Effect of mixing the low-valence transition metal atoms Y = Co, Fe, Mn, Cr, V, Ti, or Sc on the properties of quaternary Heusler compounds Co2-xYx FeSi (0≤x≤1)

PHYSICAL REVIEW MATERIALS 6, 064413 (2022) Effect of mixing the low-valence transition metal atoms Y=Co, Fe, Mn, Cr, V, Ti, or Sc on the properties of quaternary Heusler compounds Co2−xYxFeSi (0 ⩽x⩽1) R. Mahat ,1,*U. Karki,1Shambhu KC,1J. Y. Law,2V. Franco,2I. Galanakis ,3,†A. Gupta ,4and P. LeClair 1,‡ 1Department of Physics and Astronomy, The University of Alabama, Tuscaloosa, Alabama 35487, USA 2Departamento de Física de la Materia Condensada ICMSE-CSIC, Universidad de Sevilla, Sevilla 41080, Spain 3Department of Materials Science, School of Natural Sciences, University of Patras, GR-26504 Patras, Greece 4Department of Chemistry and Biochemistry, The University of Alabama, Tuscaloosa, Alabama 35487, USA (Received 4 April 2022; accepted 9 June 2022; published 29 June 2022) In this paper we report an experimental study of structural, magnetic, and mechanical properties of quaternary Heusler alloys Co2−xYxFeSi (Y=Co,Fe,Mn,Cr,V,Ti,orSc,0⩽x⩽1) and the experimental findings are supported by ab initio electronic structure calculations. The alloys were synthesized using an arc-melting technique. Single phase microstructures are observed for all alloys substituted with low-valence transition metals Yexcept Sc. X-ray powder diffraction patterns at room temperature show the presence of Heusler-like face-centered cubic crystal structure in all single phase specimens. The low-temperature saturation magnetic moments, as determined from magnetization measurements, agree fairly well with our theoretical results and also follow the Slater-Pauling rule of thumb for half-metals, a prerequisite for half-metallicity. The alloys are predicted to exhibit half-metallic ferromagnetism by ab initio electronic structure calculations using the GGA+U approach. All stable compounds are observed to have high Curie temperatures with linear dependence with the valence electrons concentration in the alloys. Relatively high hardness values are also measured, approaching 15.7 GPa for Ti-substituted material, highest among the values reported for Heuslers so far. All these properties strongly suggest the alloys are promising for the spintronic applications at room temperature and above. DOI: 10.1103/PhysRevMaterials.6.064413 I. INTRODUCTION Co2-based full Heusler compounds belong to a promising class of materials for magnetoelectronics applications because of their potential for half-metallic ferromagnetism (and resulting 100% spin polarization), high Curie temperatures, lattice matching with conventional semiconductors, and properties easily tuned through substitution. With stoichiometric composition Co2YZ,Yis usually another transition metal and Zis a main group element, and compounds typically crystallize in the cubic L21structure (space group Fm¯ 3m[1,2]). The main features of interest here—the potential for half-metallicity—is an exceptional electronic structure, one with an energy band gap at the Fermi level (EF) only for minority spin electrons [3–7], which would yield 100% spin polarization at the Fermi level. However, the experimentally observed spin polarization is always much smaller than 100%. The discrepancy between theory and experiment is expected to be due to structural and chemical disorder [8,9]. Improvements in various properties such as structure, magnetization, transport, critical temperature Tc, magnetoresistance, as well as high spin polarization can be realized in somewhat disordered Heusler alloys by the substitution of a fourth element, with the quaternary analogs observed to have reduced structural disorder. The elemental *[email protected] †[email protected] ‡[email protected] substitution also alters the degree of hybridization between the 3dorbitals of different elements, with consequent changes in the position of the Fermi level with respect to the spin subbands [10–15]. That is, adding a fourth element may serve to not only further stabilize the structure and reduce disorder, it may also help tune the properties of interest to more desirable values. In previous studies, the doping of low-valent transition metal atoms in ternary Heusler alloys has been reported to open the minority spin energy gap around Fermi level, giving 100% spin polarization and stabilizing a half-metallic state [16,17]. Our earlier work included a number of series based on Co2FeGe [18–20], substituting for both Co and Fe, and clearly demonstrating both the ability to stabilize single phase material and tune electronic and magnetic properties. The Co2FeSi (CFS) parent is even more attractive as a starting point for applications due to its larger magnetic moment of 6 μB/f.u. and high Curie temperature of 1100 K [5]. However, the half-metallicity in the parent compound is perhaps still an open question, as both half-metallic [21] and non-half-metallic [4] properties have been reported theoretically. Kandpal et al. [21] reported half-metallic band structure calculations using local spin density approximation and generalized gradient approximation, including optimum effective Coulomb exchange interaction (Ueff). On the other hand, Galanakis et al. [4] reported a non-half-metallic state using the full-potential screened Korringa-Kohn-Rostoker Green’s function approach. In that case, the Fermi level fell on the edge of the minority conduction band, leading to unstable 2475-9953/2022/6(6)/064413(12) 064413-1 ©2022 American Physical Society R. MAHAT et al. PHYSICAL REVIEW MATERIALS 6, 064413 (2022) half-metallicity. Naturally, half-metallic ferromagnets with a stable energy gap in minority spin channel are desired for technical applications, particularly when one considers finite temperature effects [22,23]. If the Fermi energy is near one of the band edges, the energy gap may easily be smeared out at finite temperatures or destroyed by quasiparticle excitations [22,23]. To achieve robustness, compounds with Fermi level located at the middle of the minority energy gap are highly preferred [22,23]. As such, there is great utility in being able to slightly shift the position of the Fermi level in a system that is nearly half-metallic to stabilize a robust half-metallic state, or to improve the robustness of a marginal half-metal. This is where quaternary substitution can play a decisive role: if Co2FeSi is not quite a stable half-metal, can the gentle substitution of a fourth element push it toward a stable halfmetallic state? And, at the same time, can this also improve other useful properties that have led people to this system, such as magnetic or thermoelectric characteristics? This is the basic starting point for the present work: if oneoftheCoatominCo 2FeSi is substituted by another lower valence transition metal atom Y=Fe, Mn, Cr, V, Ti, or Sc, a spectrum of alloys with rich and useful properties can be generated. In fact this idea is already well understood in the Heusler alloys in general. The inverse Heusler alloy Fe2CoSi (which one could view as Co2−xFe1+xSi with x=1) has been reported to be zero-gap half-metal with very low Gilbert damping [24,25]. The quaternary Heusler CoFeMnSi has been observed theoretically and experimentally to be a spin-gapless semiconductor [26–28], CoFeCrSi has been reported to be half-metallic with some structural disorder [29], while CoFeVSi and CoFeTiSi are reported theoretically to be nearly half-metallic and half-metallic respectively, but both have been observed experimentally to show multiphase behavior in bulk form [30,31]. In all these quaternary Heusler alloys, the Fermi level lies on the edge of the minority valence band. As we go from Co2FeSi to CoFeYSi, for a lower valence substituentY, the Fermi level is shifted from the lower edge of the conduction band to the upper edge of the valence band in the minority spin channel, in accordance with the calculations by Galanakis et al. [32]. They suggested that an expansion of the lattice should shift the Fermi level lower in energy, while a contraction of the lattice should shift it higher. Since one can expect robust half-metallicity with Fermi level exactly in the middle of the minority spin band gap, this gives us a prescription for a potentially marginal half-metal Co2FeSi. Since according to Galanakis et al. the Fermi level fell on the edge of the minority conduction band, we would like to move the Fermi level lower in energy, and this means a lattice expansion. This in turn means that if we substitute a lower valence Yelement with larger atomic radius than Co [33]inCo 2−xYxFeSi, we should be able to move the Fermi level toward midgap. The substitution of a Yatom for Co in Co2FeSi may then be also seen as d-electron deficiency. There have already been several detailed studies on Co2FeSi showing that substitution plays an important role in realizing useful electronic and magnetic properties and tuning the Fermi level towards the center of the minority band gap [10,22,34–36]. The band gap at the Fermi level can be varied by substituting a fourth element at any of the three X/Y/Z sites, i.e., Co2−xY∗ xYZ,Co 2Y1−xY∗ xZ,orCo 2YZ1−xZ∗ xwhere Y,Y∗are low-valence transition elements and Z,Z∗are main group elements [9,37–42]. Substitution at X/Ysite is perhaps more convincing as the X/Ysite elements play the main role in tailoring the half-metallicity and magnetic properties compared to the Zsite element [32]. For example: Cr substitution for Fe in Co2FeSi has been observed to increase the spin polarization [10]; low Gilbert damping has been observed in a half-metallic Co2FexMn1−xSi substitutional series [35]; and the tuning of Fermi level for half-metallicity has been demonstrated in Heusler alloy Co2FeAl0.5Si0.5[34,36]. It is the aim of this work to synthesize Co2FeSi and investigate the effect of low-valence transition metal (Y=Fe, Mn, Cr, V, Ti, or Sc) substitution for Co on structural, electronic, magnetic, and mechanical properties. II. METHODS A. Experimental methods Polycrystalline Co2−xYxFeSi (Y=Co, Fe, Mn, Cr, V, Ti, or Sc, 0 ⩽x⩽1) off-stoichiometric Heusler alloys were prepared by conventional arc melting of constituents of 99.99% purity on a water-cooled Cu hearth under argon flow, with a base pressure of 10−4mbar. The mixture was flipped and melted at least 6 times to ensure chemical homogeneity. Ti was melted inside the vacuum chamber separately as an oxygen getter before melting the compound to avoid oxygen contamination. The weight loss during the process was less than 1%. The resulting ingots were cut into pieces and examined using an energy dispersive x-ray spectroscopy (EDS) detector equipped in a JEOL 7000 field emission scanning electron microscope (FESEM) to ensure the target composition after the arc melting. These pieces were annealed in evacuated quartz tubes for different heat treatments, and cooled slowly in the furnace to get optimum crystallization to promote the formation of L21structure. To make the comparison uniform across all compositions, only the samples annealed under similar heat treatments (i.e., 900 ◦Cfor 7 days) are reported. The heat treatments were followed by metallography (see details in the Supplemental Material of our previous publications [43,44]) to produce a metallic shiny surface for microstructure analysis by optical and electron microscopes. After heat treatment and metallography, the composition and homogeneity of the samples were again confirmedbyEDS. The crystal structure was investigated by means of xray diffraction (XRD) using a Bruker D8 Discover x-ray diffractometer equipped with monochromatic Co-Kα(λ= 0.179 nm) radiation at room temperature. The specimens were crushed by hand using a mortar and pestle, and the XRD measurements were carried out on the crushed powder samples by rotating around the φaxis to minimize surface effects. It should be noted that ball milling can result in a distortion of the crystalline structure due to mechanical robustness of our alloys (discussed in a subsequent section). CaRIne crystallography 4.0 software [45] as well as in-house PYTHON code [46] including the dispersive corrections to the atomic scattering factors were used to simulate the XRD patterns to compare with the experimental XRD patterns. Rietveld refinements of the XRD data were performed using MATCH! software based 064413-2 EFFECT OF MIXING THE LOW-VALENCE TRANSITION … PHYSICAL REVIEW MATERIALS 6, 064413 (2022) on the FullProf algorithm [47]. Magnetization isotherms at 5 and 300 K were studied by means of Quantum Design Physical Properties Measurement System (PPMS) using small spherical sample pieces of ∼20–30 mg, while the high temperature magnetization was measured using LakeShore VSM 7407. The mechanical properties in terms of Vickers hardness were measured by using Buehler model 1600–6100 microhardness tester. B. Computational methods Ab initio calculations are performed using densityfunctional theory (DFT) employing the projector augmented wave (PAW) pseudopotentials by Blöchl [48], implemented by Kresse and Furthmüller in the Vienna ab initio simulation package (VASP)[49]. We have adopted the generalizedgradient approximation (GGA) as formulated by Perdew, Bueke, and Ernzerhof (PBE) for the electronic exchangecorrelation potential [50]. A 16-atom supercell, i.e., 4 formula units of the underlying L21structure adopted by the perfect full-Heusler compounds like Co2MnGe is used in all of our calculations. The integrals in the reciprocal space of cubic systems was done considering a 20 ×20 ×20 -centered Monkhorst-Pack grid [51] using the linear tetrahedron method with Blöchl corrections. Total energies were converged up to 10−7eV/cell with a cutoff for the kinetic energy of the plane waves of 520 eV. Full relaxation of cell (initially cubic) volume, shape, and atomic positions were performed until the forces on each atom become less than 10−2meV/cell using the conjugate-gradient method. Spin-orbit interaction is ignored in our calculations as it is not crucial for the halfmetallic properties of Heusler compounds [52]. Ab initio electronic structure calculations using GGA approach in the case of parent compound CFS with 30 valence electrons per formula unit has been reported to predict a significantly reduced magnetic moment with respect to experiment and the Slater-Pauling value, due to the well-known on-site electronic correlations of the delectrons and related fractional state occupation [21]. The observed half-metallic properties of CFS is reported to be recovered by introducing an appropriate Hubbard Uterm into the electronic Hamiltonian [21]. In our study we have also presented GGA+U calculations on Co2−xYxFeSi system and explore how the CFS electronic properties are affected by low-valence atomic substitutions. The Hubbard Uparameter cannot be calculated simultaneously with the minimization of the total energy because total energy remains constant with respect to the Uterm. Both experimental and computational determination of the U values are very difficult and tedious tasks. In 2013 Sasioglu and collaborators employed the constrained random-phase approximation (CRPA) scheme to calculate the Uvalues for several half-metals [53]. For the calculations presented in the rest of this work, we have used the semiempirical values mentioned in Ref. [54], where Kandpal et al. have employed the LDA+Uscheme to study the electronic structure of several half-metallic Heusler compounds. The Uvalues used for the dorbitals of Co, Fe, Mn, Cr, V, Ti, and Sc are 1.92, 1.80, 1.69, 1.59, 1.34, 1.36, and 1.30 eV, respectively. Finally, it should be noted that the inclusion of Uartificially opens a FIG. 1. Optical micrograph of Co2−xYxFeSi (Y=Co, Fe, Mn, Cr, V, or Ti, x=0.50) annealed at 900 ◦C for 7 days followed by slow cooling showing the granular microstructure. The samples were etched for 60 s using the Adler etchant. band gap in the minority spin channel and only comparison to experimental data guarantees that the Uparameters used in the calculations are adequate for a particular material. III. RESULTS AND DISCUSSIONS A. Experimental results and discussions 1. Microstructural and compositional analysis Optical microscopy and SEM of polished and etched samples are very helpful to characterize the microstructure specially when the impurity phase contents are either below the detection limit of XRD (less than roughly 5% of the overall volume) or amorphous in nature [18,19,55,56]. These methods provide a morphological image which can clearly expose secondary phases and grain boundary segregation even for minor constituents. We can first speculate the presence of impurity phases by observing areas of different contrast in optical microscopy, and subsequently SEM with EDS can be utilized to quantify whether regions of different contrasts truly have different compositions or are, for instance, just different crystallite orientations. Figure 1shows the microstructures of all single phase specimens Co2−xYxFeSi (Y=Co, Fe, Mn, Cr, V, or Ti, x=0.50) annealed at 900 ◦C for 7 days, observed using an optical microscope. With the substitution of 50% Ycontent (Co, Fe, Mn,Cr,V,Ti,orSc)forCoinCo 2FeSi, we observed single phase microstructures except for 50% Sc. Our results are in accordance with previous reports for 50% Co and Fe for Co in Co2FeSi. It is found that the grain size of the alloys decreased 064413-3 R. MAHAT et al. PHYSICAL REVIEW MATERIALS 6, 064413 (2022) FIG. 2. SEM micrograph of Co2−xYxFeSi (Y=Co,Fe,Mn,Cr, V, or Ti, x=0.50) alloys annealed at 900 ◦C for 7 days followed by slow cooling, showing the granular microstructure. greatly with the substitution of less valence Ycontent. The contrast developed in micrograph (see Figs. 1–5 in the Supplemental Material [57]) suggests significant compositional differences between phases in the case of 50% Sc for Co. The composition was measured to differ from the target composition by more than 5% with the secondary phase mainly located in grain boundaries. The stoichiometry within the grains of all the single-phase specimens was confirmed as the target composition within an instrumental uncertainty of ∼5% using EDS (see Table I in the Supplemental Material [57]). Figure 2shows the typical electron images displaying the microstructure of single phase alloys. The optical and electron micrographs of all the remaining alloys in the series are presented in the Supplemental Material [57]. 2. Crystal structure and atomic order analysis The structural and chemical order of the alloys is important for their potential use in any kind of spintronics applications, and to this end structural analysis has been performed with XRD. Figure 3shows the powder XRD spectra of the studied alloys with x=0.50, measured at room temperature, using aCo-Kαradiation source (see Fig. 6 in the Supplemental Material [57]). All the alloys showed single phase behavior except for Sc, consistent with microstructures observed in previous section. For the Sc sample, asterisks denote possible Heusler cubic peaks while other peaks are from secondary phases/unknown impurity phases. All the XRD peaks in single-phase alloys can be indexed to a face-centered cubic (fcc) structure, with h,k,lall odd or even. As expected only three distinct types of peaks are observed: fundamental FIG. 3. Experimental XRD patterns of Co2−xYxFeSi (Y=Co, Fe,Mn,Cr,V,TiorSc,x=0.50) alloy series annealed at 900 ◦C for 7 days investigated at room temperature, here ∗corresponds to Heusler cubic peaks in Sc-based alloy while others are from secondary phase/unknown impurity phase. The first from the bottom is the simulated XRD pattern for ordered L21structure of Co2FeSi. The relative intensity (yaxis) is plotted in log scale so that all the peaks can be seen clearly. peaks with h+k+l=4n, even superlattice peaks with h+ k+l=4n+2, and odd superlattice peaks with h+k+l= 2n+1. Heusler alloys in the ordered L21structure are characterized by the presence of superlattice reflection (SR) peaks; the presence of (111) peak indicates the chemical ordering of atoms in octahedral positions, and (200) peak indicates the order for atoms in tetrahedral positions, while the (220) peak is a principal reflection which is independent of the state of the order [58]. In full Heusler alloys (FHA) of the type X2YZ in the L21structure, Zis the main group element with highest electronegativity which occupies 4a (0,0,0) Wyckoff sites in the Fm¯ 3mspace group, Yis the lower valence transition metal atom with smallest electronegativity and occupies the 4b(1 2,1 2,1 2) Wyckoff sites, and the transition metal X atoms are of intermediate electronegativity and occupy the 8c(1 4,1 4,1 4) Wyckoff sites [corresponding to the 4c(1 4,1 4,1 4), and 4d(3 4,3 4,3 4) Wyckoff positions in the “half Heusler” C1b structure of space group F¯ 43m][8,59]. Hereafter, we refer to the 4a and 4b sites as the A sublattice and 4c and 4d together as the B sublattice, as shown in Fig. 4. The intensities of superstructure peaks are affected by various types of 064413-4 EFFECT OF MIXING THE LOW-VALENCE TRANSITION … PHYSICAL REVIEW MATERIALS 6, 064413 (2022) FIG. 4. Crystal structure in a unit cell of (a) CFS and (b) Co1.50Y0.50FeSi (Y=Fe, Mn, Cr, V, Ti, or Sc) (I) configuration mentioned in Table Iassuming L21structure. The structures are shown in their ideal, unrelaxed forms. atomic disorders, e.g., (i) A2 (bcc) disorder due to random distribution of atoms over lattice sites 4a, 4b, 4c, and 4d which results in vanishing superstructure peaks, (ii) B2 (CsCl) disorder due to random distribution between atoms in 4a and 4b sites which results only the (200) superstructure peak and vanishing (111) peak, and (iii) DO3(BiF3) disorder when disorder is between atoms in 4b, 4c, and 4d sites only [60]. This disordered structure DO3results in a (111) peak with much higher intensity than the (200) peak. All these types of disorder would destroy the half-metallic property of the material by introducing density of states (DOS) at Fermi level in the minority spin channel [41], even though the magnetic moment of the materials may still follow a Slater-Pauling rule. AsshowninFig.3(see also Fig. 8 in the Supplemental Material [57]), the superlattice reflection peaks (111) and (200) are clearly visible as expected for the defect-free ordered Heusler structure (the degree of chemical ordering has been obtained using the Webster’s model [61]asdiscussedin Sec. I B of the Supplemental Materials [57]), indicating the presence of a long range ordering in all single phase specimens. The measured and expected values for I111/I220 and I200/I220 are observed to agree with each other qualitatively (see Fig. 8 in the Supplemental Material [57]). In order to gain more insight on chemical ordering, we performed Rietveld refinement of experimental XRD pattern for Co2−xYxFeSi (Y=Co, Fe, Mn, Cr, V, or Ti, x= 0.50) considering three nondegenerate configurations as presented in Table I. Details of the refinements for the best fit configuration (I) are provided in Table II. The observed, calculated and difference profiles for the best fit configuration (I) after performing the Rietveld refinement are provided in the Supplemental Material [57]. The crystal structure for TABLE I. Possible site assignments for cubic Co2−xYxFeSi (Y= Co,Fe,Mn,Cr,V,Ti,orSc,x=0.50) Heusler system. 4a 4b 4c 4d Type (0,0,0) (1 2,1 2,1 2)( 1 4,1 4,1 4)( 3 4,3 4,3 4) ISiFe 0.50Y0.50 Co0.50Fe0.50 Co II Si Co0.50Y0.50 Fe Co III Si Fe Co0.50Y0.50 Co TABLE II. Goodness of fit parameters (χ2and RBragg factor) obtained from Rietveld refinement for Co2−xYxFeSi (Y=Co, Fe, Mn, Cr, V, or Ti, x=0.50) alloys. Yelement χ2RBragg Co 1.1 5.3 Fe 1.3 6.9 Mn 1.5 11.2 Cr 1.9 9.1 V 1.6 8.3 Ti 1.5 7.7 this configuration is shown in Fig. 4(b) (see Fig. 9 in the Supplemental Material [57] for other possible configurations). In this configuration, we presumed that low-valence Ysubstituent atoms will displace Fe atoms from 4b sites towards vacated Co sites, and Yatoms will subsequently fill the sites previously occupied by Fe. This results in Yatoms forming an ionic-type sublattice with Si, which has a larger electronegativity, rather than with Co and Fe and the system becomes stable by Ydonating its electrons to other elements in the alloy. The Co and displaced Fe atoms have intermediate electronegativities and occupy tetrahedral sites [8,59]. In other words, Co and Fe atoms are assumed to be on the tetrahedral sublattice B (4c and 4d) and Fe, Y, and Si on the octahedral sublattice A (4a and 4b). This Hume-Rothery condition of phase stability of substitutional solid solution also supports this atomic configuration. According to this rule, the atomic size difference between two elements should be no larger than 15% and electron negativity difference no higher than 0.4 in order to form the stable solid solution [62–64]. However, complementary measurements like neutron diffraction, synchrotron x-ray diffraction techniques which are capable of differentiating elements that are close to Fe/Co are required to better understand the chemical ordering in the crystal lattice. We used Cohen’s method with a Nelson-Riley extrapolation to accurately determine the lattice parameters from XRD data [66]. The dependence of the lattice parameter aon the Y content for Co2−xYxFeSi (Y=Co, Fe, Mn, Cr, V, or Ti, 0⩽x⩽1) is shown in Fig. 5(a) while Fig. 5(b) shows the variation of lattice parameter with atomic number of Yele- ( a ) ( b ) FIG. 5. Variation of lattice parameter with (a) Ycontent in Co2−xYxFeSi (Y=Co,Fe,Mn,Cr,V,orTi,0⩽x⩽1), and (b) atomic number of low-valence transition metal element Yin Co2−xYxFeSi (Y=Co, Fe, Mn, Cr, V, or Ti, x=0.50) showing linear behavior. The pink data points represent literature values [5,65]. 064413-5 R. MAHAT et al. PHYSICAL REVIEW MATERIALS 6, 064413 (2022) ( a ) ( b ) FIG. 6. (a) Isothermal magnetization curves of Co2−xYxFeSi (Y =Co,Fe,Mn,Cr,V,orTi,x=0.50) at 5 K. (b) The saturation magnetic moment versus valence electron counts per formula units with element Y, both experimental (at 5 and 300 K) and expected from the Slater-Pauling rule for half-metals. The pink data points represent reported literature values [5,65]. ment in Co1.50Y0.50FeSi (Y=Co, Fe, Mn, Cr, V, or Ti). It is noticed that the lattice parameter increases linearly with the substitution of less valence Ycontent, consistent with Vegard’s law [67] as atomic radii decrease in the order Ti >V >Cr >Mn >Fe >Co [33]. 3. Magnetic characterization Most of the Co-based half-metallic Heusler alloys show a Slater-Pauling-like behavior for the magnetization when crystallized in a fully ordered state [68]. The Slater-Pauling (SP) rule relates the dependence of the magnetic moment with the valence electron concentration (Zt) following a simple electron counting scheme for ordered, half-metallic ferromagnetic Heusler compounds. If the value of the saturation magnetization changes with Yelement according to the Slater-Pauling rule of thumb for half-metals, then we expect the total magnetization to be [4,8] Mt=[(2 −x)ZCo +xZY+ZFe +ZSi]−24,(1) where Mtis the total spin magnetic moment per f.u. in μBand Ziis the number of valence electrons of each individual atom. In Co2−xYxFeSi (Y=Co, Fe, Mn, Cr, V, or Ti, 0 ⩽x⩽1) system, the total number of valence electrons change from 30 in CFS to 25 in CoFeTiSi. Therefore, the SP behavior predicts that the saturation magnetic moment should decrease with the substitution of Yelement for Co. Specifically, a saturation magnetic moment of M(Y)=6−x(ZCo −ZY)(2) is thus expected for Co2−xYxFeSi. For magnetic properties, we primarily used the VSM option of a Quantum Design PPMS Dynacool working in the temperature range of T=5 to 400 K and with maximum magnetic field of 9 T to observe low temperature magnetizations for all single-phase alloys. Figure 6(a) shows the isothermal magnetization curves measured at 5 K for x=0.50 (see Figs. 11–13 in the Supplemental Material [57] for magnetization curves of all other alloys in the series), as expected for ferromagnets. All the alloys are saturated in a magnetic field of about 4 kOe which indicates small magnetocrystalline anisotropy in the specimens. The Arrot plot method [69] (a) (b) FIG. 7. (a) Temperature dependence of magnetization at 100 Oe, and (b) variation of Curie temperature as a function of valence electron counts per formula units with element Y(x=0.50). The inset shows the first-order derivative of magnetization as a function of temperature, the minima of which is used to extract Tc. The pink data points represents reported literature values [5,65]. (i.e., by linear extrapolation to H/M=0ofM2versus H/M curves) was utilized to determine the spontaneous magnetizations [see inset to Fig. 6(a)]. Total saturation magnetic moments (Ms) obtained from the spontaneous magnetization at 5 K are observed to follow the Slater-Pauling rule of thumb for half-metals (see red data points) and decrease with the decrease of valence electrons in Yatoms [see Fig. 6(b)]. The decrease of Msis expected due to the decrease in the number of Co atoms. The magnetic moment per formula unit for x=0, i.e., CFS, is measured to be 5.92 μB, which is also in good agreement with reported results [5,65]. The systematic variation of saturation magnetic moments with Yatom concentration (0 ⩽x⩽1) in the series is provided in Fig. 14 in the Supplemental Material [57]. The slight deviation of magnetic moments from expected Slater-Pauling values could be due to the slight variation in the stoichiometry of the alloys, weighing and measurement errors, partial surface oxidation, and the measurement temperature of 5 K. The experimentally determined magnetic moments are also in good agreement with those obtained from first-principle calculations (see Table IV), as discussed in a forthcoming section. Figure 7(a) shows the temperature dependent specific magnetization of the alloys for x=0.50 (see Fig. 14 in the Supplemental Material [57] for all other alloys in the series), measured by means of a vibrating sample magnetometer (LakeShore VSM 7407) equipped with a high temperature stage. We present the results above 300 K so that the behavior close to the Curie temperature Tcis not masked by the rapid decrease of the magnetization at lower temperatures. Moreover, the measurements were not performed at saturation but in a constant magnetic field of 100 Oe. This leads to a more drastic drop of the magnetization at the Tcbut it allows the more precise determination of Tcwhich is our goal. The Curie temperatures Tcwere extracted from the inflection point, i.e., by taking the minima of the first-order derivative of M(T) curves [see inset in Fig. 7(b)]. The Curie temperature is observed to decrease with the substitution of low-valence transition metal element Ydue to the weakening of the exchange interaction caused by a small magnetic moment of substituted element Ycompared to Co. The decrease in Tccan also be attributed to the increase in lattice parameter 064413-6 EFFECT OF MIXING THE LOW-VALENCE TRANSITION … PHYSICAL REVIEW MATERIALS 6, 064413 (2022) TABLE III. Experimental lattice parameters and saturation magnetic moments at T=5 K along with the Slater-Pauling (SP) values, and the measured Curie temperature (Tc)ofCo 2−xYxFeSi (Y=Co,Fe,Mn,Cr,V,orTi,0⩽x⩽1) alloy series. The numbers in parentheses are the uncertainty in the last digit, e.g., 5.92(3) =5.92 ±0.03. Values in square brackets are taken from the literature. Expt. lattice Expt. MsSP TcVickers hardness Series Concentration parameter (Å) (μB/f.u.) (μB/f.u.) (K) (GPa) Co2FeSi x=0a=5.641(2)[5.636] 5.92(3)[6.00] 6.00 1094(10)[1100][5,70] 7.33(4) Co2−xFexFeSi x=0.25 a=[5.641] [5.75] 5.60 [1058][65,70]– x=0.50 a=5.646(2)[5.642] 5.58(2)[5.62] 5.50 1040(10)[1069][65,70] 7.55(6) x=0.75 a=[5.647] [5.60] 5.20 [1052][65,70]– x=1a=[5.655] [5.20] 5.00 [1036][65,70]– Co2−xMnxFeSi x=0.25 a=5.646(2) 5.57(4) 5.50 – 7.51(4) x=0.50 a=5.651(2) 5.06(3) 5.00 947(10) 7.94(3) x=0.75 a=5.658(3) 4.49(2) 4.50 869(10) 8.51(5) x=1a=5.661(2) 4.03(3) [3.99] 4.00 761(10)[763] 9.69(7) Co2−xCrxFeSi x=0.25 a=5.650(2) 5.20(4) 5.25 969(10) 7.82(6) x=0.50 a=5.662(1) 4.46(3) 4.50 873(10) 8.61(8) x=0.75 a=5.673(2) 3.72(2) 3.75 790(10) 9.78(9) x=1a=5.687(3) 2.91(2)[2.82] 3.00 710(10) 11.33(9) Co2−xVxFeSi x=0.25 a=5.656(1) 4.89(4) 5.00 924(10) 8.52(5) x=0.50 a=5.671(1) 3.90(3) 4.00 791(10) 9.85(7) x=0.75 a=5.683(3) 2.89(4) 3.00 553(10) 11.37(8) x=1†a=5.694(6) 1.45(5) 2.00 345(10) 11.79(10) Co2−xTixFeSi x=0.25 a=5.665(4) 4.75(5) 4.75 902(10) 10.75(7) x=0.50 a=5.681(2) 3.45(2) 3.50 720(10) 12.58(3) x=0.75 a=5.707(3) 2.23(5) 2.25 487(10) 13.81(9) x=1aa=5.716(6) 0.88(9) 1.00 331(10) 15.72(14) aMultiphase specimen. with the substitution of Ychanging the distance between magnetic ions leading to a weak exchange interaction. A linear dependence is obtained when plotting Tcas a function of number of valence electron concentration, and hence Ms [see Fig. 7(b)], which is expected in half-metallic Co-based Heusler alloys [38]. According to this plot, Tcis the highest for those that exhibit a large magnetic moment, or equivalently for those with a high valence electron concentration as derived from the Slater-Pauling rule. The high values of Tcusually imply stable magnetism and half-metallicity over wide temperature range, necessary in practical applications. The systematic variation of Curie temperatures with Yatom concentration (0 ⩽x⩽1) in the series is provided in Fig. 14 in the Supplemental Material [57]. The experimental values of lattice parameters, saturation magnetic moments at 5 K, Curie temperatures, and corresponding mechanical hardness values of all single phase specimens in Co2−xYxFeSi (Y=Co, Fe, Mn, Cr, V, or Ti, 0⩽x⩽1) alloy series are summarized in Table III. 4. Vickers microhardness For industrial applications, materials require mechanical robustness to undergo repetitive thermal cycling and resist cracking from vibrations. Here we have measured the mechanical properties in terms of Vickers hardness. Figure 8(a) displays the variation of Vickers microhardness with transition metals of increasing atomic number in Co2−xYxFeSi (Y=Co, Fe, Mn, Cr, V, or Ti) series with 0 ⩽x⩽1 and Fig. 8(b) shows the variation for allows with x=0.50, all measured at room temperature. The corresponding harness values are given in Table III. The data were taken from at least 12 different regions of each sample with 0.2 kg load and 10 s loading time and average values are reported here. The Vickers hardness is calculated from HV =1.8544F/D2[kg/mm2],(3) where Dis the diagonal length of the impression of the diamond probe. Relatively high hardness values are measured, approaching 15.72 GPa for CoFeTiSi, highest among the values reported for Heuslers so far [18–20,43,44,71–73]. The hardness is observed to increase with the substitution of Y ( a ) ( b ) FIG. 8. Vickers hardness versus Ycontent in Co2−xYxFeSi (Y= Co, Fe, Mn, Cr, V, Ti, or Sc), all annealed at 900 ◦Cfor7days (a) for all the alloys 0 ⩽x⩽1, and (b) for alloys with x=0.50. The imprints of the indenter with radial cracks for Ti =1 [bottom right of (a)] and Ti =0.50 [top right of (b)] are shown. 064413-7 R. MAHAT et al. PHYSICAL REVIEW MATERIALS 6, 064413 (2022) TABLE IV. Parameters extracted from DFT calculations (both GGA and GGA+Uapproach) for type I configuration. In the table M,MSP, a,andrepresent calculated magnetic moment, Slater-Pauling moment, optimized lattice parameter, and energy gap at Fermi level. The last column shows the tetragonality in the structure a/c−1. The values in the parentheses represent the calculated values using GGA approach. YMM SP aTet.  element Configurations 4d 4c 4b 4a (μB/f.u.) (μB/f.u.) (Å) (a/c−1) (eV) Co Co8-Fe4Si44Co 4Co 4Fe 4Si 6.000(5.484) 6.000 5.636 0.012 0.791 Fe Co6Fe2-Fe4Si44Co 2Fe,2Co 4Fe 4Si 5.502(5.369) 5.500 5.640 0.012 0.387 Mn Co6Fe2-Fe2Mn2Si44Co 2Fe,2Co 2Mn,2Fe 4Si 5.000(4.999) 5.000 5.645 0.012 0.575(0.138) Cr Co6Fe2-Fe2Cr2Si44Co 2Fe,2Co 2Cr,2Fe 4Si 4.500(4.480) 4.500 5.657 0.012 0.626 VCo 6Fe2-Fe2V2Si44Co 2Fe,2Co 2V,2Fe 4Si 3.999(3.856) 4.000 5.678 0.012 0.176 Ti Co6Fe2-Fe2Ti2Si44Co 2Fe,2Co 2Ti,2Fe 4Si 3.500(3.463) 3.500 5.690 0.012 0.597 Sc Co6Fe2-Fe2Sc2Si44Co 2Fe,2Co 2Sc,2Fe 4Si 3.000(2.994) 3.000 5.717 0.012 0.719 element of increasing atomic radius and depends on phases present as reported in the literature [74]. B. Theoretical results and discussions The parent compound Co2FeSi of the series Co2−xYxFeSi (Y=Co, Fe, Mn, Cr, V, Ti, or Sc, x=0.50) has already been reported in the literature to form the L21structure with a low degree of chemical disorder [22] and our experimental investigations confirmed the low-valence transition metals Y substitution for Co in Co2FeSi also give stable single phases with XRD patterns consistent with the ordered L21structure (except for scandium substituted alloy). These experimental facts allow us accurate comparison between experiment and theory. We note that DFT using the GGA approach predicts a significantly reduced magnetic moment with respect to experiment and Slater-Pauling values, but that the introduction of Hubbard Uterms in the GGA approach, i.e., GGA+U,resolves the discrepancy in Co2FeSi [21,22]. In order to predict the size and nature of band gaps and magnetic moments, we have therefore performed the electronic-structure calculations using both GGA and GGA+Uapproaches. For theoretical calculations, bulk Co1.50Y0.50FeSi (Y=Co, Fe, Mn, Cr, V, Ti, or Sc) cubic supercell structures consisting of 16 atoms were constructed using the Monte Carlo special quasirandom structure (MCSQS) method [75] which is a part of the open source ATAT toolkit [76] accessible from [77]. The MCSQS method can handle double-site substitutions as described in the experimental section above taking care of nearest neighbor interaction and predicts a special quasirandom structure by generating a set of clusters with specific correlations relative to a target random structure. The best MCSQS structures were confirmed after waiting for a long enough time until a correlation difference relative to the target random structure approaches zero. The predicted MCSQS structures are in good agreement with configuration I predicted in Table I[see also Fig. 4(b)]. The predicted MCSQS structures were then optimized using GGA method. The experimental lattice constants extracted in our experimental work were employed as starting values for the calculations. The optimized lattice parameters are in good agreement with experimental values, increasing with the substitution of atoms with low valency. All the calculated parameters are presented in Table IV. Figure 9shows the calculated spin polarized density of states (DOS) plots for majority and minority spin channels using both GGA (blue) and GGA+U(red) where the Fermi level is represented by the zero energy. Our calculations show the systematic shifting of Fermi level from conduction band edge in the parent compound Co2FeSi towards the energy gap in minority spin channel after substituting low-valence transition metals (see Fig. 15 in the Supplemental Material [57] FIG. 9. Spin polarized total density of states (TDOS) of Co1.50Y0.50FeSi (Y=Co, Fe, Mn, Cr, V, Ti, or Sc) alloys using both GGA (blue) and GGA+U(red) methods. Number of states in each plot is scaled with respect to 1 f.u. 064413-8 EFFECT OF MIXING THE LOW-VALENCE TRANSITION … PHYSICAL REVIEW MATERIALS 6, 064413 (2022) for the atom-resolved DOS). In the GGA approach, only the Co1.50Mn0.50FeSi alloy is observed to be a perfect half-metal with the Fermi level within the energy gap in the minority spin channel. Moreover, in the case of the Co1.50Cr0.50FeSi alloy, the presence of the Cr atom leads to a peak in the majority spin dstates in the vicinity of Fermi level consistent with previous observations [18,78,79]. The nonzero contribution to DOS from Fe(I) (which shares the same sublattice A with Y atoms) at Fermi level in the minority spin channel is observed to play a major role in destroying the half-metallicity in all other alloys. The inclusion of electron-electron correlation in GGA+Uapproach shifts the Fermi level within the gap for all compounds resulting in a half-metallic behavior. We should note that the minority spin energy band gap decreases as we substitute lower-valence transition metal atoms for Co in Co2FeSi. The ab initio calculated energy gaps are provided in Table IV. In Table III we provide the experimentally determined total spin magnetic moments in μBfor all the samples which we have grown, and in Table IV we summarize the total spin magnetic moments calculated using both the GGA functional and the GGA+Uapproach for the x=0.5 case. The inclusion of electron-electron correlation in the GGA+Uapproach opens the gap, as expected, in the minority spin channel, the Fermi level shifts within the gap for all compounds resulting in calculated total spin magnetic moments slightly larger than GGA ones and in almost perfect agreement with the ones predicted by the Slater-Pauling rule. Although differences between both GGA and GGA+Ucalculated values and the experimental ones are quite small, we expect that GGA+U performs slightly better than GGA since (a) calculations are done at 0 K and experimental magnetic moments were measured at 5 K and (b) samples have an intrinsic degree of disorder despite their very high crystallinity. Thus calculations should slightly overestimate the spin magnetic moments with respect to the experimentally measured ones. IV. CONCLUSION In summary, quaternary Heusler alloys Co2−xYxFeSi (Y= Co, Fe, Mn, Cr, V, Ti, or Sc, 0 ⩽x⩽1) were synthesized and a combined experimental and theoretical study of structural, electronic, magnetic, and mechanical properties of quaternary Heusler alloys Co2−xYxFeSi (Y=Co, Fe, Mn, Cr, V, Ti, or Sc, x=0.50) were carried out. The alloys were identified as potential half-metallic ferromagnets by ab initio electronic structure calculations using the GGA+Uapproach while only Co1.50Mn0.50FeSi is predicted to be potential half-metal in GGA approach. The structural analysis reveals that the alloys crystallize in a cubic Heusler structure. A certain amount of disorder is observed in V and Ti substituted alloys. The magnetic properties were analyzed at both 5 and 300 K. The saturation magnetic moments of the alloys measured at 5 K are in fair agreement with those expected from Slater-Pauling rule. The results are also in accordance with the electronic structure calculations, indicating the half-metallicity and high spin polarization required for spintronics applications. The Curie temperatures of all compounds are higher than 700 K, allowing use at room temperature and above. Robust mechanical properties with hardness values increasing with the substitution of Yelement and with its atomic radius are also observed. This manner of substitution of low-valence transition metal atoms to design new quaternary Heusler compounds gives enormous potential for many room temperature applications such as in spintronics or thermoelectrics and other areas of research, and clearly deserve further exploration on thin films in the future. ACKNOWLEDGMENTS We would like to acknowledge Dr. Mark Weaver for helpful discussions on measurements of mechanical properties and for providing the instrument for hardness measurements. This work utilizes the facilities offered by Central Analytical Facility (CAF) of University of Alabama. We are thus grateful to the members of CAF for helping us with measurements. The computational resources were provided by the UA High Performance Computing Facility (UAHPC). The financial support to conduct this work was sourced from NSF DMREF Grant No. 1235396, and NSF DMR Grant No. 1508680. The authors are thankful to NSF for providing the support to carry out this work. [1] T. 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