´s look closer at the electronic structure of the Co atoms in NaxCoO2. For x=0, simply CoO2, each Co atom is in the Co4+ valence state and 5 electrons occupy the 3d orbitals (assuming a purely ionic picture). In a low-spin configuration, only one electron is unpaired and Co4+ has a spin ½. As Na+ ions are added to the structure, each contributes one electron, thereby changing Co4+ to a diamagnetic Co3+ state. At x=1, NaCoO2, all the 34 M. L. Foo, R. E. Schaak, V. L. Miller, T. Klimczuk, N. S. Rogado, Y. Wang, G. C. Lau, C. Craley, H. W. Zandbergen, N. P. Ong and R. J. Cava. Solid State Comm. 127, 33 (2003). & Motivation 21 Co atoms would be in the Co3+ valence state, rendering a diamagnetic system. The energy levels of these two limiting spin configurations are represented in the diagram of Figure P.6. x=0 Co4+ (d5) x=1 Co3+ (d6) Figure P.6: Schematic representation of the energy levels and spin configurations for NaxCoO2 x=1 and x=0. The possibility of mixed valence, along with the resulting spin configurations and the strong Co-3d:O-2p hybridization, are responsible for the richness of the phase diagram of NaxCoO2. At the beggining of this thesis, the accepted phase diagram for this system was that one reported by Shaak et al35, which shows a wide variety of magnetic and electric phases with doping and temperature (Figure P.7). A number of different magnetic phases like Pauli paramagnetism (PM), Curie- Weiss temperature dependence (CW), antiferromagnetic order (AFM), spin density waves (SDW) are found as a function of Na+. All of these have a metal-like behaviour, except at x=0.5, where the system goes through a “metal-insulator” transition due to a certain type of charge order36. At 1/4x1/3 superconducting state appears below 5 K as water is intercalated into the structure. 35 R. E. Schaak, T. Klimczuk, M. L. Foo and R. J. Cava. Nature, 424, 527 (2003). 36 M. L. Foo, Y. Wang, S. Watauchi, H. W. Zandbergen, T. He, R. J. Cava and N. P. Ong. Phys. Rev. Lett. 92, 247001 (2004). Low-S p in t 6-x Low-S p in t 6-x Chapter 1 22 Figure P.7: Magnetic/electric phase diagram of NaxCoO2 propposed by Schaak et al in Ref. 16. In this narrow range of Na+ compositions in which superconductivity is achieved, the dependence of superconducting temperature transition (Tc) as a function of Na+ doping remains still unclear. Initially, a strongly correlation between Tc and the Na+ content of the samples was established, and an optimal chemical doping level for superconductivity with Tc ≈ 4.5 K at x0.3 was reported35. This “dome-like” dependence of Tc with doping shows the same kind of trend that cuprates. For this reason, it has been thought that this material would be a good candidate to shed a light on the superconductivity mechanism in these compounds. However, a great controversy was generated when subsequent reports observed an almost independent value of Tc with x.37,38 37 D. P. Chen, H. C. Chen, A. Maljuk, A. Kulakov, H. Zhang, P. Lemmens, and C. T. Lin. Phys. Rev. B 70, 024506 (2004). T (K) 0.28 0.37 0.50 0.750 0.70 10 30 50 40 20 SC (H2O intercaled) PM metal CW metal SDW metal Insulator CO x,Na Synthesis, characterization… 29 calculated from Rietveld analysis for this phase, a=2.8355(1) Å and c=10.8987(4) Å are close to the values reported by Fouassier et al,47 a=2.833 Å and c=10.88 Å. 10 20 30 40 50 60 70 80 -5000 0 5000 10000 15000 20000 Na0.67CoO2 293 K Counts 2 Figure 1.3: X-ray diffraction pattern (+) and Rietveld refinment (red line) of Na0.67CoO2 at room temperature. Vertical blue lines mark the expected position for the reflexions of the space group P63/mmc. The green line is the difference between the experimental and calculated intensities. Rwp=9.92%. We also tried to synthesize other samples with a different Na+ content, in the range 0.5<x<1, from the direct solid state reaction of the corresponding stochiometric mixture of reactants. However, in all the cases, the product obtained finally presented a similar Na+ content of x0.7. Therefore, it is important to remark that the Na+ content of the final cobalt oxides obtained directly from this conventional solid-state reaction does not depend on the initial Na/Co ratio. The most stable phase for NaxCoO2 system obtained directly from the synthesis corresponds to x0.7. So, this observation should be considered in the case of the older papers where NaxCoO2 samples with x≠0.7 were reported from direct, solid state reactions48,49. 47 C. Fouassier, G. Matejka, J. M. Reau and Hagenmuller. J. Solid State Chem. 6, 532 (1973). 48 V. M. Jansen and R. Hoppe. Z. anorg. Allg. Chem. 408, 104 (1974). Chapter 1 30 Scanning electron microscopy (SEM) images from polycrystalline samples were taken for some representative Na+ compositions in the NaxCoO2 system to study the morphology of this compound. Micrographs were taken in a LEO-435VP scanning electronic microscope working at 20 kV with a maximum resolution of 6 nm (under P~10 Pa). Figure 1.4 shows SEM and optical photographs for polycrystalline samples of NaxCoO2 with x=0.67. Pictures were taken over the surface of cold-pressed pellets of ~5 mm, which were pressed mechanically at 12-13 Ton/cm2. In the case of the non-hydrated sample (a), as it would be deduced by Energy Dispersive X-ray (EDAX) analyses later, we can visually verify by SEM that the surface of the pellet is actually homogeneous in composition. It can also be observed the presence of several porous along the whole surface. This fact is a general characteristic of the NaxCoO2 system in a wide range of x. This porosity complicates intrinsic resistivity and thermal conductivity measurements in polycrystalline samples of these compunds. In picture (b), an optical photograph of exactly the same pellet after being exposed to ambient conditions for one week is shown. These compounds are highly hygroscopic. Their ageing under ambient conditions leads to the formation of small white crystals appreciable over the whole surface of the pellet. They resulted to be NaOH crystals as determined by EDAX analyses and X-ray diffraction. They are formed because of the reaction of Na+ ions at the surface and the water present in the atmosphere at normal conditions of pressure and temperature. It is important to realize that this spontaneous reaction of formation of NaOH will leave behind a surface of the sample with a Na+ content lower than inside the pellet, so the Co4+ concentration will be higher in the surface than in the inner regions. It is indicative of an inhomogeneous composition, resulting in a different distribution of charge carriers through the sample. This is something not normally considered in the literature, although it could determine the behaviour of the system to a large extent, even in single crystals. 49 T. Valla, P. D. Johnson, Z. Yusof, B. Wells, Q. Li, S. M. Loureiro, R. J. Cava, M. Mikami, Y. Mori, M. Yoshimura and T. Sasaki. Nature 417, 627 (2002). Synthesis, characterization… 31 (a) (b) Figure 1.4: (a) SEM and (b) optical photographs from the surface of a (a) fresh sample of Na0.67CoO2 and (b) the same sample after being exposed to ambient for one week. There is a Cu wire (20  m) attached with silver epoxy resin to the surface of the sample in (b). 1.1.2. NaxCoO2 series, 0.3<x<0.7 In order to obtain samples with different values of Na+, intercalation/deintercalation processes were done by using chemical methods of oxidation/reduction of the Co4+/Co3+ redox pair. 1.1.2.1. Na+ deintercalation There are different methods in the literature that can achieve an efficient Na+ deintercalation from Na0.7CoO2. They can be grouped in two types: chemical and electrochemical methods. In the first group are included those procedures involving a chemical oxidation of the transition metal redox pair. Among them, Br2/CH3CN4, I2/CH3CN3,50, 50 X. Z. Chen, Z. A. Xu, G. H. Cao, J. Q. Shen, L. M. Qiu and Z. H. Gan. arXiv:condmat/0412299 (unpublished). Na0.67CoO2 Chapter 1 32 KMnO4/H2O51, Na2S2O8/H2O52 or NaClO3/H2O53 oxidizing solutions are employed. On the other hand, using KMnO4 as oxidizing agent can result in substitutions at the Na and Co sites, being replaced by K and Mn, respectively, even at room temperature. However, the oxidizing deintercalation with Br2 in non-aqueous medium4 is the method more extensively used to reduce the sodium content between the CoO6 sheets in layer cobalt oxides. Its simplicity and speed make it a very useful method for Na+ deintercalation. Furthermore, it is possible to reach low Na+ contents x~0.3. Using I2 instead of Br2 allows a more accurate control over the experimental Na/Co ratio due to the softer oxidation strenght. The use of a non-aqueous medium is also strongly recommended to avoid the water intercalation between the CoO2 layers54. The dependence of the redox potential of the Co4+/Co3+ pair in NaxCoO2 upon x reported in the literature suggests that the minimum x value which can be obtained using Br2 as the oxidizing agent is x=0.4-0.5 (the potential of the Co3+/Co4+ redox pair increases as Na+ content decreases). However, it is usual to find x values lower than x=0.40 in the bibliography, and also our results show a minimum Na+ content of x=0.31. Chou et al55 used an electrochemical technique for deintercalating Na+ from Na0.7CoO2 as an alternative to chemical deintercalation. They highlighted the precise control over the final Na+ content and the reduction of the environmental hazards derivated of the use of high concentrations of Br2 as the main advantages of their procedure. In this thesis, samples of NaxCoO2 with sodium contents between 0.25<x<0.67 were obtained by Na+ deintercalation from polycrystalline Na0.67CoO2 by stirring the powder in a Br2/CH3CN oxidizing solution for 5 days at room temperature56. Bromine oxidizes the Co3+ to Co4+, favoring the motion of the Na+ ions out from the interlayer space to keep the charge electroneutrality in the compound. 51 (a) C.-J. Liu, C.-Y Liao, L.-C. Huang, C.-H. Su, S. Neeleshwar and Y.-Y. Chen. Chin. J. Phys. 43, 547 (2005) (b) C.-J. Liu, W.-C. Hung, J.-S. Wang and C.-J. C. Liu. J. Amer. Chem. Soc. 127, 830 (2005). (c) C.-J. Liu, C.-Y Liao, L.-C. Huang, C.-H. Su, S. Neeleshwar, Y.-Y. Chen and C.-J.C. Liu. Physica C 416, 43 (2003). 52 S. Park, Y. Lee, A. Moodenbaugh and T. Vogt. Phys. Rev. B 68, 180505(R) (2003). 53 M. L. Foo, Y. Wang, S. Watauchi, H. W. Zandbergen, T. He, R. J. Cava and N. P. Ong. Phys. Rev. Lett. 92, 247001 (2004). 54 K.Takada, K. Fakuda, M. Osada, I. Nakai, F. Izumi, A. R. Dilanian, K. Kato, M. Takata, H. Sakurai, E. Takayama-Muromachi, E. J. Sasaki. J. Mater. Chem. 14, 1448 (2004). 55 F. C. Chou, E. T. Abel, J. H. Cho and Y. S. Lee. J. Phys. Chem. Solid 66, 155 (2005). 56 K. Takada, H. Sakurai, E. Takayama-Muromachi, F. Izumi, R. A. Dilanian and T. Sasaki. Nature 422, 53 (2003). Synthesis, characterization… 33 By adjusting the Br2 concentration of the solution, various phases with different x can be obtained.53,57 Bromine concentrations representing substoichiometric (0.5), stochiometric (1) and molar excess (5, 10, 50, 100) relative to the amount that would be needed to remove all of the Na+ from Na0.67CoO2 were employed, according to the following reaction:            BryNaysCoONalBr y sCoONa yxx 222 2 After this time, the samples were filtered, washed with generous amounts of CH3CN and acetone, dried in an oven at low temperature (60-70 ºC) and stored in a desicator under vacuum. In this way, samples with a wide range of sodium compositions were obtained. All the samples, independently of their sodium content, are highly hygroscopic. For this reason, their manipulation was carried out minizing as much as possible any exposure to ambient moisture. The Na and Co contents were determined in the NaxCoO2 phases by inductively coupled plasma optical emission spectroscopy (ICP-OES). To dissolve the samples, an exactly weighted amount of the dried powder was added to a water diluted HCl solution (1:1) under stirring and heated in an autoclave at low temperature for 12 hours. Na and Co volumetric standars provided by Aldrich were used in the determination of these ions in the samples. The Na/Co ratios obtained are shown in Table 1.2 for each concentration of Br2. 57 R. E. Shaak, T. Klimczuk, M. L. Foo and R. J. Cava. Nature 2003, 424, 527. Chapter 1 34 Table 1.2: Results of the ICP-OES of NaxCoO2 Br2 excess Na/Co Ratio Precursor 0.673(7) 1 0.450(4) 5 0.429(6) 10 0.402(5) 20 0.381(6) 30 0.369(5) 40 0.362(4) 50 0.322(4) 100 0.310(3) The analysis confirms that the amount of Na+ decreases systematically as the excess of Br2 increases. The Na+ content drops very fast to x~0.45, even for the lowest amount of Br2. Then, increasing the amount of the oxidant reduces x down to ~0.30. The structural data of NaxCoO2 samples have been determined from a lebail refinment of the X-ray powder diffraction patterns (XRD) using the program Rietica58. The Na+ deintercalated sample using a stochiometric amount of Br2 (1) was single phase, and can be indexed within the space group P63/mmc, like the original Na0.7CoO2. For the sodium deintercalated samples with Br2 excesses above the stochiometric amount (5, 10, 20…100) new additional reflections were found. These new reflections were indexed after considering two minority phases with hexagonal symmetry, P63/m and P6/m, with lattice parameters a=5.3443(4), c=19.525(3) and a=5.4027(7), c=20.466(2), respectively. Figure 1.5 shows all the X-ray patterns for the NaxCoO2 series. So a mixture of 3 phases is present from x~0.43 down to x~0.3. 58 Rietica: B. A. Hunter and C. J. Howard. Australian Nuclear Science and Technology Organization. Lucas Heights Research Laboratories, 1998. Synthesis, characterization… 35 10 20 30 40 50 60 ‡ * ‡ * ** **** * Br x100 Br x10 Br x20 Br x30 Br x40 Br x50 Br x5 Br x1 parent phase (x=0.67) Intensity (a. u.) 2 Figure 1.5: X-ray diffraction patterns for NaxCoO2 deintercalated samples. Reflections belonging to hexagonal space groups P63/mmc, P63/m (*) and P6/m (‡) are shown. As indicated before, there is no precise control over the stochiometry of the parent compounds that are obtained directly from solid state reaction, although most of them correspond to sodium content about x0.7. In addition, the Na+ deintercalation with Br2 is a process controlled by the diffusion of the Na+ ions through the material, from bulk to surface. As a consequence, the presence of inhomogeneities in several zones of the material is expected and several crystallographic phases can result in the same sample due to slight variation of Na+ content. For this reason, the appearance of several phases with different symmetry is expected, although the ratio among them unpredictable. There are several reports in the literature of samples with an equal Na+ content that belong to different space groups44,45,47,48. In my oppinion, this is most probably a consequence of an inhomogeneous distribution of Na+ along the sample and/or possible Na+ ordering53. So, discrepancies between results obtained by different groups could result from small variations in the temperature of synthesis, number of heat treatments, Br2 concentration used in the Na+ deintercalation process or the time employed in each one of these experimental steps. Chapter 1 36 Another important factor to take into account is the time that the samples are kept in an open atmosphere before being measured, due to their high hygroscopic character. Moreover, this hygroscopic character increases as Na+ content decreases; so deintercalated samples with higher Br2 excess will be more easily hydrated. The water absorption in between the CoO6 layers provokes important structural changes characterized by the appearance of new reflections, especially at low angles59 (to be discussed later).These can be erronously indexed as a new phase of the “dry” sample. A significant displacement of the (002) reflection to lower (2θ) angles is clearly observed after Na+ deintercalation at the P63/mmc phase (Figure 1.6). This reflection is indicative of the separation between adjacent CoO6 planes, indicating an appreciable expansion of the lattice in the direction perpendicular to them after Na+ removal. Figure 1.6: Displacement of the (002) reflection of the majority phase P63/mmc after Na+ deintercalation in NaxCoO2. The lattice parameters calculated for the majority P63/mmc phase were obteained for each sample, by fitting all the reflections of the X-ray 59 J. D. Jorgensen, M. Avdeev, D. G. Hinks, J. C. Burley and S. Short. Phys Rev. B 68, 214517 (2003). 14 15 16 17 18 x=0.31 x=0.32 x=0.36 x=0.37 x=0.38 x=0.40 x=0.43 x=0.45 x=0.67 Intensity (a. u.) 2 Synthesis, characterization… 37 pattern with Rietica. The results are shown in the Table 1.3. A significant increase of the c-axis lattice parameter is observed with decreasing Na+ content while the a-axis parameter decreases slightly, but continuously over all the sodium content range. This appreciable expansion of the unit cell along the c-axis is signaling a decrease in bonding strength between the CoO2 layers as Na+ is removed. This has been typically associated to the increase of the Coulomb repulsion between the CoO6 sheets as the Co4+/Co3+ ratio increases. Surprisingly, the expansion of the c-axis parameter is less marked below x=0.40, leading to an approximately constant c/a ratio down to x=0.30. If the explanation of the Coulomb repulsion is correct, this fact could be signaling the impossibility of further charging the CoO2 planes upon doping beyond x0.4. Figures 1.7 and 1.8 show different plots of the lattice parameters as a function of the Na+ content in the NaxCoO2 samples. Table 1.3: Lattice parameters for NaxCoO2 (for the majority phase P63/mmc). The hexagonal symmetry of the space group P63/mmc implies that a=b. x a=b c 0.673(7) 2.8355(1) 10.8987(4) 0.642(6) 2.8295(1) 10.9287(6) 0.450(4) 2.8145(1) 11.1207(2) 0.429(6) 2.8132(5) 11.114(2) 0.420(6) 2.8152(1) 11.1324(2) 0.402(5) 2.8125(7) 11.169(2) 0.381(6) 2.8129(6) 11.128(3) 0.380(6) 2.8149(1) 11.1761(2) 0.369(5) 2.8097(1) 11.162(1) 0.362(4) 2.8108(1) 11.177(2) 0.322(4) 2.8113(4) 11.163(1) 0.310(3) 2.8074(3) 11.146(2) Chapter 1 38 0.3 0.4 0.5 0.6 0.7 2.80 2.81 2.82 2.83 10.8 10.9 11.0 11.1 11.2 11.3 c (Å) a (Å) x, Na content Figure 1.7: Lattice parameters for NaxCoO2 as a function of the Na+ content. Line is a guide to the eye. 0.3 0.4 0.5 0.6 0.7 3.84 3.86 3.88 3.90 3.92 3.94 3.96 3.98 c / a x, Na content Figure 1.8: Evolution of the c/a ratio in NaxCoO2 for the majority phase P63/mmc. Line is a guide to the eye. Synthesis, characterization… 45 Na0.32CoO2 was splitted in several parts (0.200 g each one) and added into NaI/acetonitrile mixtures (25 mL) presenting different amounts of NaI (0.0075-1.5 g). The time of the reaction was also a parameter of control, varying from 23 h to 140 h for a given NaI concentration. At the end of the reaction all the samples were filtered and washed several times with acetonitrile in order to avoid possible rests of NaI. All the samples were characterized structurally by X-ray diffraction. All the diffraction patterns resulted to be single phase and they were indexed to the hexagonal P63/mmc space group. Figure 1.10 shows the evolution of the (002) reflexion peak for some representative Na+ intercalated samples. Large amounts of NaI, and longer times led to phases with the highest Na+ content. The continuous displacement of the (002) reflexion to higher angles indicates that the Na+ content in the samples is increasing, reducing the interlayer distance. On the other hand, the width of the peaks remains constant after the intercalation process, which supports an homogeneous distribution of Na+ through the sample. It is important to remark that with this technique the highest Na+ content achieved was x~0.63, only slightly lower than the Na+ composition of the initial precursor obtained directly through solid state reaction, x=0.67. However, we were able to obtain a wide range of compositions in the range of 0.5<x<0.7. Figure 1.10: Evolution of the (002) reflexion peak as Na+ is intercalated into Na0.32CoO2. 15.8 16.0 16.2 0.0 0.4 0.8 x=0.32 x=0.49 x=0.53 x=0.54 x=0.55 x=0.56 x=0.58 x=0.63 x=0.67 Intensity normalized 2 Chapter 1 46 All the diffraction patterns were fitted with Rietica in order to calculate the cell parameters of the different phases. Figure 1.11 shows the evolution of the the cell parameters of the Na+ intercalated/deintercalated series. 0.3 0.4 0.5 0.6 0.7 2.80 2.81 2.82 2.83 10.8 10.9 11.0 11.1 11.2 c (Å) a (Å) x, in NaxCoO2 Figure 1.11: Lattice parameters for Na+ deintercalated (open symbols) and Na+ intercalated (closed symbols) NaxCoO2 series, as a function of the Na+ content. Lines are guides to the eye. The magnetic and transport properties of these samples will be discussed in the following chapters, paying special attention to the comparison of samples with the same x but obtained after deintercalation/intercalation from a higher/lower x. Combining the deintercalation and intercalation approaches, it is possible to cover a broad range of compositions between 0.3x0.7. Synthesis, characterization… 47 It is important to mention here that Na+ deintercalation/intercalation processes can be also performed electrochemically, in which a NaxCoO2 host would act as a cathode. Moreover, phase transitions in intercalation materials can be identified electrochemically by studying the open circuit voltage (o.c.v.) of a battery as a function of the amount of intercalated ion present in the host structure. In a battery configuration the anode potential is constant, the net concentration of Li+ ions in the electrolyte is also constant and the variations in the o.c.v. with deintercalation/intercalation are the relative to the electrochemical potential of electrons in the cathode material. Therefore, the shape of the o.c.v.-composition curve depends on the electronic structure of the cathod material and the related variation of their Fermi level. The o.c.v.-composition curve73 for NaxCoO2 shows a discontinuous potential change with several characteristic plateaus that are associated to different phase transitions along x. These structural phase transitions are related to the alteration of sodium coordination from octahedral to trigonal prismatic. In fact, the coexistence of two different structural phases (O3 and P3) has been observed for Na+ compositions 0.65x0.8. Figure 1.12: Open circuit voltage data for a NaxCoO2 cell. (Plot taken from Ref. 35). Blue crosses correspond to the o.c.v. measured for three different NaxCoO2 cells. 73 S. Kikkawa, S. Miyazaki and M. Koizumi. J. Power Sources 14, 231 (1985). 2-PHASES x x x 2-PHASES2-PHASES x x x Chapter 1 48 Three NaxCoO2 batteries with different x were performed in order to measure their o.c.v. and compare it with that one obtained in Ref. 35. The Na+ composition estimated from the o.c.v. curve is similar to that determined by ICP-OES. On the other hand, sodium cobaltates are highly higroscopic. However, the amount of water absorbed and the chemical stability depends strongly on the sodium content of the samples. As a general rule, as sodium content decreases, the hygroscopic character increases notably. Figure 1.13 shows the thermogravimetric analysis (TGA) up to 360 ºC for the parent compound (x0.7) and for a Na+ deintercalated sample (x0.4) after being synthetized and kept for one day in a desicator with a 40% of humidity. The x=0.4 sample shows a drastic weight loss of about 3% below 100 ºC, while the mass of the x0.7 sample remains almost invariant in the whole range of temperature. This weight loss is related to the humidity present in the powder. Above 100 ºC, the x0.4 sample shows a continuous weight loss with temperature up to the highest temperature measured, which must be due to intercalated water. 100 200 300 93 94 95 96 97 98 99 100 x=0.4 x=0.7 weight loss (%) Temperature (K) Figure 1.13: TGA analysis of the x  0.7 and x  0.4 samples with temperature up to 360 ºC at 10 ºC/min under N2 flowing. Figure 1.14 shows SEM images for a Na+ deintercalated sample with x0.5, before and after hydration. Their layered strcture is clearly evidenced in both of them by the stacking of the CoO2 sheets. The micrograph at the Synthesis, characterization… 49 right corresponds to the hydrated sample and a larger exfoliation between the stacked layers can be observed. Figure 1.13: SEM micrographs of the non-hydrated (left) and hydrated (right) x  0.5 sample. 1.1.3. NaxCoO2, x>0.70 The achievement of NaxCoO2 phases with x>0.7 is not trivial. The direct synthesis by solid state reaction from the most common starting materials, Na2CO3 and Co3O4, leads always to the more stable phase, Na~0.7CoO2. The preparation of phases with a low Na+ content (x<0.7), is relatively easy through Na+ deintercalation. Taking this into account, other methods of synthesis involving different experimental procedures were carried out in order to obtain different NaxCoO2 compositions with x>0.7. Among the most popular, we can distinguish those based on the direct synthesis between Na2O2 and Co3O474,75, Co metal and NaOH to obtain the NaCoO2 (O3) phase76 or Na2CO3 and Co3O4 to give, after several annealings at high temperature, x>0.8 samples77. Also an original chemical method where the parent compound Na0.7CoO2 reacts with Na metal was 74 G. Lang, J. Bobroff, H. Alloul, P. Mendels, N. Blanchard and G. Collin. Phys. Rev. B, 74, 094404 (2005). 75 Q. Huang, M. L. Foo, R. A. Pascal, Jr., J. W. Lynn, B. H. Toby, Tao He, H. W. Zandbergen and R. J. Cava. Phys. Rev. B, 70, 184110 (2004). 76 B. L. Cushing and J. B. Wiley. Synth. React. Inorg. Met.-Org. Chem, 29(7), 1199 (1999). 77 H. Sakurai, S. Takenouchi, N. Tsujii and E. Takayama-Muromachi. J. Phys. Soc. Jpn. 73, 2081 (2004). Chapter 1 50 used to obtain x>0.8 samples78. However, in spite of the existence of several methods of synthesis, in many cases the sodium composition of the resultant products reported in the literature is very ambiguous and uncertain, and actually not well intercalated between the CoO2 layers. In order to obtain a sample of NaxCoO2 with x>0.7 sample, we have checked the efficence of some of these methods. After an exhaustive analysis of the final product to determine unambiguously the actual sodium composition of the sample, we obtained the best results with the methods reported in the references 39 and 40. Below, we will describe the experimental procedures carried out following these methods for our specific case of NaxCoO2 (x>0.7) synthesis: 1) Solid state reaction77. In order to obtain a final product with x=0.82, stochiometric amounts of Na2CO3 and Co3O4 (previously dried at 300ºC overnight) were well mixing and pestle under mechanical cold pressure at ~15 tons/cm2. The reaction that takes place is exactly the same that one previously described in the synthesis of the parent compound Na0.7CoO2. All the pellets were placed in a tubular furnace under O2 flow gas and three heat treatments were performed at different temperatures: 800ºC, 850ºC and 900ºC respectively. Each thermal annealing took 6h and the samples were regrinding and pressed before each new annealing. A more detailed description about the experimental conditions of the annealings performed in the samples is found in reference 38. 2) Chemical synthesis78. For the synthesis of samples with x>0.75, sodium metal (0.3g) and tetrahydrofuran (40 ml) were placed in a 25mm x 150mm Pyrex screwcapped tube, and were heated by placing the lower 25mm in an silicon bath maintained at 95 °C. After 1 h, benzophenone (2g) was added. After heating another hour, powdered Na0.7CoO2 precursor (1.5g) was added, and the mixture was heated, with agitation by a magnetic stirring bar, for 48 h. As the mixture was cooled down to room temperature, ethanol (20 ml) was added to destroy the benzophenone ketyl radical anion and any unreacted sodium metal. After 20 min, the mixture was centrifuged for 3 min at 2000 rpm in a 78 Q. Huang, M. L. Foo, R. A. Pascal, Jr., J. W. Lynn, B. H. Toby, Tao He, H. W. Zandbergen and R. J. Cava. Phys. Rev. B, 70, 184110 (2004). Synthesis, characterization… 51 stainless-steel centrifuge tube. The organic supernatant was decanted, the solid was resuspended in dichloromethane (20ml), the mixture was centrifuged, and the organic supernatant was again decanted. Two more dichloromethane washes were performed in the same way, and then the final black pellet was broken up and air dried overnight. This process led in different syntheses to sodium-enriched materials with 0.80<x<0.90. This difference may be associated to the presence of a two-phase region in the phase diagram at these compositions, or possibly due to uncertainties in the temperature or any other variable of the reaction. The sodium content of the samples was determined by the ICP-OES method. The stochiometry of the resultant samples was Na0.82CoO2. Also the increase in the Na+ content of the samples was confirmed through structural refinements of the XRD patterns. Figure 1.14 shows the X-ray diffraction pattern for Na0.69CoO2 as well as for the samples with a high Na+ content obtained by solid state reaction and chemical synthesis, respectively. Both of them are single phase and were indexed with the hexagonal space group P63/mmc, maintaining the P3 symmetry. This is opposite to other works where a change from P3 to O3 structure was reported for samples with stochiometry x=0.75 and 0.9279. Only the pattern of the sample obtained by chemical synthesis present a couple of small reflexions marked with stars which have not been identified, probably due to partially hydrated phases. The displacement observed of the (002) reflexion peak to higher angles indicates that the interlayer distance is shorter than in the case of the parent compound Na0.69CoO2. This is consistent with a higher number of sites being ocupped by Na+ ions. 79 L. Viciu, J. W. G. Bos, H. W. Zandbergen, Q. Huang, M. L. Foo, S. Ishiwata, A. P. Ramirez, M. Lee and N. P. Ong. Phys. Rev. B, 73, 174104 (2006). Chapter 1 52 10 20 30 40 50 60 70 80 15.5 16.0 16.5 17.0 * ** Na0.67CoO2 precursor solid state reaction (ref 4) chemical synthesis (ref 5) (002) Intensity ( u. a. ) 2 (002) Figure 1.14: XRD patterns for the parent compound Na0.67CoO2 and the samples with a higher Na+ content obtained by solid state reaction and chemical synthesis, respectively. The inset shows the position of the (002) reflexion for all these samples, indicating a shift to higher angles in the case of the samples presenting a higher Na+ content. The stars (*) indicate reflections belonging to impurities which have not been identified. 1.2. Synthesis of Na0.7CoO2 single-crystal. There are basically two synthetic routes in the literature to obtain single crystals of NaxCoO2: the flux method and growth by the optical floating-zone (FZ) technique. Single crystals obtained from the latter can be several centimetres long and width, so they are easily orientable and their transport and magnetic properties can be measured as a function of a particular crystallographic direction. In this work, due to the lack of a FZ furnace, single crystals of Na0.7CoO2 have been synthesized by the flux method from Co(NO3)3.5H2O and NaOH following a slight modification of the method by Shivakumara et Synthesis, characterization… 53 al80. The reactants were weighted in the ratio 1:10 (Co(NO3)3.5H2O:NaOH), grounded and mixed under Ar atmosphere in a dry box to avoid water absorption. Then, they were placed in an Al2O3 crucible and heated at 400 ºC in air for 12 hours. The heating rate was 3 ºC/min while the cooling rate was 0.5 ºC/h from 400 ºC to 200 ºC, and 3 ºC/min from 200 ºC to room temperature. The size of the crystals obtained using the flux method is of the order of a few tens of m. Some of the micrographs obtained for Na0.7CoO2 single crystals are shown in Figure 1.15. In all of them, the hexagonal structure can be clearly appreciated. It is also distinguishable the stacking of layers along the c-axis, slightly exfoliated. Figure 1.15: SEM micrographs of Na  0.7CoO2 single crystals. 80 C. Shivakumara and M. S. Hegde. Proc. Indian Acad. Sci (Chem. Sci.) 115, 447 (2003). Chapter 1 54 Single crystals of KxCoO2 were also synthetized by this technique. The techniques described previously to deintercalate sodium from polycrystalline samples, are equally applicable to NaxCoO2 single crystals. However, it is important to remark that chemical deintercalation from single crystals results in an inhomogeneous distribution of Na+ along the sample. This is due to the smaller effective surface area of the single crystal compared to the powder. This makes the results in deintercalated single crystals very much sample-dependent. This, along with the difficulty to obtain large enough crystals to make reliable transport experiments, drove us to focus on the polycrystalline samples. Magnetic and transport properties… 61 phase. Figure 2.5 shows the TEP of the new NaxCoO2 series with three representative samples very close to x=0.5. Figure 2.4: Evolution of the temperature dependence of the thermopower with Na+ content. Below x~0.42, the thermopower does not show a dependence on the Na/Co ratio due to the invariance of doping at the CoO2 planes in this range of x. Dash curve shows a DSC analysis with temperature for a x  0.4 sample performed at 10 ºC/min. 100 200 300 400 -20 0 20 40 60 0.52(1) 0.51(1) 0.48(1) S ( V / K ) T ( K ) Figure 2.5: Thermoelectric power of a Na+ deintercalated NaxCoO2 series. 100 200 300 400 0 20 40 60 80 100 0 5 10 x = 0.69(1) x = 0.450(4) x = 0.429(6) x = 0.402(5) x = 0.381(6) x = 0.369(5) x = 0.362(4) S (V/K) Temperature (K) dH/dT (mW) Chapter 2 62 Now, we are in a position to establish general trends related to the Na+ content, which can be summarized in: (a) At large x (0.5<x<0.7) the TEP is always large and positive, and increases almost linearly over the whole temperature range. (b) In the samples very close to x0.5 (0.47<x0.5) S(T) also increases continuously over the whole temperature range, although a characteristic crossover to negative values is clearly observed below 150K. (c) For x<0.5 the positive sign of the TEP is recovered in the whole temperature range. (d) As x decreases below x<0.5 the thermopower shows a temperature independent plateau which is practically insensitive to variations in the Na+ content. The linear T-dependence is recovered above ~375 ºC, in agreement with the exothermic peak observed in DSC calorimetry. It could be presumibly associated to Na+ ion mobility. The invariance of the thermopower in the lowest doping region corroborates the inefficiency of Na+ removal to introduce charge carriers in the CoO2 layers. The same TEP behaviour with temperature was confirmed for a NaxCoO2 series in which Na+ was progresively intercalated from x=0.47 (Figure 2.6). Figure 2.6: Temperature dependence of the thermopower of a Na+ intercalated NaxCoO2 series from a sample with x=0.47. 100 150 200 250 300 350 400 450 -20 0 20 40 60 80 0.63(1) 0.57(1) 0.56(1) 0.55(1) 0.54(1) 0.53(1) 0.52(1) 0.50(1) 0.47(1) S (V / K) T ( K ) Magnetic and transport properties… 63 These measurements were extended down to ~10 K for three representative samples of these doping ranges (Figure 2.7). 0 100 200 300 400 -20 0 20 40 60 80 Na0.50 S (V/K) Na0.36 Na0.70 Temperature ( K ) Figure 2.7: Temperature dependence of the thermoelectric power of representative Na+ compositions in NaxCoO2 (x= 0.70, 0.50 and 0.36).The low-T (open) and high-T (filled) data were measured in different equipments. It is highly improbable that exactly the same Na+ arrangement is reached after chemical removal/insertion of Na+. So, these results demonstrate that only the Na+/Co3+/IV ratio is important in determining the S(T) of NaxCoO2. An important information about the band structure of NaxCoO2 could be obtained from the analysis of these data. Of special interest here are the increase of the slope with increasing Na+ content at low-T and the crossover to negative values at T~190 K in the x0.5 sample. At this specific composition, x0.5, the Seebeck coefficient is negative at low temperatures and crosses to positive values between 100-150 K, depending on the exact composition. Chapter 2 64 Kaurav et al99 showed similar results although the negative cuadrant and the minimum Seebeck were observed at T~85 K and T~50 K, respectively. Based on previous neutron scattering, susceptibility, magnetic resonance and transport results in Na0.5CoO284,100,101, the authors associated this crossover to the charge and antiferromagnetic orders. The difference of these characteristic temperatures with our data for the same Na+ composition could lie in very small differences in the Na+ content. Such a change in the sign of S(T) and the broad peak observed at low temperature indicates that the electronic structure of this sample must be fundamentally different to the neighboring compositons. However, for an AFM phase with an associated conventional charge-odering below ~40 K, there should be a substantial increase of the absolute value of hte thermopower and a thermal activated conduction; none of these are observed. On the other hand, the combination of an electrical resistivity as low as that of a metal, with a thermoelectric power that is typically an order of magnitude larger than expected on the basis of this, is not easily understood within the framework of conventional band theory for metals. So, the question being asked here is…what is the origin of this enhancement of the thermoelectric power? The magnitude of the linear temperature dependence of the Seebeck coefficient in an itinerant-electron system is determined by the band structure around the Fermi energy, according to Mott’s equation102:    F E B dE Nd e Tk TS          ln 3 22 eq. [3.1] which represents the solution of the Boltzman transport equation94 in the low temperature limit (KBT<W, where W is the bandwidth) and where B k is the 99 N. Kaurav, K. K. Wu, Y. K. Kuo, G. J. Shu and F. C. Chou. Phys. Rev. B 79, 075105 (2009). 100 G. Gasparovic, R. A. Ott, J-H. Cho, F. C. Chou, Y. Chu, J. W. Lynn and Y. S. Lee. Phys. Rev. Lett. 96, 046403 (2006). 101 F. L. Ning, S. M. Golin, K. Ahilan, T. Imai, G. J. Shu and F. C. Chou. Phys. Rev. Lett. 100, 086405 (2008). 102 N. F. Mott and H. Jones. “The theory of the properties of metals and alloys”. Ed. By Dover, NY 1958. Magnetic and transport properties… 65 Boltzman constant, T is the temperature, e is the charge of the electron and   N is the density of electronic states at the Fermi level. Rapidly varying   N, characteristic of many strongly correlated systems, result in large values of S(T), through the increse of the derivative part of equation [3.1] The complex band structure derived from the trigonal-field splitting of the Co3+/CoIV t 2g manifold, could in principle justify the large slope of S(T). Chemical doping with different cations could help testing this hypothesis, as we will discuss later. On other hand, Boltzmann transport equation tends to a temperature-independent solution at the high temperature limit (KBT>W), resulting in the so-called Heikes formula         x x e k Sb 1 ln eq. [3.2] where x is the concentration of mobile holes (CoIV) in the Co3+ lattice. So, on the basis of conventional Boltzmann transport theory, the general behavior that can be expected for a correlated (not so large W) system is schematically pictured in Figure 2.8. Chapter 2 66 Figure 2.8: General behaviour of S(T) expected for a correlated system in basis of Boltzman transport theory. The transition between the Mott and Heikes limits will be determined by the band width and its structure around EF for each particular material. In the last few years some alternative explanations have been given for the temperature dependence of S(T) in layered cobaltites.103 Terasaki et al104 speculated that the high thermoelectric power in NaxCoO2 could arise from spin fluctuations, as in the case of heavy fermions and/or valencefluctuation systems105. Particulary, Koshibae et al96,97 proposed a generalization of the Heikes formula106 to include the spin entropy contribution from Co3+ and CoIV. In their theory, the competition between the crystalline field and Hund coupling leads to large degeneracy in the cobalt 3d states, where the electrons would be rather localized. They took into acount these considerations in a new term that includes the different possible spin configurations (LS, IS and HS) in addition to the Heikes formula, 103 J. O. Haerter, M. R. Peterson and B. S. Shastry. Phys. Rev. Lett. 97, 226402 (2006) 104 I. Terasaki, Y. Sasago and K. Uchinokura. Phys. Rev. B 56, 685 (1997). 105 C. S. Garde and J. Ray. Phys. Rev. B 51, 2960 (1995). 106 P. M. Chaikin and G. Beni. Phys. Rev. B 13, 647 (1976). S T Heikes ~W Mott Magnetic and transport properties… 67           x x g g e k Sb 1 ln 4 3 eq. [3.3] where 3 gand 4 grepresent the degeneracy of the spin sate of the Co3+ and CoIV ions. Initial support for this interpretation came from the strong suppression of the thermopower under a magnetic field107,108. However, it has been demonstrated recently109 that the suppression of S(T) by a magnetic field can be explained by the field-induced spin polarization, in the context of Boltzman transport theory110. In fact, the applicability of equation [3.3] to systems like NaxCoO2 is doubtful. First of all, it predicts a temperature independent thermoelectric power, not observed in NaxCoO2 at large doping (see Figure 2.4). Since this equation is strictly applicable only in the limit where incoherent charge excitations dominate the electronic transport (kBT > W), the temperature dependence of S(T) in metallic NaxCoO2 (x≈0.7) demonstrate that this limit is still not reached at room temperature. On the other hand, for x=0.35 and x=0.5 there is a temperatureindependent plateau in which the applicability of Heikes formula can be tested. It is important to remember at this point that in NaxCoO2 the amount of holes is not exactly determined by the Na+ content111,112,113,114. For x≈0.7 the average valence is ≈3.2+ instead of 3.3+, and a constant charge of 3.57(3)+ is reached for x<0.45. For a comparison between the results from equation [3.3] and the experiment, a precise determination of the actual concentration of holes in the system is crucial. Using the experimental values for Co3+/CoIV, the values of S(x=0.35, x=0.5) at the plateau are well 107 Y. Wang, N. S. Rogado, R. J. Cava and N. P. Ong. Nature 423, 425 (2003). 108 P. Limelette, S. Hébert, V. Hardy, R. Frésard, Ch. Simon, and A. Maignan. Phys. Rev. Lett. 97, 046601 (2006). 109 H. J. Xiang and D. J. Singh. Phys. Rev. B 76, 195111 (2007). 110 T. Takeuchi, T. Kondo, T. Takami, H. Takahashi, H. Ikuta, U. Mizutani, K. Soda, R. Funahashi, M. Shikano, M. Mikami, S. Tsuda, T. Yokoya, S. Shin and T. Muro. Phys Rev. B 69, 125410 (2004). 111 M. Karppinen, I. Asako, T. Motohashi and H. Yamauchi. Chem. Mater. 16, 1693 (2004). 112 H. Sakurai, S. Takenouchi, N. Tsujii and E. Takayama-Muromachi. J. Phys. Soc. Jpn. 73, 2081 (2004). 113 M. Bañobre-López, F. Rivadulla, R. Caudillo, M. A. López-Quintela, J. Rivas and J. B. Goodenough. Chem. Mater., 17, 1965 (2005). 114 C. A. Marianetti, G. Kotliar and G. Ceder. Phys. Rev. Lett. 92, 196405 (2004). Chapter 2 68 reproduced by the Heikes equation without the need to include the spin degeneracy term. On the other hand, the Heikes limit seems to be reached also at higher doping (Na0.84CoO2) and in misfit Ca3Co4O9 (also sharing a triangular Co-lattice), as can be seen in Figure 2.9. For Na0.84CoO2 using equation [3.3] with a LS configuration (g3/g4=1/6) will require an unphysical number of holes to justify the plateau at S(kBT > W)≈ 105 μVK-1. However, the conventional Heikes formula (g3/g4=1) predicts the correct experimental value for a concentration of holes of 0.23, roughly consistent with the chemical formula. The same trend is observed for Ca3Co4O9. In this material photoemission spectroscopy experiments measured a concentration of holes [Co4+]≈0.23, consistent with a LS configuration in the 3+/4+ ionic species. Using equation [3.3] would predict a S(kBT > W)≈ 258 μVK-1, while the conventional Heikes equation results in S(kBT > W)≈ 105 μVK-1. The latter value is very close to the experimental one (see Figure 2.9). So, the conclusion with respect to x=0.7 is that the Heikes limit is not reached and, therefore, our experimental data only show the progresive S(T) evolution from a dominant Mott to Heikes state. To reconcile this with the large slope of the thermopower at low temperatures is only possible if a complex band structure with contributions from a narrow a1 and a broad e band at EF is considered.115 An important point that remains to be explained is the rapid increase of the TEP with temperature above 350 K, particularly evident at low x. The formation of larger polarons and/or a dynamic spin transition from LS to IS or HS spin configurations with temperature would explain this behavior from the renormalized statistics (number of holes vs available sites) that must be considered in the Heikes formula. 115 F. Rivadulla, J.-S. Zhou and J. B. Goodenough. Phys. Rev. B 68, 07510 (2003). Magnetic and transport properties… 69 0 100 200 300 400 0 25 50 75 100 125 Na0.84CoO2 Na0.7CoO2 Ca3Co4O9 S (V/K) Temperature (K) Figure 2.9: Temperature dependence of the thermoelectric power for two compositions of NaxCoO2 (data for x=0.84 taken from Ref.20, and Ca3Co4O9. Note that in Na0.70CoO2 the linear behaviour predicted by eq. [4] is not obeyed in the whole temperature range. Instead S(T) shows a change of slope about 150 K, although it does not reach saturation. We have taken the low temperature part to fit the data to equation [3.1]. So, the agreement between the results of equation [3.3] with the experiment is most probably based on an erroneous estimation of the concentration of holes. Conventional Heikes formula predicts the correct value of the high temperature limit of the thermopower in layered cobaltites, once the correct number of charge carriers is considered. Magnetic measurements performed in NaxCoO2 are presented below. It is important to mention again that no further thermal annealings of the samples were performed after synthesis and special attention has been paid in their storage during the time passed between the electrical, thermoelectric and magnetic measurements in order to preserve their intrinsic chemical and physical properties, and to make these measurements fully comparable among them. The time between the transport and magnetic measurements for each specific Na+ composition did not exceed more than one day in any case. Figure 2.10 shows the evolution of the zero field and field cooled (ZFC-FC) magnetization curves with x in the NaxCoO2 series. In general, an almost temperature independent magnetization region over a large range of Chapter 2 70 temperature (above ~100 K) is appreciated. However, a careful analysis of the results shows a slight and continuous increase of the magnetization from ~140 K up to 300 K for Na+ contents between 0.52x0.40 (see inset to Fig. 2.10). Figure 2.10: ZFC-FC curves as a function of temperature in NaxCoO2 at an applied magnetic field of H=100 Oe. Inset: Zoom in the temperature region T>100 K to show the thermically activated term of the magnetization. This observation has been already reported by other authors84,116 and it could be attributed to a continuous excitation above a spin gap whose origin is unknown. Below T~140K,  (T) increases in all the samples with decreasing temperature. The magnetization is not fitted by a Curie-Weiss law, so it should be separated in two different magnetic behaviours: divergent susceptibility at low temperature and Pauli susceptibility above a certain temperature (it is not as temperature independent as expected because of the spin gap transition, which provokes a slight increase of the magnetization at that temperature range. 116 G. Lang, J. Bofroff, H. Alloul, G. Collin and N. Blanchard. Phys. Rev. B 78, 155116 (2008). 0 100 200 300 0.0 3.0x10-3 6.0x10-3 9.0x10-3 150 200 250 300 2.0x10-4 3.0x10-4 4.0x10-4 5.0x10-4 H=100 Oe x=0.70 (precursor) x=0.52 x=0.50 x=0.48 x=0.43 x=0.40 x=0.37 x=0.32 x=0.31 M ( emu.g-1 ) Temperature ( K ) T ( K ) M ( emu / g ) Magnetic and transport properties… 77 Figure 2.16: Diamond anvil cell used in the measurements of X-ray with pressure, and scheme of the cell assembly. A small ruby mixed with the sample was used to monitor the internal pressure through the pressure dependence of its fluorescence peak. The fluorescence lines exhibit a pronounced red-shift with applied pressure, as shown in Figure 2.17. A 4:1 ethanol-methanol mixture was used as the hydrostatic pressure-transmitting medium. Data for each pattern were collected for 10 minutes. A standard of Silicon was refined to obtain the instrumental parameters that we need to refine our measurements by the Rietveld method. 690 692 694 696 698 0,0 0,2 0,4 0,6 0,8 1,0 Ruby P=0 kbar P=3.0 kbar P=5.7 kbar P=11.3 kbar P=25.6 kbar P=33.6 kbar P=59.0 kbar Intensity (a.u.)  (nm) Figure 2.17: Example of the red-shift of the fluorescence lines of ruby with pressure. force gascket rub y sample diamond Chapter 2 78 In Figure 2.18 we show all the x-ray diffraction patterns obtained for polycrystalline Na0.82CoO2 as pressure is increased. The inset shows a detail of the evolution of the main peak of the XRD patterns with pressure. 5 10152025 10.3 10.4 10.5 10.6 0.3 GPa 0.6 " 0.7 " 1 " 1.6 " 2 " 2.3 " 2.8 " 4 " 4.9 " 5.6 " Intensity ( u. a. ) 2  P Figure 2.18: Evolution of the XRD with pressure at room temperature for Na0.82CoO2. The inset shows the evolution of the main peak to higher angles as pressure increases. The wave length of the beam line used was  =0.44397 Å. Through Lebail fittings with Rietica of all the diffraction patterns at different pressures, we have derived the evolution of the volume with the pressure, and fitted the volume-pressure data to the Birch-Murnaghan equation, to obtain the bulk modulus, K0, of the material127.       EEE fKffKP )4'( 2 3 1)21(3 2/5 0 (Eq. A1) 127 R. J. Angel, in “High-Temperature and High-Pressure Crystal Chemistry”, Reviews in Mineralogy and Geochemistry, Vol. 41, Mineralogical Society of America, Virginia (2000). Magnetic and transport properties… 79 where K0 is the zero pressure bulk modulus, K’=  K0/  P, and               1 2 13/2 0 V V fE is the Eulerian strain. Figure 2.19 shows the results obtained considering the first order of the Birch-Murnagan equation, k’=4. The fitting of the P(V0/V) data to the Birch Murnagham equation, let us to estimate an experimental value of K0 of the order of 120(3) kbar. 1.00 1.01 1.02 1.03 1.04 0 1 2 3 4 5 6 Na0.82CoO2 P ( GPa ) Vo/V Figure 2.19: Fitting of the experimental P(V0/V) data to the Birch- Murnaghan equation, truncated at second order, k’=4. In order to analyze the effect of the pressure separately on the c and ab-directions, we plotted in the Figure 2.20 the evolution of the c and alattice parameters with increasing pressure and fitted the data to the same Birch-Murnaghan equation described above. Chapter 2 80 1.000 1.005 1.010 0 1 2 3 4 5 6 1.000 1.005 1.010 1.015 1.020 1.025 0 1 2 3 4 5 6 P (GPa) a0/a P (GPa) c0/c Figure 2.21: Fitting of the P(a0/a) (upper) and P(c0/c) (lower) data to the Birch-Murnaghan equation, truncated at second order, k’=4. The pseudo Bulk modulus estimated were 537(14) GPa in the abplane and 232(9) GPa in the c-axis. This indicates that the system is more compresible in the c-direction, as it is expected from the layered structure. The compressibility of the unit cell along the c-direction with pressure is strongly related to the pressure dependence of the AFM ordering temperature observed by Wooldridge et al 128 in x>0.7 single-crystals, increasing from 21.5 K to 25.5 K at 10 Gpa. This pressure dependence of Tm is similar to dTm/dP = 4.4(3) K/GPa estimated in x=0.8.126 These results indicate the existence of a direct effect of the interlayer distance on the AFM exchange interaction, which is stabilized as the CoO2- 128 J. Wooldridge, D. McK. Paul, G. Balakrishnan and M. R. Lees. Condens. Matter. J. Phys.: Condens. Matter 18, 4731 (2006). Magnetic and transport properties… 81 CoO2 separation is reduced. Therefore, they suggest that not only the CoO2 planes dominate the physical properties of the system at x>0.7, the 3D dimensionality plays an active role that should be considered. We will take this into acount and will be discussed in next chapters. To sumarize, we reported a detailed analysis of the magnetic susceptibility, , and thermoelectric power, S, of metallic NaxCoO2 and Ca3Co4O9, as representative examples of layered cobalt oxides with a triangular Co lattice. We have shown that the magnetic and transport properties are mostly determined by CoO2 planes in the range 0.3<x<0.7. This fact explains the similar phenomenology found in different 2D cobalt oxides based on hexagonal Co arrangments, particulary the puzzling temperature dependent  (T) and large thermoelectric power combined with a metallic resistivity. We have demonstrated that the temperature dependence of the magnetic susceptibility in triangular lattice Co-oxides cannot be justified assuming a spin localized model. We suggest that the origin of the temperature dependence of the magnetization is due to the temperature dependence of the spin fluctuations of itinerant electrons. We have also shown that the unusually large thermopower is related to a band-structure effect understandable within the framework of Boltzmann transport theory, withouth the need to consider an extra spin-entropy contribution. In the high temperature limit the Heikes formula predicts correctly the sign and magnitude of the temperature independent thermopower in these systems, when a correct estimation of the charge carrier density is available. In the special case around x0.5, our data evidence the differentiate nature of the electronic properties. Finally, we have shown that the AFM exchange interaction is strongly influenced by the 3D character of the strucuture for x>0.7, that plays a more than expected active role. 3 3. . Proximity to a quantum phase transition In this chapter we carry out an exhaustive study of the magnetic properties of metallic NaxCoO2, both above and below x=0.5. We will focus on the two representative compounds x≈0.69 and x≈0.36. These experiments provide a good evidence of the proximity of this material to a magnetic phase transition at very low temperature. Our data show that the actual temperature of this transition is well below 1.8 K and probably at zero Kelvin (quantum phase transition, QPT). The possible role of magnetic fluctuations in the superconductivity is discussed to the light of the observed (H, T) scaling of the magnetization. The new electronic phases identified lead us to proposs a new (T, H) phase diagram for these two distinguishable metallic states. Chapter 3 84 It is commonly believed that the microscopic explanation for high temperature superconductivity can be constrained by determining the interplay between band-filling, magnetic interactions and dimensionality. In this sense, the report129 of superconductivity in NaxCoO2•yH2O generated an intense debate about the nature of the pairing interaction in this material, which is becoming a test ground for the theories of superconductivity. Although the layered structure, the mixed valence character, and the proximity of the superconductive compositions to a localized charge-ordered phase130 makes it very tempting to make a straightforward comparison with the cuprates, the metallic precursor of the superconducting phase shows its own peculiarities: an electronically active triangular cobalt lattice is supposed to be responsible for the strong temperature dependence of the metallic susceptibility (so called “Curie-Weiss metal” behaviour at high x)131, the anomalous temperature dependence of the resistivity132, or the surprisingly large thermopower133. Moreover, local density approximation (LDA) calculations134,135 predicted a ferromagnetic (FM) ground state in the metallic precursor, although the material never orders down to the lowest temperature probed. The discrepancy between theory and experiment was tentatively attributed to the proximity to a quantum phase transition (QPT)135, which would imply the existence of strong FM fluctuations in the metal. This opens the possibility of a magnetically mediated superconducting state due to exchange of FM spin fluctuations, like it was proposed for Sr2RuO4 136 and high-pressure UGe2137. Actually, 59Co NMR and 23Na NQR experiments138 129 K. Takada, H. Sakurai, W. T. Muromachi, F. Izumi, R. A. Dilanian and T. Sasaki. Nature 422, 53 (2003). 130 R. E. Schaak, T. Klimczuk, M. L. Foo and R. J. Cava. Nature. 424, 527 (2003) 131 M. L. Foo, Y. Wang, S. Watauchi, H. W. Zandbergen, T. He, R. J. Cava and N. P. Ong. Phys. Rev. Lett. 92, 247001 (2004). 132 F. Rivadulla, J.-S. Zhou and J. B. Goodenough. Phys. Rev. B 68, 75108 (2003). 133 Y. Wang, N. S. Rogado, R. J. Cava and N. P. Ong. Nature 423, 425 (2003) 134 D. J. Singh. Phys. Rev. B 61, 13397 (2000). 135 D. J. Singh. Phys. Rev. B 68, 20503 (2003). 136 I. I. Mazin and D. J. Singh. Phys. Rev. Lett. 79, 733 (1997). 137 S. S. Saxena, P. Agarwal, K. Ahilan, F. M. Grosche, R. K. W. Haselwimmer, M. J. Steiner, E. Pugh, I. R. Walker, S. R. Julian, P. Monthoux, G. G. Lonzarich, A. Huxley, I. Sheikin, D. Braithwaite and J. Flouquet. Nature 406, 587 (2000). 138 K. Ishida, Y. Ihara, Y. Maeno, C. Michioka, M. Kato, K. Yoshimura, K. Takada, T. Sasaki, H. Sakurai and E. Takayama-Muromachi, J. Phys. Soc. Japan 72, 3041 (2003); Y. Ihara, K. Ishida, C. Michioka, M. Kato, K. Yoshimura, H. Sakurai and E. Takayama-Muromachi. J. Phys. Soc. Japan 73, 2963 (2004). Proximity to a QPT 85 revealed an unconventional form of a superconducting spin-triplet phase in NaxCoO2•yH2O, as well as the existence of strong FM spin fluctuations in the metallic counterpart, confirmed by inelastic neutron scattering139,140. However, a solid evidence for any particular pairing state remains lacking in NaxCoO2•yH2O, although most of the proposals found in the literature have been excluded after testing them against the well established properties of the compound.141 Having in mind that understanding superconductivity requires a deep knowledge of the electronic precursor from which it forms, we have performed a detailed magnetic study of the water-free metallic precursors at representative compositions of the NaxCoO2 series. For high Na+ content (x0.69, when superconductivity is never achieved under hydration) we have found that the temperature independent magnetic susceptibility, (T,H), in the Fermi liquid (FL) state is renormalized at low temperature. This behavior is consistent with previous resistivity142 and specific heat143,144 results, which support the existence of a strongly correlated state at high Na+ content, with m* strongly field dependent. On the other hand, at x0.36, near the optimum value for superconductivity, strong magnetic fluctuations introduce a new phase with non-FL behavior and spin-glass relaxation. A detailed scaling analysis of the low temperature (T, H) suggests that these effects are due to the proximity of metallic NaxCoO2 to a magnetic QPT. Samples with compositions NaxCoO2, x0.69 and x0.36 were synthesized as described in Chapter 1. All the results discussed here correspond to single-phase materials, where long-time X-ray scans revealed the complete absence of any secondary phase; we paid special attention to avoid any trace of Co3O4. The peaks are very narrow, which ensures a good crystallinity, and the lattice parameters are in accordance with the literature145. 139 A. T. Boothroyd, R. Coldea, D. A. Tennant, D. Prabhakaran, L. M. Helme and C. D. Frost. Phys. Rev. Lett. 92, 197201 (2004). 140 L. M. Helme, A. T. Boothroyd, R. Coldea, D. Prabhakaran, D. A. Tennant, A. Hiess and J. Kulda. Phys. Rev. Lett. 94, 157206 (2005). 141 I. I. Mazin and M. D. Johannes. Nature Physics 1, 91 (2005). 142 S. Y. Li, L. Taillefer, D. G. Hawthorn, M. A. Tanatar, J. Paglione, M. Sutherland, R. W. Hill, C. H. Wang and X. H. Chen. Phys. Rev. Lett. 93, 56401 (2004). 143 M. Brühwiler, B. Batlogg, S. M. Kazakov and J. Karpinski. Cond-mat/0309311. 144 F. C. Chou, J. H. Cho, P. A. Lee, E. T. Abel, K. Matan and Y. S. Lee. Phys. Rev. Lett. 92, 157004 (2004). 145 C. Fouassier, G. Matejka, J. M. Reau and P. Hagenmuller. J. Solid State Chem. 6, 532 (1973). Chapter 3 86 10 20 30 40 50 60 70 80 0 5000 10000 15000 20000 10 20 30 40 50 60 70 80 15.0 15.5 16.0 16.5 17.0 x=0.69 I (a.u.) 2 x=0.36 I (a.u.) 2º x=0.69 x=0.36 2º Figure 1: X-ray diffraction patterns of two samples with x=0.36 and x=0.69. Main panel: Experimental dots are marked by crosses and the red line is a lebail fitting with the program Rietica, using the space group P63/mmc. In both Na+- compositions, all the peaks belong to this phase. The vertical blue lines mark the positions of the reflections expected on the basis of a P63/mmc space group. The left inset shows the evolution of the (002) reflection after Na+-deintercalation, which indicates the expected increase in the interlayer distance. It is important to remark that the following results presented here for x0.36 correspond to samples that we have verified to become superconductive after water insertion. Superconducting samples were obtained by stirring NaxCoO2, x0.36, in water for two days at room temperature. Only those that showed the non-FL phase at low temperature that will be discussed in the following pages became superconductive after water immersion. Here is an example in Figure 2. Proximity to a QPT 93 The most probable scenario is that the spin polarization achieved with an applied magnetic field attenuates the amplitude of the magnetic fluctuations and restores progressively the normal FL behavior. From the minimum in the derivative of  (T) we can determine the existence of an inflexion point in the susceptibility curve. This would mark the flattening of the curve and hence would point to the recovery of constant FL behaviour. Figure 7 shows the derivative of the temperature-dependent susceptibility below 20 K at different applied magnetic fields. This result is consistent with the observation of an anomalously large AT2 coefficient in the electrical resistivity142 or a sublinear temperature variation of the specific heat143,144, strongly field dependent. Figure 7: Derivative of the  vs. T curves at different applied magnetic fields (H=1, 3 and 5T) in the x=0.69 sample. In Figure 8,  (T) is shown for x=0.36 at two different fields. The behaviour is completely different to the sample with high Na+ content. A clear irreversibility between the zero-field and field cooling (ZFC-FC) magnetization curves shows up below Tirr12 K, which is suppressed at 10 -0.2 -0.1 0.0 Na0.69CoO2 H= 1 T H= 3 T H= 5 T dM/dT Temperature (K) Chapter 3 94 moderately large fields. Figure 9 shows the disappeareance of this irreversibility in the ZFC magnetization curve as H increases from 0.05 T to 0.1 T. The existence of the irreversibility, its field dependence, and the logarithmic variation of the relaxation rate below Tirr (Figure 10) would suggest the emergence of a new phase with spin-glass (SG) like dynamics at low temperatures, and for low values of x. This has been observed in other samples and is representative of compositions around x~0.3-0.4. In the SG phase,  (T) remains strongly temperature-dependent down to the lowest temperature probed (1.8 K), not recovering the constant behavior. The degree of disorder or frustration in the system must be absolutely comparable between samples with different doping levels, so we think that the SG phase at x=0.36 is an effect of the underlying mechanism that introduces strong quasiparticle correlations. One possibility for the breakdown of the FL description in itinerant paramagnets is the proximity to a QPT. In some cases, the proximity to the QPT only renormalizes the scattering rate or the effective mass of the quasiparticles, but the description in terms of a FL model is still applicable, as it happens at x=0.69. Figure 8: ZFC magnetic susceptibility of x=0.36 at two different magnetic fields. The dotted line is the Pauli susceptibility calculated from high temperature M(H) isotherms. Upper inset: Detail of the ZFC-FC irreversibility visible at low fields below  12 K. 0 5 10 15 20 3.0x10-3 6.0x10-3 9.0x10-3 0 100 200 300 0.0 2.0x10-3 4.0x10-3 6.0x10-3 FC ZFC H=0.05 T  (emu.mol-1.Oe-1) Temperature (K) Na0.36CoO2 H=1 T H=0.05 T Pauli  (emu.mol-1.Oe-1) Temperature (K) Proximity to a QPT 95 0 5 10 15 20 1 2 3H =0.1T H =0.05T M (emu.mol-1) Temperature (K) Figure 9: ZFC magnetization curve of x=0.36 at low temperature at two different magnetic fields, H=0.05 and 0.1 T. Figure 10: Relaxation rate of the normalized magnetization for x=0.36. Above Tirr, the relaxation departs from the slow logarithmic behavior observed at low temperatures. 102103104 1 4 K 17 K 13 K M/M(t=0) time (s) Chapter 3 96 The experimental signatures of the proximity to a second-order phase transition are the divergent character of the susceptibility, and over all, its scaling. In Figure 11 we show the divergence of  (T) as T0 K, and the progressive recovery of the constant behavior as H increases. Below 5 K, the low temperature susceptibility shows a power-law temperature dependence of the form    T eq. [1] with  strongly field dependent. The values of  go from ~0.30 at low fields to close to zero at high fields (Figure 12), which indicates the recovery of the FL state at low temperatures, due to the field suppression of spin fluctuations. Figure 11: The divergent character of the low field (T  0) fits to equation [1] below  5 K (marked by the arrow) for x=0.36. At high fields the susceptibility recovers FL behaviour, with a decreasing constant value of (T  0) as H increases. 01234 5 5 1.38 10-3 9.17 10-3 10 2 Temperature (K) 0.01 T H (T) 5 T  (emu.mol-1.Oe-1) Proximity to a QPT 97 012345 0.0 0.1 0.2 0.3  H ( T ) Figure 12: Values of  obtained from fittings of the M(T) curves to equation [1] below ≈5 K at different applied magnetic fields from 0.01 T to 5 T. (Dashed line is a guide to the eye). The value of  goes asimtotically to zero at high field. Another indirect evidence of the proximity of Na0.36CoO2 to a magnetic phase transition comes from the behaviour of the 3; at the vicinity of a phase transition non-linear magnetization becomes relevant and the higher order terms of the magnetization must be retained in the equation of state. In the paramagnetic range M is an odd function of H, so M = 1H + 3 H3 + 5 H5 +… eq. [2] where the third-order susceptibility, 3, is normally quoted as the nonlinear susceptibility. In a mean field approximation we can get some information Chapter 3 98 about the behavior of the linear and cubic terms of the susceptibility when the critical temperature is approached from above153 4 3 1 1 1 1 1                    C C T T T T   eq. [3] Equation [3] gives a positive divergence for 1 and a negative divergence of 3 above the Curie point. A similar treatment gives a positive divergence of 3 as T→TC from below. This provides an accurate method to determine the transition temperature of a ferromagnetic-paramagnetic transition. However, and in spite of the critical behavior of 3 is commonly used to characterize the spin-glass transition154, it has been rarely applied for the characterization of conventional second order FM-PM phase transitions.153 We have fitted the M(H) curves of several compositions of NaxCoO2 in the interval 0.33≤x≤0.69 every degree below 25 K down to 1.8 K to extract  3(T), and the results are plotted in Figure 13 for two representative compositions. There is a clear departure from the high temperature value (3→0) and a negative divergence of 3 below 15 K. The nonlinear susceptibility shows the typical signatures of a system just above the transition temperature from a magnetically ordered state. We should remind here that the possibility of a saturating paramagnetic impurity as the source of the non-linear susceptibility has been discarded before. An important point is whether this magnetic transition occurs at zero kelvin or if it takes place at low but finite temperature. Although our experiments cannot reassure the absence of the transition below 1.8 K, 3 does not show any sign of rounding still at this temperature, which indicates that we are still far from the critical point. 153 S. Nair and A. Banerjee. Phys. Rev. B 68, 94408 (2003). 154 Spin Glasses and Random Fields. Ed. by A. P. Young, World Scientific (1998). Proximity to a QPT 99 Figure 13: Temperature dependence of the nonlinear susceptibility as T→0 K for x  0.69 (open circles) and x  0.36 (solid circles). Similar behaviour was observed in the whole range of x checked (between 0.3 and 0.69). In the conventional theory of metals close to a magnetic QCP, longwavelength fluctuations (q0) of the order parameter (paramagnons) are the relevant low-energy magnetic excitations. For 2D magnetic systems close to a QPT Si et al155 predicted the presence of spatially localized magnetic fluctuations (q) coexisting with the spatially extended ones (q0). In this scenario close to a second order QPT, hyperscaling relationships ensure that the following scaling law must be obeyed by the singular part of the susceptibility, once the reduced temperature has been replaced by T to account for the 0 K transition temperature,156,157 155 Q. Si, S. Rabello, K. Ingersente and J. L. Smith. Nature 413, 804 (2001). 156 N. Goldenfeld in “Lectures on phase transitions and the renormalization group”, Frontiers in Physics Vol 85, Addison-Wesley, NY 1992. 157 G. R. Stewart. Rev. Mod. Phys. 73, 797 (2001). 0 5 10 15 20 25 -4 -3 -2 -1 0 x=0.69 x=0.36 3 (a.u.) Temperature (K) Chapter 3 100          T H fT H M eq. [4] The result of the scaling is shown in Figure 14. The best fittings were obtained with the values  =0.31(1) and  =1.12(3). The value of  is consistent with the fitting of the low-field susceptibility to equation [1], and both  and  are internally consistent (1+  /2=  ) within the error. For a true FL, no such scaling behavior should be observable as its mere presence shows that there is an energy scale other than Fermi energy that dominates its thermodynamic properties. 100 1000 1.8x10-6 3.2x10-6 1.8 K 2.0 K 2.2 K 2.5 K 3.0 K 3.5 K 5.0 K 7.0 K  = 0.31 (1)  = 1.12 (3) (M/H)T- (H/T) Figure 14: Scaling of the divergent low temperature susceptibility for x=0.36. The data departs from the low temperature scaling above  4 K, i.e. as the limit of the divergent behavior in  (T  0) is approached from below (see Fig. 11). The 5 K and 7 K curves are shown as an example of deviation of the scaling at higher temperatures. Proximity to a QPT 101 To discard completely the proximity to a magnetic phase transition at very low temperature but above zero, measurements at the milikelvin range are desirable. As discussed before, Li et al.142 related the anomalously high value of the Kadowaki-Woods ratio in Na0.7CoO2 (and its suppression by a magnetic field)to the proximity to a magnetic QPT. This scenario is now supported by the fitting of the data to equations [1] and [4] shown in Figures 11 and 14. A fundamental issue that has to be explored is the origin of the SG phase and the nature of the magnetic fluctuations at low temperature, as well as its relationship with the appearance of superconductivity. NaxCoO2 is an itinerant paramagnet normally considered as a frustrated antiferromagnet due to the triangular arrangement of the Co atoms in the close-packed CoO2 planes158. However, according to Goodenough,159 a simple extension of the cation-cation superexchange spin correlations for localized electrons to the low-spin octahedral-site Co-t2g itinerant electrons would predict the existence of an itinerant FM ground state for this material. Even partial splitting of the threefold-degenerate t2g orbitals into an a1T and twofold-degenerate eT orbitals by the trigonal field, will keep the same prediction. The O:2p-Co:eg rehybridization process proposed by Marianetti et al,160 would introduce the possibility of a Zener-like double exchange mechanism, also resulting in a ferromagnetic, metallic ground state like in SrCoO3 or Sr2CoO4.161,162 The contraction of the a-axis on Na+ removal, as well as the almost constant cobalt valence,163 ensures that rehybridization is indeed playing a role in the material. These arguments are in clear agreement with NMR138 and neutron scattering140 experiments which demonstrate the existence of strong FM fluctuations. Fluctuations can be the source of a short-range partial ordering of the conduction electrons, as it was observed in the high-pressure non-FL phase of MnSi.164 The coexistence of partially ordered regions (super-spins), was proposed to be responsible of the non-FL and SG characteristics of 158 N. P. Ong and R. J. Cava. Science 305, 52, (2004). 159 J. B. Goodenough, in Magnetism and the Chemical Bond, John Willey & Sons, New York (1963). 160 C. A. Marianetti, G. Kotliar and G. Ceder. Phys. Rev. Lett. 92, 196405 (2004). 161 R. H. Potze, G. A. Sawatzky and M. Abbate. Phys. Rev. B 51, 11501 (1995). 162 J. Matsuno, Y. Okimoto, Z. Fang, X. Z. Yu, Y. Matsui, N. Nagaosa, M. Kawasaki and Y. Tokura. Phys. Rev. Lett. 93, 167202 (2004). 163 M. Bañobre-López, F. Rivadulla, R. Caudillo, M. A. López-Quintela, J. Rivas and J. B. Goodenough. Chem. Mater, 17, 1965 (2005). 164 C. Pfleiderer, D. Reznik, L. Pintschovius, H. v. Löhneysen, M. Garst and A. Rosch. Nature 427, 227 (2004). Chapter 3 102 many heavy-fermions,147 in which a divergence of the type  (T)  C(T)/T  T-1+  was predicted.165 This electronically inhomogeneous state is characterized by an exponent <1, and is equivalent to the Griffiths phase of dilute magnetic systems.166 Reanalysis of our data following this argument leads to 0.7 from the fitting of the divergent low-temperature susceptibility at low applied magnetic fields (Figure 15). 012345 0.6 0.7 0.8 0.9 1.0  H ( T ) Figure 15: Values of  obtained from fittings of the  (T)curves to the relation  (T)  C(T)/T  T-1+  below ≈5 K at different applied magnetic fields from 0.01 T to 5 T. (Dashed line is a guide to the eye). The results for the electronic heat capacity,  C(T)/T, are shown in Figure 16. To obtain the electronic part, a lattice contribution was fitted to  3T3+  5T5, and subtracted from the total specific heat. From our specific heat measurements, 0.4(2). This value is very much influenced by the temperature range taken to fit the lattice contribution (  3 and  5 change considerably with the range fitted, between 0.15-0.30 mJ.mol-1.K-4 and 210-3-710-4 mJ.mol-1.K-6, respectively). Very important is that the electronic component is suppressed by a magnetic field below ~5 K, which is approximately the same temperature below which the low field  (T) diverges 165 A. H. Castro Neto, G. Castilla and B. A. Jones. Phys. Rev. Lett. 81, 3531 (1998). 166 R. B. Griffiths. Phys. Rev. Lett. 23, 17 (1969). Role of water in SC the configuration of the electronic properties of this system170. Also, it is not clear whether H2O, H3O+ or both are playing the decissive role for the appearance of superconductivity in hydrated NaxCoO2. On other hand, strong magnetic fluctuations could be important in such geometry and play a role in the occurrence of superconductivity171,172 Investigations to clarify if the superconducting state of Na+ is conventional (BCS) or not, have been carried out from both theoretical and experimental sides. Although a definitive conclusion has not been reached yet, most authors opted for an unconventional mechanism of superconductivity, in which the magnetic fluctuations originated in the adjacent magnetic ordered phase (x~0.5) would be intense enough to drive the system SC. However, from our point of view, other basic points have not been still elucidated, and could play a role in the ocurrence of superconductivity in NaxCoO2. Mainly, we can list the following open questions: 1. What is the role of intercalated water in the achievement of superconductivity in this system? 2. It is really important the charge ordered phase at x=0.5, very close in composition to the superconducting host? 3. Can NaxCoO2 still be considered as a 2D system after water intercalation? Does it behave like a 2D system from the electronic point of view? Obviously, intercalated water into the galleries between CoO6 sheets leads to a substantial increase of the interlayer distance, increasing the 2D character of the system (at least structurally), which is believed to play an important role in inducting superconductivity. The superconductive hydrated phase corresponds to that one with an amount of water of y=1.3 molecules per unit formula H2O molecules coordinate to the Na+ ions and form two water layers in the gallery sandwiching the Na+ plane, transforming the parent oxide into a bilayer-hydrate (BLH). On the other hand, the most common partially hydrated phases contain around y=0.6 water molecules 170 M. Roger, D. J. P. Morris, D. A. Tennant, M. J. Gutmann, J. P. Goff, J.-U. Hoffmann, R. Feyerherm, E. Dudzik, D. Prabhakaran, A. T. Boothroyd, N. Shannon, B. Lake and P. P. Deen. Nature 445, 631 (2007). 171 N. D. Mathur, F. M. Grosche, S. R. Julian, I. R. Walker, D. M. Freye, R. K. W. Haselwimmer and G. G. Lonzarich. Nature 394, 39 (1998). 172 P. Monthoux, D. Pines and G. G. Lonzarich. Nature 450, 1177 (2007). Chapter 4 110 per unit formula, in which H2O molecules occupy positions in the same layer of Na+ ions, forming a monolayer-hydrate (MLH)173. H2O Na -H2O N Na/H2O +H2O BLH-NaxCoO2 MLH-NaxCoO2 Figure 4.2: Structural drawings of (left) BLH-NaxCoO2 and (right) MLH- NaxCoO2. (From Ref. 6). Also other partially hydrated and no superconductive phases with smaller water content, such as y=0.3 and y=0.1, have been reported174,175,176,177. Although direct water content is very difficult to be measured, it is translated in different interlayer distances178,179,180,181. It 173 K. Takada, H. Sakurai, E. Takayama-Muromachi, F. Izumi, R. A. Dilanian and T. Sasaki. J.Solid State Chem. 177, 372 (2004). 174 D. P. Chen, H. C. Chen, A. Maljuk, A. Kulakov, H. Zhang, P. Lemmens and C. T. Lin. Phys. Rev. B 70, 024506 (2004). 175 M. L. Foo, R. E. Schaak, V. L. Miller, T. Klimczuk, N. S. Rogado, Y. Wang, G. C. Lau,C. Craley, H. W. Zandbergen, N. P. Org and R. J. Cava. Solid State Commun. 127, 33 (2003). 176 J. Cmaidalka, A. Baikalov, Y. Y. Xue, R. L. Meng and C. W. Chu. Physica C 403, 125 (2004). 177 C. T. Lin, D. P. Chen, P. Lemmens, X. N. Zhang, A. Maljuk and P. X. Zhang. Journal of Crystal Growth 275, 606 (2005). 178 K. Takada, H. Sakurai, E. Takayama-Muromachi, F. Izumi, R. A. Dilanian, and T. Sasaki, Phys. C 14, 412 (2004). Role of water in SC suggests that the separation between CoO2 layers appears to be critical in obtaining superconductivity, since it is only achieved for a hydrated phase with c~19.8 Å, while intermediate hydrated phases with c~12 Å and anhydrous phases with even smaller CoO2-CoO2 interlayer spacing are not superconducting173,175. The importance of a reduced interlayer coupling for stabilizing the superconducting ground state in this compound is evidenced by the hydrostatic pressure dependence of Tc, where a suppression of the superconducting state takes place at high pressure as a consequence of a significant reduction of the caxis182 (Figure 4.3). In fact, synchrotron measurements with pressure in Na~0.8CoO2 evidenced that the compressibility in the c-direction is much higher than in the a-direction (see Chapter 2). Figure 4.3: Superconducting transition temperature (Tc) dependence of the applied hydrostatic pressure (p). Tc was estimated from the onset of the diamagnetic signal. Fill square represents the recovery of the initial superconducting properties as highest pressure is released. (From Ref. 15). 179 K. Ishida, Y. Ihara, H. Takeya, C. Michioca, K. Yoshimura, K. Takada, T. Sasaki, H. Sakurai and E. Takayama-Muromachi. Phys. C 460-462, 192 (2007). 180 H. Sakurai, K. Takada, F. Izumi, R. A. Dilanian, T. Sasaki and E. Takayama-Muromachi. Phys. C 412-414, 182 (2004). 181 C. J. Milne, D. N. Argyriou, A. Chemseddine, N. Aliouane, J. Veira, S. Landsgesell and D. Alber. Phys. Rev. Lett. 93, 247007 (2004). 182 B. Lorenz, J. Cmaidalka, R. L. Meng and C. W. Chu. Phys. Rev. B 68, 132504 (2003). Chapter 4 112 Although the interlayer distance increases as sodium content decreases and still more after water intercalation, does it behave like a 2D system also from an electronic point of view? Electrical resistance measurements in single crystals from Wang et al183 show a dimensional crossover from 2D to 3D with decreasing concentration of Na+, opposite to what we expected for an increase of the interlayer distance between the CoO6 sheets because of a lower sodium content. In this sense, the behaviour is very similar to what happens in intercalated graphite184, in which 2D to 3D transition has been obtained after intercalation. Recovery of the 2D character takes place as water is intercalated into the structrue after hydration process. So, the fact that the carrier density in the CoO6 is kept unchanged in both BLH and MLH phases strongly suggests that only an optimum level of carrier doping into the CoO6 layers is not enough for inducing the superconductivity, and also that an optimum interlayer separation between the CoO6 layers is indispensable for the superconductivity. But the most important and maybe the most controversial question is the dependence of Tc with Na+ doping. It is well know the existence of a certain range of Na+ composition where the superconductivity occurs in this material (0.3x0.45), but the dependence of Tc as a function of Na+ doping inside this interval remains still unclear. The first superconducting phase diagram for the hydrated superconductor Na0.3CoO2•1.3H2O has been proposed by Schaak et al185 (Figure 4.4). 183 C. H. Wang, X. H. Chen, J. L. Luo, G. T. Liu, X. X. Lu, H. T. Zhang, G. Y. Wang, X. G. Luo and N. L. Wang. Phys. Rev. B 71, 224515 (2005). 184 T. E. Weller, M. Ellerby, S. S. Saxena, R. P. Smith and N. T. Skipper. Nature Physics 1, 39 (2005). 185 R. E. Schaak, T. Klimczuk, M. L. Foo and R. J. Cava. Nature 424, 527 (2003). Role of water in SC Figure 4.4: Superconducting phase diagram for NaxCoO2•1.3H2O. Main panel: Tc as a function of x as determined from the AC susceptibility measurements. (From Ref. 18). These experimental results show a strong correlation between Tc and the Na+ content of the samples. Bulk superconductivity with Tc>2 K has been reported to exist over a very narrow range of Na+ compositions, approximately 1/4x1/3, where it is established an optimal chemical doping level for superconductivity with Tc≈4.5 K around x=0.3. And Tc decreases for both underdoped and overdoped materials. This “dome-like” dependence of superconducting transition temperature with doping shows the same trend as in cuprate superconductors. For this reason, it has been thought that the origin of SC in this material could have some points in common with the superconductivity in cuprates. To explain this dependence Baskaran et al186 presented a theory based on the idea that this compound would give different ordered phases at the Na+ compositions of x=1/4 and x=1/3 respectively. They argued that charge ordering at these doping levels in the CoO2 layers would be a competitor to superconductivity leading to a strong decrease in Tc. Therefore, the highest Tc would be achieved between these specific compositions. However, experimental results from Chen et al174 disagree with the superconducting “dome” of Tc(x) by Shaak et al185: 186 G. Baskaran. Phys. Rev. Lett. 91, 097003 (2003). Chapter 4 114 1. No variation in Tc as a function of sodium content in the range 0.22<x<0.47 is found (Figure 4.5). Out of this doping level interval no superconducting transition has been detected. 2. The superconducting phase approaches to the phase line where the non-hydrated Na0.5CoO2 shows a metal-insulator transition187. We will see from our results in the next chapter that this fact could be more important than previously thought. Figure 4.5: Superconducting transition temperature, Tc, as a function of sodium doping, x, in NaxCoO2•1.3 H2O. The dashed line is a guide to the eye. The dashed bar marks the metal-insulator transition observed in non-hydrated Na0.5CoO2. (From Ref. 20) Also Milne et al181 have found that Tc does not change significantly with x over the region 0.28<x<0.37. In the superconducting phase diagram determined from their measurements, Figure 4.6 (a), Tc differs from 4.3 K to 4.8 K in that Na+ composition range, which is very close to the optimum value reported by Shaak et al for this material185. All papers that have appeared after the report of Schaak et al185 on physical properties and theoretical calculations have been based on the Co oxidation state of ca. 3.7+, which is deduced directly from the Na+ content 187 Q. Huang, M. L. Foo, J. W. Lynn, H. W. Zandbergen, G Lawes, YayuWang, B. H. Toby, A. P. Ramirez, N. P. Ong and R J Cava. J. Phys.: Condens. Matter 16, 5803 (2004). Role of water in SC (x~0.3). But, as we have already shown in Chapter 1 and also from other works, the Co valence state does not vary notably in the sodium composition range where SC is obtained, the electronic band filling is the result of a complex Co(t2g):O(2p) hibridization plus the t2g splitting. That makes that representation of Tc as a function of the sodium content not totally correct, since the oxidation state of Co is lower that the expected only from Na+ content174,181,188,189 (see Figure 1.9 in Chapter 1). On the other hand, Milne et al181 reported a significant discrepancy between the expected valence of Co based on Na+ content and the values obtained from redox titration, drawing a more correct representation where Tc is plotted against Co formal valence and not as a function of Na+ content. Figure 4.6 (b) shows this representation in comparison with that one obtained from the data of Schaak et al185. Figure 4.6: (a) Tc as a function of Na+ content, x, in NaxCoO2•1.3 H2O. (b) Tc as a function of the Co valence state (right) obtained from redox titration in comparison with (left) plot derived from Shaak’s data185. (From Ref. 14). In this superconducting phase diagram they find that optimal Tc is reached over the region of cobalt valence 3.24-3.35 (that will correspond to an x~0.6), while Tc decreases to values of <3 K for Co valence states >3.35+. They also demonstrated that the occurrence of superconductivity is strongly linked to the dimensionality of the structure. They observed that the c/a ratio increases as Co oxidation state is tuned into the optimal Tc region. 188 M. Karppinen, I. Asako, T. Motohashi and I. Yamauchi. Phys. Rev. B 71, 092105 (2005). 189 H. Sakurai, S. Takenouchi, N. Tsujii and E. Takayama-Muromachi. J. Phys. Soc. Jpn. 73, 2081 (2004). Chapter 4 116 Structural characterization of the hydrated superconducting cobalt oxide phase has been carried out by several groups169,190,191,192. But most of them considered just the Na+ ions and H2O molecules as the guest species. That means that the formation process of the superconducting phase was though to involve just the oxidative extraction of Na+ ions and the topotactic insertion of H2O molecules. However, the actual achivement of superconductivity in this system is more complicated and other chemical species and more complex reactions take place. In fact, the stochiometry of this superconductor has been again revised by Takada et al190 and more recently Sakurai et al193. They concluded that H3O+ ions are necessarily inserted substituting partially the Na+ ions between two CoO2 layers to compensate the charge, in addition to water molecules. This topotactic ionexchange of Na+ ions by H3O+ mechanism maintains a constant Co valence and is strongly supported by their structural studies based on Raman spectroscopy and X-ray powder diffraction, which also suggested that the oxonium ions occupy the same crystallographic sites as Na+ ions. That means that guest species in the new structure model are not only Na+ ions and H2O molecules but also H3O+ ions, giving a composition of the superconducting phase of Na0.337(H3O)0.234CoO2•yH2O instead of the previous Na0.3CoO2•yH2O. Afterwards, that was also confirmed by Milne et al181, indicating that Na+ substoichiometry alone does not control the electronic doping of these materials, H3O+ playing an important role also. However, none of these recent works considered the possibility of a presence of oxygen vacancies in the chemical composition of the superconducting phase (already propposed by Molenda et al 194 in 1989). Previously, Rivadulla et al195 discussed that possibility in the superconducting hydrated phase and they propossed a model where, if existing, they would be refilled by the O2- heads of the intercalated water molecules, leading to a creation of H+ protons into the structure. Later, our results and those ones from other authors196,197,198 confirmed the presence of 190 K. Takada, K. Fukuda, M. Osada, I. Nakai, F. Izumi, R. A. Dilanian, K. Kato, M. Takata, H. Sakurai, E. Takayama-Muromachi and T. Sasaki. J. Mater. Chem. 14, 1448 (2004). 191 J. W. Lynn, Q. Huang, C. M. Brown, V. L. Miller, M. L. Foo, R. E. Schaak, C. Y. Jones, E. A. Mackey and R. J. Cava. Phys. Rev. B 68, 214516 (2003). 192 J. D. Jorgensen, M. Avdeev, D. G. Hinks, J. C. Burley and S. Short. Phys. Rev. B 68, 214517 (2003). 193 H. Sakurai, M. Osada and E. Takayama-Muromachi. Chem. Mater. 19, 6073 (2007). 194 J. Molenda, C. Delmas, P. Dordor and A. Stoklosa. Solid State Ionics 12, 473 (1989). 195 F. Rivadulla, J.-S. Zhou and J. B. Goodenough. Phys. Rev. B 68, 75108 (2003). 196 M. Karppinen, I. Asako, T. Motohashi and H. Yamauchi. Chem. Mater. 16, 1693 (2004). 197 Morita et al. J. Solid State Chem. 177, 3150 (2004). Role of water in SC oxygen vacancies in the system below x<0.7, which increase as Na+ content decreases. But, even though a lower than expected Co valence state was also found by other authors in both non-superconducting and superconducting phases, in the case of the superconducting phase they could not distinguish which effect took place to raise the charge balance: if oxygen vacancies or formation of extra H3O+. Figure 4.7 shows the X-ray diffraction patterns for the unhydrated Na+ deintercalated precursor and the superconducting phase after hydration. Both of them were single phase without the presence of any impurity. However, the pattern corresponding to the hydrated sample shows a complex mixture constituted by both unhydrated and hydrated phases with different amounts of H2O per formule unit, as reported by other authors174. This fact leads to an overlapping of the reflexions from different phases and made difficult their indexing. For this reason the refinment of the structure could not be carried out in the hydrated and superconductive phase. On the other hand, it can be observed, looking at the reflexion indexed as (002), that the CoO2 interlayer distance increases as water is introduced into the structure. 20 40 60 80 100 Intensity ( a. u. ) 2 Figure 4.7: X-ray diffraction patterns for (red) Na0.36CoO2 and (green) Na0.36CoO2•yH2O. 198 F. C. Chou, E. T. Abel, J. H. Cho and Y. S. Lee. J. Phys. Chem. Solids 66, 155 (2005). Chapter 4 118 The determination of the actual content of water of different hydrated samples by a direct method is highly inaccurate. Thermogravimetric analysis of superconducting phases can be found in the literature.175,177 However, the continuous and fast decrease of the mass in the whole temperature range makes difficult a certain determination of the water content for each stable hydrated phase. Therefore, it is important to take into account that the stochiometry of the water content of the fully and partially hydrated phases appearing in the literature could be affected by similar inaccuracies. Figure 4.8 shows the ZFC-FC of the sample before hydration. Once the sample has been hydrated by stirring in destilled water for two days, a diamagnetic response, characteristic of the superconducting state, shows up at T<4 K. 0 50 100 150 1.0x10-3 2.0x10-3 3.0x10-3 4.0x10-3 5.0x10-3 Na0.36CoO2  (emu.mol-1.Oe-1) Temperature (K) Figure 4.8:  (T) curves for Na0.36CoO2 in ZFC-FC conditions at a magnetic applied field of H=100 Oe. Figure 4.9 shows the superconducting behaviour of Na0.36CoO2•1.3H2O at different magnetic applied fields. It is important to remark that the magnetic transition at T~30 K in the ZFC curve of the nonhydrated sample dissapears completely once the sample became superconductive. That reinforces our theory about its intrinsic magnetic character, not due to impurities. 125 5 5. . The especial case of half doping: Na0.5CoO2 After our systematic exploration of the magnetic and thermoelectric properties of NaxCoO2, we considered interesting to focus on the half-doped sample (x=0.5) because of its particular/original physical properties, i.e. it is the only member of the series at x0.7that shows some kind of magnetic ordering, it undergoes a metal-to-semiconductor transition associated to a CO transition and it displays a crossover to a negative Seebeck coeficient with temperature. Therefore, after a brief introduction about this specific phase, we will show a more detailed study about the characteristic physical properties of the Na0.5CoO2 phase and the decisive role that we think this phase plays in the appearance of superconductivity in NaxCoO2•yH2O. Chapter 5 126 The superconducting phase in hydrated NaxCoO2 is considered to condense from a Fermi liquid (FL) with AFM correlations at low values of x, typically around x0.35202. At high doping, x0.7, the coupling of itinerant carriers to localized S=1/2 spins is normally considered as the origin of the non-FL behaviour, establishing a candidate quantum spin-liquid state at low temperature203. These two thermodynamically distinguishable metals are separated at zero Kelvin by an AFM charge ordered state at half doping, x=0.5204. The origin of this state is not absolutely clarified, although it has been tentatively related to the influence of an ordered pattern of Na+ ions between the CoO2 layers, which disturbs the potential over the Co3+/4+ sheets and forces the system to a certain type of charge ordering205,206,207. Several superestructures have been observed experimentally from electron diffraction studies in a wide composition range205 and it was suggested that the low temperature CO is a spin density wave (SDW) state driven by a nesting of the Fermi surface characteristic of the ordered Na+ pattern at x=0.5 208,209. In an alternative possibility, the SDW could result from the strong nesting tendencies of a hexagonal Fermi surface in which six small hole pockets derived from the eg’ bands are symmetrically placed around the  point210. Polycrystalline γ-Na0.7CoO2 was obtained by conventional solid state reaction with a final firing at 900 ºC as described previously in Chapter 1. The XRD pattern shows a single phase consistent with a hexagonal unit cell, 202 G. Lang, J. Bofroff, H. Alloul, G. Collin and N. Blanchard. Phys. Rev. B 78, 155116 (2008). 203 L. Balicas, Y. J. Jo, G. J. Shu, F. C. Chou and P. A. Lee. Phys. Rev. Lett. 100, 126405 (2008). 204 M. L. Foo, Y. Wang, S. Watauchi, H. W. Zandbergen, T. He, R. J. Cava and N. P. Ong. Phys. Rev. Lett. 92, 247001 (2004). 205 H. W. Zandbergen, M. Foo, Q. Xu, V. Kumar, and R. J. Cava. Phys. Rev. B 70, 024101 (2004). 206 D. N. Argyriou, O. Prokhnenko, K. Kiefer and C. J. Milne. Phys. Rev. B 76, 134506 (2007). 207 T. P. Choy, D. Galanakis and P. Phillips. Phys. Rev. B 75, 073103 (2007). 208 J. Bobroff, G. Lang, H. Alloul, N. Blanchard and G. Collin. Phys. Rev. Lett. 96, 107201 (2006). 209 N. L. Wang, Dong Wu, G. Li, X. H. Chen, C. H. Wang and X. G. Luo Phys. Rev. Lett. 93, 147403 (2004). 210 M. D. Johannes, I. I. Mazin, D. J. Singh and D. A. Papaconstantopoulos. Phys. Rev. Lett. 93, 097005 (2004). Half doped: Na0.5CoO2 127 space group P63/mmc, and lattice parameters a=2.8328(1) Å and c=10.8511(6) Å. To obtain Na0.5CoO2, Na+ was removed with Br2/acetonitrile The Na/Co ratio was confirmed by ICP-OES to be 0.51(1). Reflexions from Co3O4 or other minority phases are completely absent (see Figure 5.1). 10 20 30 40 50 60 Intensity (a.u.) Na0.51CoO2 Na0.70CoO2 2 Figure 5.1: X-ray diffraction pattern of NaxCoO2 (x=0.70 and x=0.51). The vertical blue lines show the expected reflections for the space group P63/mmc. The Na/Co ratio was measured by ICP-OES. Figure 5.2 shows the temperature dependence of the absolute electrical resistance and the ZFC-FC magnetization curves in Na0.51CoO2. The results are similar to those reported by Shu et al211 for electrochemically deintercalated crystals. We want to emphasize that we have not performed any additional annealing to the samples after Na+ extraction and before the transport/magnetic experiments. This was done so in order to prevent any possible rearrangement of Na+, oxygen loss, etc. after the synthesis, and to 211 G. J. Shu, A. Prodi, S. Y. Chu, Y. S. Lee, H. S. Sheu and F. C. Chou. Phys. Rev. B 76, 184115 (2007). Chapter 5 128 make the results as much comparable to the process followed in single crystals as we can. Then, only the relative changes in the resistance should be considered and not its absolute value. Figure 5.2: ZFC-FC magnetization curves at H=100 Oe, and electric resistance of Na0.51CoO2. The arrows indicate the direction followed during the measurement. We have found an increase in the resistance reminiscent of a CO effect below 45 K, similar to the reported in single crystals204, although it is very modest compared with that in single crystals. This effect is related to the formation of a SDW212 and hence does not result in such an effective localization as it does the CO state in manganites or nickelates for example213, in which the step in resistance involves several orders of magnitude. 212 J. Bobroff, G. Lang, H. Alloul, N. Blanchard and G. Collin. Phys. Rev. Lett. 96, 107201 (2006). 213 “Colossal Magnetoresistance, Charge Ordering and Related Properties of Manganese Oxides”, C. N. R. Rao, B. Raveau, Eds. World Scientific, Singapore (1998). 0 20406080100 0.0 1.0x10-3 2.0x10-3 3.0x10-3 4.0x10-3 5.0x10-3 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 R (  ) M (emu.g-1) Temperature ( K ) Half doped: Na0.5CoO2 129 On the other hand, intrinsic transport properties can be proved through the Seebeck coefficient, a magnitude that is not sensitive to intergrain scattering as now current flows through the sample. Figure 5.3 shows the temperature dependence of the thermopower for two representative Na+ compositions. As it was discussed in the previous chapter, S(T) shows a crossover towards negative values in the x=0.5 phase which is absent at larger and lower concentrations of Na+. This is consistent with a local change in the curvature of the N(εF) close to x=0.5, due to a partial gaping of the density of states, that develops gradually as temperature is reduced (not like a conventional phase transition). Scheme 5.1: Representation of the density of states proposed for Na0.5CoO2. The sign of S depends on the position of the Fermi level (dot lines) at a specific temperature, which develops as indicated with temperature (arrow). Recent 23Na NMR results found a crossover at T*200 K that changes the nature of the spin correlation in x=0.5 from AFM at low temperatures to FM at high temperatures202. On the other hand, evidences for a pseudogap at low doping were obtained from photoemission S<0 S=0 S>0  N(  ) T Chapter 5 130 spectroscopy214. All these results are consistent with a partial gaping of the Fermi surface by a SDW instability occurring below ~200 K, where we have observed the change of sign of S(T) in x0.5. 0 100 200 300 400 500 -20 0 20 40 60 80 NaxCoO2 x=0.51 x=0.7 S (V.K-1) Temperature (K) Figure 5.3: Temperature dependence of the Seebeck coefficient at different x. At x  0.5 thermopower goes negative below T  200 K. The increase in the electronic resistance is accompanied by a magnetic transition, indicating a partial spin polarization. Two additional magnetic transitions are observed at 18 K and 86 K (the latter not visible on the scale of Figure 5.2 but in Figure 5.4), consistent with previous reports, which reported up to three magnetic transitions for the half-doped phase at ~20 K, ~50 K and ~90 K215,216,217. The magnetic transition at ~90 K has been associated to a long range AFM ordering.202 The small temperature 214 T. Shimojima, T. Yokoya, T. Kiss, A. Chainani, S. Shin, T. Togashi, S. Watanabe, C. Zhang, C. T. Chen, K. Takada, T. Sasaki, H. Sakurai and E. Takayama-Muromachi. Phys. Rev. B 71, 020505(R) (2005). 215 Q. Huang, M. L. Foo, J. W. Lynn, H. W. Zandbergen, G. Lawes, Y. Wang, B. H. Toby, A. P. R. N. P. Ong, and R. J. Cava. J. Phys.: Condens. Matter 16, 5803 (2004). 216 G. Gasparovic, R. A. Ott, J.-H. Cho, F. C. Chou, Y. Chu, J. W. Lynn and Y. S. Lee. Phys. Rev. Lett. 96, 046403 (2006). 217 C. H. Wang, X. H. Chen T. Wu, X. G. Luo, G. Y. Wang and J. L. Luo. Phys. Rev. Lett. 96, 216401 (2006). Half doped: Na0.5CoO2 131 differences with respect to our data could be due to small differences in the composition of Na+ between the samples. Also, as mentioned in Chapter 2, we have observed (as many authors reported before)202,204 the existence of a thermally activated term in (T) for x≤0.5, indicative of some kind of spin gap. Figure 5.4 shows a more detailed scale for the magnetization data of several representative Na+ compositions, where a decrease of the magnetic susceptibility with temperature in the range above the magnetic phase transition and up to room temperature is observed. In fact, the slope of the curves changes from negative to positive at around x=0.5 (see Figure 5.5), further supporting the singular nature of this point. 100 150 200 250 300 4.0x10-4 5.0x10-4 6.0x10-4 x=0.40 x=0.51 x=0.7 M (emu.g-1) Temperature (K) Figure 5.4: Temperature dependence of the magnetization for different x. Chapter 5 132 0.40.50.60.7 -8 -4 0 4 dM/dT (10-7.emu.g-1.K-1) x in NaxCoO2 Figure 5.5: Change of slope from positive (x≤0.5) to negative (x>0.5). The values are calculated from the fitting of the high temperature data to a straight line, and hence are only indicative of the general behavior. For a more detailed characterization of the magnetic properties of the half doped phase, the stability of the magnetic phases with the applied magnetic field was also studied. Figure 5.6 shows the magnetic curves at different applied magnetic fields between 2.510-3 T and 1 T. Their position at 17 K and 40 K remains unchanged until H=0.1 T, but they are slightly shifted at H=1 T. However, the irreversivility between the ZFC-FC curves is reduced as the applied magnetic field increases above 10-2 T. In order to carry out a complete magnetic characterization and determine which is the magnetic nature of the magnetic phases emerging at x=0.50, the hysterisis magnetic loops were performed at different representative temperatures below and above the magnetic transitions in ZFC conditions. Figure 5.7 shows the hysterisis cycles at T=5 K, 28 K and 80 K. Half doped: Na0.5CoO2 133 10 100 1E-4 1E-3 0.01 0.1 1 T 0.1 T 10-2 T 2.5.10-3 T M (emu.g-1) Temperature ( K ) Figure 5.6: Magnetization curves as a function of the applied magnetic field (H=2.5  10-3, 10-2, 0.1, 1 T) in a log-log scale. -1.0 -0.5 0.0 0.5 1.0 -0.10 -0.05 0.00 0.05 0.10 5K 28K 80K M (emu.g-1) H ( T ) Figure 5.7: ZFC magnetization loops at several temperatures (T=5 K, 28 K and 80 K) for the x=0.50 phase, up to an applied magnetic field of 1 T. Chapter 5 134 At T=80 K the magnetization is in the almost temperature independent regime (Pauli PM-like), what is also evidenced by the linear contribution of the magnetization with the applied magnetic field and the no presence of cohercitive field (Hc). As the temperature decreases, T=28 K, an important FM contribution with Hc4.210-2 T and higher absolut values of the magnetization are observed, although it is not saturated at the maximum applied magnetic field (H=1 T). The same effect is even more pronunced at T=5 K, where the Hc from the FM contribution is of ~0.052 T. So, from these results we think that an inhomogeneous AFM state (with a resulting net FM moment) develops at low temperature from a PM state at high temperature. So, in order to confirm the stability of the magnetic phases and its relationship with a particular Na+ arrangement, we have studied their evolution with time, doping, fast quenching to low temperatures, hydration and topotactic exchange with divalent-cations. First of all we have observed that all the magnetic and electronic transitions discussed in this paper are robust against both relatively long time aging (Figure 5.8) and fast quenching of the sample from room temperature to liquid He. The cooling rate does not affect to their appeareance, and hence it seems to be of electronic instead of ionic ordering origin. This most probably discards any link between them and a particular Na+ arrangement, as it was discussed for other magnetic transitions at high doping218. However, it also true that if any Na+ arrangement is particularly stable at x=0.5 already at room temperature, fast quenching is not expected to have any influence on it. 218 T. F. Schulze, P. S. Häfliger, Ch. Niedermayer, K. Mattenberger, S. Bubenhofer and B. Batlogg. Phys. Rev. Lett. 100, 026407 (2008).