Tight-binding Linear Muffin-tin Orbital Method Research Articles

First-Principles Calculation of Transport Properties of Heusler Alloy Co2MnAl at Finite Temperatures

We develop a framework for first-principles calculations of the transport properties of magnetic materials at finite temperatures within the coherent potential approximation. First, we calculate the grand potential by the tight-binding linearized muffin-tin orbital method and apply it to the Kubo formula to obtain the temperature dependence of the conductivities. Next, we demonstrate the computation for the magnetic moments M(T), longitudinal and transverse electrical conductivities, σxx(T), σxy(T), Seebeck coefficients Sxx(T), and anomalous Nernst coefficients Nxy(T) of Co2MnAl of both L21 and B2 structures. It is found that σxx(T) of L21 and B2 structures exhibit slow relaxation with temperature compared with most transition metal alloys, which reflects a transition of the system from a half-metallic to metallic system with increasing temperature. The σxy(T = 0) of the B2 structure is much smaller than that of the L21 structure, while σxx(T) of the B2 structure exhibits slower relaxation with temperature than the L21 structure. The Sxx(T) and Nxy(T) exhibit nonmonotonic variation in the low temperature region and the values above room temperature are in agreement with the experimental data.

Experimental and Theoretical Study on the Nonmagnetic Li/Mg Cosubstitution in the Gd5-x(Li/Mg)xGe4 (x = 1.04, 1.17, 1.53) System.

Three Li- and Mg-cosubstituted compounds in the Gd5-x(Li/Mg)xGe4 (x = 1.04(2), 1.17(2), 1.53(2)) system have been successfully prepared by conventional high-temperature reactions. According to powder and single-crystal X-ray diffraction analyses, all three compounds adopt a Gd5Si4-type phase with the orthorhombic Pnma space group (Pearson code oP16, Z = 4) and six crystallographically independent atomic sites. The crystal structure can be described as a combination of two-dimensional Mo2FeB2-type ∞2[Gd2(Li/Mg)Ge2] layers and [Ge2] dimers. Interestingly, as 64% of Li and 26% of Gd at the RE3 and RE2 sites, respectively, were exclusively substituted by Mg in Gd3.47(1)Li0.36(2)Mg1.17(3)Ge4, the lattice parameter b was selectively shortened as a result of the RE3-Ge1 bond shrinkage in comparison to that in Gd4LiGe4, while lattice parameters a and c remained nearly intact. A series of theoretical calculations using the tight-binding linear muffin-tin orbital (TB-LMTO) method indicated that the reduction of the particular RE3-Ge1 bond distance in the title compounds could also be explained by an optimization of bonding based on the corresponding RE3-Ge1 crystal orbital Hamilton population (COHP) curve. Moreover, the specific site preference of Mg for the RE3 site was supported by both size-factor as well as electronic-factor criteria on the basis of the smallest atomic size and the highest electronegativity of Mg among the three cations. Therefore, the overall electronic structure was further interrogated by a density of states (DOS) analysis. The influence of nonmagnetic Li/Mg cosubstitution for the magnetic Gd atoms in the title Gd5-x(Li/Mg)xGe4 system on the magnetic characteristics was also thoroughly studied by isofield magnetization at 100 Oe and 10 kOe and isothermal magnetization measurements at 4 K using two of the title compounds: Gd3.83(1)Li0.48Mg0.69(3)Ge4 and Gd3.47(1)Li0.36(2)Mg1.17(3)Ge4.

First-principles calculations for Gilbert damping constant at finite temperature

We propose a first-principles calculation method for the Gilbert damping constants α at finite temperature. α is described by the torque correlation model in which the electronic structure is computed by the tight-binding linear muffin-tin orbital method. We include the finite-temperature effect as the transverse spin fluctuation in the disordered local moment picture within the coherent potential approximation. Applying the present method to bcc-Fe and L10-FePt, we demonstrate this temperature-dependent α. By comparing our calculated results with experimental results, we find the calculated values are less than half of the experimental values, reflecting the characteristics of the torque correlation model.

Ab initio theory of the spin-dependent conductivity tensor and the spin Hall effect in random alloys

We present an extension of the relativistic electron transport theory for the standard (charge) conductivity tensor of random alloys within the tight-binding linear muffin-tin orbital method to the so-called spin-dependent conductivity tensor, which describes the Kubo linear response of spin currents to external electric fields. The approach is based on effective charge- and spin-current operators, that correspond to intersite electron transport and that are nonrandom, which simplifies the configuration averaging by means of the coherent potential approximation. Special attention is paid to the Fermi sea term of the spin-dependent conductivity tensor, which contains a nonzero incoherent part, in contrast to the standard conductivity tensor. The developed formalism is applied to the spin Hall effect in binary random nonmagnetic alloys, both on a model level and for Pt-based alloys with an fcc structure. We show that the spin Hall conductivity consists of three contributions (one intrinsic and two extrinsic) which exhibit different concentration dependences in the dilute limit of an alloy. Results for selected Pt alloys (Pt-Re, Pt-Ta) lead to the spin Hall angles around 0.2; these sizable values are obtained for compositions that belong to thermodynamically equilibrium phases. These alloys can thus be considered as an alternative to other systems for efficient charge to spin conversion, which are often metastable crystalline or amorphous alloys.

La3Ni4Al2: a new layered aluminide

Abstract The new ternary compound La3Ni4Al2 has been synthesized and the crystal structure has been studied by X-ray single crystal diffraction. La3Ni4Al2 is the first aluminide, crystallizing in the La3Ni4Ga2-type. The crystal structure of La3Ni4Al2 consists of La-layers and hetero-atomic Ni/Al layers, sequentially alternating along the a axis (pseudo-hexagonal c axis). According to electronic structure calculations using the tight-binding linear muffin-tin orbital method in the atomic-sphere approximation (TB-LMTO-ASA), strong Al–Ni interactions have been established. The coordination polyhedra for the Al atoms are cuboctahedra, whereas the bicapped square prism and bicapped square antiprism are typical for nickel atoms. The lanthanum atoms are enclosed in pseudo Frank–Kasper polyhedra.

Effect of Rare-Earth Metals Substitution for Ca on the Crystal Structure and Thermoelectric Properties of the Ca11–xRExSb10–y System

Four novel ternary Zintl phase compounds belonging to the Ca11–xRExSb10–y (RE = La, Ce, Nd, Sm; 0.18(4) ≤ x ≤ 0.43(2), 0.14(1) ≤ y ≤ 0.41(1)) system have been synthesized by arc-melting, and the Ho11Ge10-type crystal structure has been characterized for the isotypic title compounds by both powder and single crystal X-ray diffraction analyses. The intrinsically complex crystal structure is viewed as an assembly of the three distinctively shaped cationic polyhedra built from either seven or nine cations and the anionic frameworks constructed by the “dumbbell-shaped” Sb2 and the “square-shaped” Sb4 moieties. All of the four trivalent rare-earth metals were successfully introduced as n-type dopants to partially substitute divalent Ca atoms in the parental compound Ca11Sb10, which resulted in generating two or three Ca2+/RE3+ mixed-cationic sites. In particular, during these substitutions, we observed a unique site preference of Ca2+ and RE3+ among four available cationic sites, where the rare-earth metals with the higher electronegativities than Ca occupied particular atomic sites having the higher Q values. This type of site preference was conclusively explained by theoretical investigations using the tight-binding linear muffin-tin orbital method. Despite the successful n-type doping, the increased electrical conductivities σ and the decreased Seebeck coefficients S of Ca10.75(3)Nd0.25Sb9.82(1) and Ca10.82(4)Sm0.18Sb9.86(1) compared to those of Ca11Sb10 still presented the p-type rather than n-type characters. These unexpected behaviors should be attributed to ca. 7–20% of Sb3 deficiencies found at the “square-site” (Wyckoff 8h), which spontaneously occurred to reduce an energetically unfavorable antibonding character of the interatomic interaction between two Sb3 atoms at the square-site. Total and partial density of states of a hypothetical structural model Ca10.5Nd0.5Sb10, an SEM image of single crystals of Ca10.57(2)La0.43Sb9.59(1), and a TGA result of Ca10.82(4)Sm0.18Sb9.86(1) are also provided.

Anionic Doping and Cationic Site Preference in CaYb4Al2Sb6- xGe x ( x = 0.2, 0.5, 0.7): Origin of the Enhanced Seebeck Coefficient and the Structural Transformation.

Three Zintl phase compounds belonging to the CaYb4Al2Sb6- xGe x ( x = 0.2, 0.5, 0.7; nominal compositions) system with various Ge-doping contents were successfully synthesized by arc-melting and were initially crystallized in the Ba5Al2Bi6-type phase (space group Pbam, Pearson codes oP26). However, after post-heat treatment at an elevated temperature, the originally obtained crystal structure was transformed into the homeotypic Ca5Ga2Sb6-type structure according to powder and single-crystal X-ray diffraction analyses. Two types of crystal structures share some isotypic structural moieties, such as the one-dimensional anionic chains formed by ∞1[Al2Sb8] and the void-filling Ca2+/Yb2+ mixed cations, but the slightly different spatial arrangements in each unit cell make these two structural types distinguishable. This series of title compounds is originally investigated to examine whether anionic p-type doping using Ge can successfully enhance thermoelectric (TE) properties of the Yb-rich CaYb4Al2Sb6- xGe x series even after the phase transition from the Ba5Al2Bi6-type to the Ca5Ga2Sb6-type phase. More interestingly, we also reveal that the given structural transformation is triggered by the particularly different site-preference of Ca2+ and Yb2+ among three available cationic sites in each structure type, which is significantly affected by thermodynamic conditions of this system. Band structure and density of states analyses calculated by density functional theory using the tight-binding linear muffin-tin orbital method also prove that the Ge-doping actually increases band degeneracies and the number of resonant peaks near the Fermi level resulting in the improvement of Seebeck coefficients. Electron localization function analyses for the (0 1 0) sliced-plane and the 3D isosurface nicely illustrates the distortion of the paired-electron densities due to the introduction of Ge. The systematic TE property measurements imply that the attempted anionic p-type doping is indeed effective to improve the TE characteristics of the title CaYb4Al2Sb6- yGe y system.

Structural and magnetic properties of the RAl0.2Ge2 compounds (R = Tb, Dy, Ho, Er, Tm)

The structural and magnetic properties of the RAl0.2Ge2 (R = Tb-Tm) germanides were studied by X-ray and neutron diffraction, scanning electron microscopy and magnetometric techniques. The compounds crystallize in the CeNiSi2-type crystal structure (space group Cmcm). Magnetic measurements reveal an antiferromagnetic ordering below TN equal to 38 K (R = Tb), 23 K (Dy), 9 K (Ho) and 6.5 K (Er), and no magnetic ordering in the Tm-compound down to 1.9 K. Based on the neutron diffraction data the magnetic structures can be described by the propagation vector k = (0.4714(2), 0, 0.3128(2)) for TbAl0.2Ge2 and k = (0.4858(5), 0, 0.3214(6)) for DyAl0.2Ge2 while in HoAl0.2Ge2 and ErAl0.2Ge2 a simple collinear antiferromagnetic ordering of the G-type was observed. The electronic structures of the title compounds were calculated using the tight-binding linear muffin-tin orbital (TB-LMTO) method.

Spin-disorder resistivity of random fcc-NiFe alloys

The spin-disorder resistivity (SDR) of a disordered fcc-(${\mathrm{Ni}}_{1\ensuremath{-}x},{\mathrm{Fe}}_{x}$) alloy is determined from first principles. We identify the SDR at and above the critical temperature with the residual resistivity of the corresponding paramagnetic state evaluated in the framework of the disordered local moment (DLM) model. The underlying electronic structure is determined by means of the tight-binding linear muffin-tin orbital method, which employs the coherent potential approximation (CPA) to describe both the DLM state and the chemical disorder in alloys. An extension of the DLM fixed-spin moment method for two independent magnetic moments is used and combined with the paramagnetic lattice gas entropy to determine local moments by minimizing the corresponding free energy. The effect of phonon scattering is included through the mapping of static atomic displacements into a multicomponent random alloy which is then treated in the CPA. Finally, the Kubo-Greenwood-CPA approach is employed to estimate the SDR. We also address the problem of the validity of the Matthiessen rule at the Curie point. Good agreement of calculated and measured SDR is obtained over the whole studied concentration range; the results point to the importance of nonzero Ni magnetic moments in the limit of pure nickel.

Influence ofp-Type Double-Doping on the Crystals and Electronic Structures of Two Polar Intermetallics: La4.57(1)Li0.43Ge3.80(3)In0.20and Nd4.32(1)Li0.68Ge3.87(3)In0.13

Two quaternary polar intermetallic compounds La4.57(1)Li0.43Ge3.80(3)In0.20 and Nd4.32(1)Li0.68Ge3.87(3)In0.13 were synthesized using a conventional high temperature synthetic method as we attempted to introduce the p-type double-doping of Li and In for RE and Ge in the RE5-xLixGe4-y (RE = rare-earth metals) system, and their crystal structures were characterized by single crystal X-ray diffraction experiments. The two title compounds crystallize in the orthorhombic space group Pnma (Pearson code oP16, Z = 4) with six crystallographically independent asymmetric atomic sites and adopt the Gd5Si4-type structure. Overall crystal structures of two isotypic title compounds can be described as a 1:1 assembly of the hypothetical 2-dimensional (2D) RE2(RE/Li)(In/Ge)2 layered structure adopting the Mo2FeB2-type structure and the dumbbell-shaped inter-slab (In/Ge)2 dimers bridging two such neighboring 2D layers along the crystallographic b-axis direction. The observed “direction selective” structural transformation from the Sm5Ge4-type to the Gd5Si4-type structure can be understood as a result of the simultaneous double-doping by the relatively smaller amount of Li substitution for La at the RE3 site than that in the La4LiGe4 and the partial In substitution for Ge at both of the M1 and M3 sites. The site-preference of In for two particular anionic sites were thoroughly studied using four hypothetical La4LiGe3In models having different atomic arrangements by the tight-binding linear muffin-tin orbital (TB-LMTO) method. The overall electronic structure and individual chemical bonding influenced by the given double-doping were also discussed on the basis of the density of states (DOS) and crystal orbital Hamilton population (COHP) curves analyses.

Intricate Li-Sn Disorder in Rare-Earth Metal-Lithium Stannides. Crystal Chemistry of RE3Li4- xSn4+ x (RE = La-Nd, Sm; x < 0.3) and Eu7Li8- xSn10+ x ( x ≈ 2.0).

Reported are the syntheses, crystal structures, and electronic structures of six rare-earth metal-lithium stannides with the general formulas RE3Li4- xSn4+ x (RE = La-Nd, Sm) and Eu7Li8- xSn10+ x. These new ternary compounds have been synthesized by high-temperature reactions of the corresponding elements. Their crystal structures have been established using single-crystal X-ray diffraction methods. The RE3Li4- xSn4+ x phases crystallize in the orthorhombic body-centered space group Immm (No. 71) with the Zr3Cu4Si4 structure type (Pearson code oI22), and the Eu7Li8- xSn10+ x phase crystallizes in the orthorhombic base-centered space group Cmmm (No. 65) with the Ce7Li8Ge10 structure type (Pearson code oC50). Both structures can be consdered as part of the [RESn2] n[RELi2Sn] m homologous series, wherein the structures are intergrowths of imaginary RESn2 (AlB2-like structure type) and RELi2Sn (MgAl2Cu-like structure type) fragments. Close examination the structures indicates complex occupational Li-Sn disorder, apparently governed by the drive of the structure to achieve an optimal number of valence electrons. This conclusion based on experimental results is supported by detailed electronic structure calculations, carried out using the tight-binding linear muffin-tin orbital method.

Structure and Chemical Bonding of the Li-Doped Polar Intermetallic RE₂In1-xLixGe₂ (RE = La, Nd, Sm, Gd; x = 0.13, 0.28, 0.43, 0.53) System.

Four polar intermetallic compounds belonging to the RE2In1−xLixGe2 (RE = La, Nd, Sm, Gd; x = 0.13(1), 0.28(1), 0.43(1), 0.53(1)) system have been synthesized by the traditional solid-state reaction method, and their crystal structures have been characterized by single-crystal X-ray diffraction (SXRD) analyses. The isotypic crystal structures of four title compounds adopt the Mo2FeB2-type structure having the tetragonal space group P4/mbm (Z = 2, Pearson code tP40) with three crystallographically independent atomic sites and can be simply described as a pile of the identical 2-dimensioanl (2D) RE2In1-xLixGe2 slabs stacked along the c-axis direction. The substituting Li atom shows a particular site preference for replacing In at the Wyckoff 2a site rather than Ge at the Wyckoff 4g in this crystal structure. As the size of a used rare-earth metal decreases from La3+ to Gd3+ throughout the title system, the Ge-Ge and Ge-In/Li bond distances, both of which consist of the 2D anionic Ge2(In/Li) layer, gradually decrease resulting in the reduction of a unit cell volume. A series of theoretical investigations has been performed using a hypothetical structure model Gd2In0.5Li0.5Ge2 by tight-binding linear muffin-tin orbital (TB-LMTO) method. The resultant densities of states (DOS) value at the Fermi level (EF) suggests a metallic conductivity for this particular composition, and this calculation result is in a good agreement with the formal charge distribution assigning two extra valence electrons for a metal-metal bond in the conduction band. The thorough analyses of six crystal orbital Hamilton population (COHP) curves representing various interatomic interactions and an electron localization function (ELF) diagram indicating the locations of paired-electron densities are also provided in this article.

An Unusual Triple-Decker Variant of the Tetragonal BaAl4-Structure Type: Synthesis, Structural Characterization, and Chemical Bonding of Sr3Cd8Ge4 and Eu3Cd8Ge4

Reported are the synthesis and the crystal structures of the new ternary phases Sr3Cd8Ge4 and Eu3Cd8Ge4. The structures of both compounds have been established by single-crystal and powder X-ray diffraction methods. They crystallize in the tetragonal space group I4/mmm (No. 139, own structure type, Pearson symbol tI30) with Z = 2, and lattice parameters as follows: a = 4.4941(14) Å; c = 35.577(7) Å for Sr3Cd8Ge4, and a = 4.4643(12) Å; c = 35.537(9) Å for Eu3Cd8Ge4, respectively. The most prominent feature of the structure is the complex [Cd2Ge] polyanionic framework, derived by unique ordering of the Cd and Ge atoms in fragments that bear resemblance to the BaAl4 structure type. Temperature dependent DC magnetization measurements indicate that Eu3Cd8Ge4 displays Curie-Weiss paramagnetic behavior with no sign of magnetic ordering in the measured range. Theoretical considerations of the electronic structure on the basis of the tight-binding linear muffin-tin orbital (TB-LMTO-ASA) method are also presented and discussed.

Fully Relativistic Temperature-Dependent Electronic Transport Properties of Magnetic Alloys From the First Principles

Ab initio calculations based on the fully relativistic Dirac approach and incorporating chemical disorder and temperature-induced atomic displacements (phonons) are presented. The tight-binding linear muffin-tin orbital method is used, and the multicomponent coherent potential approximation deals with the chemical disorder and phonons on the same level. Electrical resistivities calculated without and with spin–orbit interaction are compared, and the anomalous Hall effect for magnetic alloys is investigated. The developed technique is tested on pure nickel and on random binary Cu–Ni alloys. The calculated results are found to be in good agreement with experimental and other theoretical data. The combined effect of phonons and spin disorder, simulated within the disordered local moment state, has also been studied. The results confirm the validity of Matthiessen’s rule in a wide range of temperatures for the electrical resistivity of pure nickel.

First-Principles Study on the Magnetic Damping of Transition Metals in the Presence of Spin Fluctuation

We calculated, from first principles, the Landau frequency $\lambda $ to investigate the effects of spin fluctuation on the magnetic damping of Fe and Ni metals as well as $L1_{0}$ -type ordered alloys, namely, FePt, CoPt, FePd, and MnAl, assuming random arrangements of spins as an effect of thermal activation through coherent potential approximation and the tight-binding linear muffin-tin orbital method. The results show that the $\lambda $ of these systems are similar to conductivity in the weak spin fluctuation region and resistivity in the strong fluctuation region as well as in the lattice vibration system. Qualitatively, this behavior is consistent with the experimental results for temperature dependence of the $\lambda $ of Fe and Ni metals. For $L1_{0}$ -type alloys, the magnitude of the magnetic damping is in the following (decreasing) order: CoPt, FePt, FePd, and MnAl.

Physical properties of the tetragonal CuMnAs: A first-principles study

Electronic, magnetic, and transport properties of the antiferromagnetic (AFM) CuMnAs alloy with tetragonal structure, promising for the AFM spintronics, are studied from first principles using the Vienna ab-initio simulation package. We investigate the site-occupation of sublattices and the lattice parameters of three competing phases. We analyze the factors that determine which of the three conceivable structures will prevail. We then estimate formation energies of possible defects for the experimentally prepared lattice structure. Mn$_{\rm Cu}$- and Cu$_{\rm Mn}$-antisites as well as Mn$\leftrightarrow$Cu swaps and vacancies on Mn or Cu sublattices were identified as possible candidates for defects in CuMnAs. We find that the interactions of the growing thin film with the substrate and with vacuum as well as the electron correlations are important for the phase stability while the effect of defects is weak. In the next step, using the tight-binding linear muffin-tin orbital method for the experimental structure, we estimate transport properties for systems containing defects with low formation energies. Finally, we determine the exchange interactions and estimate the N\'eel temperature of the AFM-CuMnAs alloy using the Monte Carlo approach. A good agreement of the calculated resistivity and N\'eel temperature with experimental data makes possible to draw conclusions concerning the competing phases.

Li9Al4Sn5as a new ordered superstructure of the Li13Sn5type

Alloys from the ternary Li-Al-Sn system have been investigated with respect to possible applications as negative electrode materials in Li-ion batteries. This led to the discovery of a new ternary compound, a superstructure of the Li13Sn5 binary compound. The ternary stannide, Li9Al4Sn5 (nonalithium tetraaluminium pentastannide; trigonal, P-3m1, hP18), crystallizes as a new structure type, which is an ordered variant of the binary Li13Sn5 structure type. One Li and one Sn site have -3m. symmetry, and all other atoms occupy sites of 3m. symmetry. The polyhedra around all types of atoms are rhombic dodecahedra. The electronic structure was calculated by the tight-binding linear muffin-tin orbital atomic spheres approximation method. The electron concentration is higher around the Sn and Al atoms, which form an [Al4Sn5]m- polyanion.

First-principles evaluation of intrinsic, side-jump, and skew-scattering parts of anomalous Hall conductivities in disordered alloys

We develop a first-principles procedure for the individual evaluation of the intrinsic, side-jump, and skew-scattering contributions to the anomalous Hall conductivity $\sigma_{xy}$. This method is based on the different microscopic conductive processes of each origin of $\sigma_{xy}$ in the Kubo--Bastin formula. We also present an approach for implementing this scheme in the tight-binding linear muffin-tin orbital (TB-LMTO) method with the coherent potential approximation (CPA). The validity of this calculation method is demonstrated for disordered FePt and FePd alloys. We find that the estimated value of each origin of $\sigma_{xy}$ exhibits reasonable dependencies on the electron scattering in these disordered alloys.

Exchange and spin-orbit induced phenomena in diluted (Ga,Mn)As from first principles

Physical properties induced by exchange interactions (Curie temperature and spin stiffness) and spin-orbit coupling (anomalous Hall effect, anisotropic magnetoresistance, and Gilbert damping) in the diluted (Ga,Mn)As ferromagnetic semiconductor are studied from first principles. Recently developed Kubo-Bastin transport theory and nonlocal torque operator formulation of the Gilbert damping as formulated in the tight-binding linear muffin-tin orbital method are used. The first-principles Liechtenstein mapping is employed to construct an effective Heisenberg Hamiltonian and to estimate Curie temperature and spin stiffness in the real-space random-phase approximation. Good agreement of calculated physical quantities with experiments on well-annealed samples containing only a small amount of compensating defects is obtained.

Ab Initio Theory of the Gilbert Damping in Random Ferromagnetic Alloys

We present an ab initio theory of the Gilbert damping in ferromagnetic alloys with substitutional disorder. The theory is based on nonlocal torques that are represented by nonrandom, site-off-diagonal, and spin-independent matrices, which simplifies the configuration averaging. The formalism is developed for the relativistic tight-binding linear muffin-tin orbital (TB-LMTO) method and the coherent potential approximation (CPA). The CPA-vertex corrections play a crucial role for the internal consistency of the theory and for its exact equivalence to other first-principles approaches based on random local torques. The theory is illustrated by calculations for various random transition metal alloys: FeNi, FeCo, Heusler alloys, permalloy with impurities, Fe with vacancies, and stoichiometric FePt and CoPt alloys with a varying degree of L1 0 atomic long-range order. Results are in a reasonable agreement with other calculations and accessible experimental data.