Competition between Direct and Indirect Exchange Couplings in MnFeAs: A First-Principles Investigation

The electronic and magnetic structures of the tetragonal and hexagonal MnFeAs were examined using density functional theory to understand the reported magnetic orderings and structural change induced by high-pressure synthesis. The reported magnetic ground states were confirmed using VASP total energy calculations. Effective exchange parameters for metal–metal contacts obtained from SPRKKR calculations indicate indirect exchange couplings are dominant in tetragonal MnFeAs. Weak direct exchange couplings for adjacent Fe–Fe and Fe–Mn contacts cause the coexistence of several low-energy magnetic structures in tetragonal MnFeAs and result in a near zero magnetic moment on the Fe atoms. On the other hand, the nearest-neighbor Fe–Fe and Fe–Mn interactions in hexagonal MnFeAs are a combination of direct and indirect exchange couplings. In addition, indirect exchange couplings in tetragonal MnFeAs are rationalized by both RKKY and superexchange mechanisms. Finally, to probe the high-pressure-induced phase transition, total energy changes with the change of volume was studied on both tetragonal and hexagonal MnFeAs

New Co–Pd–Zn γ‑Brasses with Dilute Ferrimagnetism and Co₂Zn₁₁ Revisited: Establishing the Synergism between Theory and Experiment

A synergism between electronic structure theory and the targeted synthesis of new ternary γ-brass compounds is demonstrated in the Co–Zn system. Co₂Zn₁₁, which adopts a cubic γ-brass structure, is shown to be at the Zn-rich end of a homogeneity range that varies from 15.4 to 22.1 atom % Co. Four samples were examined by single-crystal diffraction, all of which crystallize in space group <i>I</i>4̅3<i>m</i> with the lattice parameter ranging from 8.9851(1) to 8.8809(1) Å as the Co content increases. In the 26-atom γ-brass clusters, Co atoms preferentially occupy the outer tetrahedron (OT) sites and then replace Zn atoms at the octahedron (OH) sites at higher Co concentrations. In addition, a small fraction of vacancies occurs on the inner tetrahedron (IT) sites. The electronic structure of Co₂Zn₁₁ shows two distinct pseudogaps near the Fermi level: one at 292 valence electrons per primitive unit cell and the other at 302–304 valence electrons per primitive unit cell. Using molecular orbital arguments applied to the body-centered cubic packing of the 26-atom Co₄Zn₂₂ γ-brass cluster, these pseudogaps arise from (i) splitting among the valence s and p orbitals, which gives rise to the Hume–Rothery electron counting rule, and (ii) splitting within the manifold of Co 3d orbitals via Co–Zn orbital interactions. Co₂Zn₁₁ is Pauli paramagnetic, although the density of states at the Fermi level is large, whereas Curie–Weiss behavior emerges for higher Co concentrations. Because Pd has a size and an electronegativity similar to those of Zn, and inspired by the pseudogaps in the electronic density of states curve of Co₂Zn₁₁, Pd-doped γ-brass compounds were designed and two new γ-brass compounds were obtained: Co_0.92(2)Pd_1.08Zn₁₁ and Co_2.50(1)Pd_2.50Zn₈. In these, the site preferences for Co and Pd can be rationalized by electronic structure calculations. The densities of states indicate that Co 3d states are the major contributors near their Fermi levels, with the Pd 4d band lying ∼2–3 eV below this. The magnetic properties of the Co–Pd–Zn γ-brasses are quite different from those of Co₂Zn₁₁: a giant magnetic moment on the Co atom is induced by the Pd atom, and Co_2.50(1)Pd_2.50Zn₈ shows magnetization consistent with a dilute ferrimagnet. The results of first-principles calculations on two different models of the 26-atom γ-brass clusters indicate that intracluster Co–Co exchange is ferromagnetic, whereas intercluster Co–Co exchange is antiferromagnetic. These different magnetic exchange interactions provide rationalization for the high-temperature magnetization behavior of Co_2.50(1)Pd_2.50Zn₈

Validation of Interstitial Iron and Consequences of Nonstoichiometry in Mackinawite (Fe_1+<i>x</i>S)

A theoretical investigation of the relationship between chemical composition and electronic structure was performed on the nonstoichiometric iron sulfide, mackinawite (Fe_1+xS), which is isostructural and isoelectronic with the superconducting Fe_1+<i>x</i>Se and Fe_1+<i>x</i>(Te_1–<i>y</i>Se_<i>y</i>) phases. Even though Fe_1+xS has not been measured for superconductivity, the effects of stoichiometry on transport properties and electronic structure in all of these iron-excess chalcogenide compounds has been largely overlooked. In mackinawite, the amount of Fe that has been reported ranges from a large excess, Fe_1.15S, to nearly stoichiometric, Fe_1.00(7)S. Here, we analyze, for the first time, the electronic structure of Fe_1+<i>x</i>S to justify these nonstoichiometric phases. First principles electronic structure calculations using supercells of Fe_1+<i>x</i>S yield a wide range of energetically favorable compositions (0 < <i>x</i> < 0.30). The incorporation of interstitial Fe atoms originates from a delicate balance between the Madelung energy and the occupation of Fe–S and Fe–Fe antibonding orbitals. A theoretical assessment of various magnetic structures for “FeS” and Fe_1.06S indicate that striped magnetic ordering along [110] is the lowest energy structure and the interstitial Fe affects the values of moments in the square planes as a function of distance. Moreover, the formation of the magnetic moment is dependent on the unit cell volume, thus relating it to composition. Finally, changes in the composition cause a modification of the Fermi surface and ultimately the loss of a nested vector

New Co–Pd–Zn γ‑Brasses with Dilute Ferrimagnetism and Co₂Zn₁₁ Revisited: Establishing the Synergism between Theory and Experiment

A synergism between electronic structure theory and the targeted synthesis of new ternary γ-brass compounds is demonstrated in the Co–Zn system. Co₂Zn₁₁, which adopts a cubic γ-brass structure, is shown to be at the Zn-rich end of a homogeneity range that varies from 15.4 to 22.1 atom % Co. Four samples were examined by single-crystal diffraction, all of which crystallize in space group <i>I</i>4̅3<i>m</i> with the lattice parameter ranging from 8.9851(1) to 8.8809(1) Å as the Co content increases. In the 26-atom γ-brass clusters, Co atoms preferentially occupy the outer tetrahedron (OT) sites and then replace Zn atoms at the octahedron (OH) sites at higher Co concentrations. In addition, a small fraction of vacancies occurs on the inner tetrahedron (IT) sites. The electronic structure of Co₂Zn₁₁ shows two distinct pseudogaps near the Fermi level: one at 292 valence electrons per primitive unit cell and the other at 302–304 valence electrons per primitive unit cell. Using molecular orbital arguments applied to the body-centered cubic packing of the 26-atom Co₄Zn₂₂ γ-brass cluster, these pseudogaps arise from (i) splitting among the valence s and p orbitals, which gives rise to the Hume–Rothery electron counting rule, and (ii) splitting within the manifold of Co 3d orbitals via Co–Zn orbital interactions. Co₂Zn₁₁ is Pauli paramagnetic, although the density of states at the Fermi level is large, whereas Curie–Weiss behavior emerges for higher Co concentrations. Because Pd has a size and an electronegativity similar to those of Zn, and inspired by the pseudogaps in the electronic density of states curve of Co₂Zn₁₁, Pd-doped γ-brass compounds were designed and two new γ-brass compounds were obtained: Co_0.92(2)Pd_1.08Zn₁₁ and Co_2.50(1)Pd_2.50Zn₈. In these, the site preferences for Co and Pd can be rationalized by electronic structure calculations. The densities of states indicate that Co 3d states are the major contributors near their Fermi levels, with the Pd 4d band lying ∼2–3 eV below this. The magnetic properties of the Co–Pd–Zn γ-brasses are quite different from those of Co₂Zn₁₁: a giant magnetic moment on the Co atom is induced by the Pd atom, and Co_2.50(1)Pd_2.50Zn₈ shows magnetization consistent with a dilute ferrimagnet. The results of first-principles calculations on two different models of the 26-atom γ-brass clusters indicate that intracluster Co–Co exchange is ferromagnetic, whereas intercluster Co–Co exchange is antiferromagnetic. These different magnetic exchange interactions provide rationalization for the high-temperature magnetization behavior of Co_2.50(1)Pd_2.50Zn₈

New Co–Pd–Zn γ‑Brasses with Dilute Ferrimagnetism and Co₂Zn₁₁ Revisited: Establishing the Synergism between Theory and Experiment

A synergism between electronic structure theory and the targeted synthesis of new ternary γ-brass compounds is demonstrated in the Co–Zn system. Co₂Zn₁₁, which adopts a cubic γ-brass structure, is shown to be at the Zn-rich end of a homogeneity range that varies from 15.4 to 22.1 atom % Co. Four samples were examined by single-crystal diffraction, all of which crystallize in space group <i>I</i>4̅3<i>m</i> with the lattice parameter ranging from 8.9851(1) to 8.8809(1) Å as the Co content increases. In the 26-atom γ-brass clusters, Co atoms preferentially occupy the outer tetrahedron (OT) sites and then replace Zn atoms at the octahedron (OH) sites at higher Co concentrations. In addition, a small fraction of vacancies occurs on the inner tetrahedron (IT) sites. The electronic structure of Co₂Zn₁₁ shows two distinct pseudogaps near the Fermi level: one at 292 valence electrons per primitive unit cell and the other at 302–304 valence electrons per primitive unit cell. Using molecular orbital arguments applied to the body-centered cubic packing of the 26-atom Co₄Zn₂₂ γ-brass cluster, these pseudogaps arise from (i) splitting among the valence s and p orbitals, which gives rise to the Hume–Rothery electron counting rule, and (ii) splitting within the manifold of Co 3d orbitals via Co–Zn orbital interactions. Co₂Zn₁₁ is Pauli paramagnetic, although the density of states at the Fermi level is large, whereas Curie–Weiss behavior emerges for higher Co concentrations. Because Pd has a size and an electronegativity similar to those of Zn, and inspired by the pseudogaps in the electronic density of states curve of Co₂Zn₁₁, Pd-doped γ-brass compounds were designed and two new γ-brass compounds were obtained: Co_0.92(2)Pd_1.08Zn₁₁ and Co_2.50(1)Pd_2.50Zn₈. In these, the site preferences for Co and Pd can be rationalized by electronic structure calculations. The densities of states indicate that Co 3d states are the major contributors near their Fermi levels, with the Pd 4d band lying ∼2–3 eV below this. The magnetic properties of the Co–Pd–Zn γ-brasses are quite different from those of Co₂Zn₁₁: a giant magnetic moment on the Co atom is induced by the Pd atom, and Co_2.50(1)Pd_2.50Zn₈ shows magnetization consistent with a dilute ferrimagnet. The results of first-principles calculations on two different models of the 26-atom γ-brass clusters indicate that intracluster Co–Co exchange is ferromagnetic, whereas intercluster Co–Co exchange is antiferromagnetic. These different magnetic exchange interactions provide rationalization for the high-temperature magnetization behavior of Co_2.50(1)Pd_2.50Zn₈

New Co–Pd–Zn γ‑Brasses with Dilute Ferrimagnetism and Co₂Zn₁₁ Revisited: Establishing the Synergism between Theory and Experiment

A synergism between electronic structure theory and the targeted synthesis of new ternary γ-brass compounds is demonstrated in the Co–Zn system. Co₂Zn₁₁, which adopts a cubic γ-brass structure, is shown to be at the Zn-rich end of a homogeneity range that varies from 15.4 to 22.1 atom % Co. Four samples were examined by single-crystal diffraction, all of which crystallize in space group <i>I</i>4̅3<i>m</i> with the lattice parameter ranging from 8.9851(1) to 8.8809(1) Å as the Co content increases. In the 26-atom γ-brass clusters, Co atoms preferentially occupy the outer tetrahedron (OT) sites and then replace Zn atoms at the octahedron (OH) sites at higher Co concentrations. In addition, a small fraction of vacancies occurs on the inner tetrahedron (IT) sites. The electronic structure of Co₂Zn₁₁ shows two distinct pseudogaps near the Fermi level: one at 292 valence electrons per primitive unit cell and the other at 302–304 valence electrons per primitive unit cell. Using molecular orbital arguments applied to the body-centered cubic packing of the 26-atom Co₄Zn₂₂ γ-brass cluster, these pseudogaps arise from (i) splitting among the valence s and p orbitals, which gives rise to the Hume–Rothery electron counting rule, and (ii) splitting within the manifold of Co 3d orbitals via Co–Zn orbital interactions. Co₂Zn₁₁ is Pauli paramagnetic, although the density of states at the Fermi level is large, whereas Curie–Weiss behavior emerges for higher Co concentrations. Because Pd has a size and an electronegativity similar to those of Zn, and inspired by the pseudogaps in the electronic density of states curve of Co₂Zn₁₁, Pd-doped γ-brass compounds were designed and two new γ-brass compounds were obtained: Co_0.92(2)Pd_1.08Zn₁₁ and Co_2.50(1)Pd_2.50Zn₈. In these, the site preferences for Co and Pd can be rationalized by electronic structure calculations. The densities of states indicate that Co 3d states are the major contributors near their Fermi levels, with the Pd 4d band lying ∼2–3 eV below this. The magnetic properties of the Co–Pd–Zn γ-brasses are quite different from those of Co₂Zn₁₁: a giant magnetic moment on the Co atom is induced by the Pd atom, and Co_2.50(1)Pd_2.50Zn₈ shows magnetization consistent with a dilute ferrimagnet. The results of first-principles calculations on two different models of the 26-atom γ-brass clusters indicate that intracluster Co–Co exchange is ferromagnetic, whereas intercluster Co–Co exchange is antiferromagnetic. These different magnetic exchange interactions provide rationalization for the high-temperature magnetization behavior of Co_2.50(1)Pd_2.50Zn₈

Rhombohedrally Distorted γ‑Au_5–<i>x</i>Zn_8+<i>y</i> Phases in the Au–Zn System

The region of the Au–Zn phase diagram encompassing γ-brass-type phases has been studied experimentally from 45 to 85 atom % Zn. The γ phases were obtained directly from the pure elements by heating to 680 °C in evacuated silica tubes, followed by annealing at 300 °C. Powder X-ray and single-crystal diffraction studies show that γ-“Au₅Zn₈” phases adopt a rhombohedrally distorted Cr₅Al₈ structure type rather than the cubic Cu₅Zn₈ type. The refined compositions from two single crystals extracted from the Zn- and Au-rich loadings are Au_4.27(3)Zn_8.26(3)□_0.47 (<b>I</b>) and Au_4.58(3)Zn_8.12(3)□_0.3 (<b>II</b>), respectively (□ = vacancy). These (<b>I</b> and <b>II</b>) refinements indicated both nonstatistical mixing of Au and Zn atoms as well as partially ordered vacancy distributions. The structures of these γ phases were solved in the acentric space group <i>R</i>3<i>m</i> (No. 160, <i>Z</i> = 6), and the observed lattice parameters from powder patterns were found to be <i>a</i> = 13.1029(6) and 13.1345(8) Å and <i>c</i> = 8.0410(4) and 8.1103(6) Å for crystals <b>I</b> and <b>II</b>, respectively. According to single-crystal refinements, the vacancies were found on the outer tetrahedron (OT) and octahedron (OH) of the 26-atom cluster. Single-crystal structural refinement clearly showed that the vacancy content per unit cell increases with increasing Zn, or valence-electron concentration. Electronic structure calculations, using the tight-binding linear muffin-tin orbital method with the atomic-sphere approximation (TB-LMTO-ASA) method, indicated the presence of a well-pronounced pseudogap at the Fermi level for “Au₅Zn₈” as the representative composition, an outcome that is consistent with the Hume–Rothery interpretation of γ brass

Rhombohedrally Distorted γ‑Au_5–<i>x</i>Zn_8+<i>y</i> Phases in the Au–Zn System

The region of the Au–Zn phase diagram encompassing γ-brass-type phases has been studied experimentally from 45 to 85 atom % Zn. The γ phases were obtained directly from the pure elements by heating to 680 °C in evacuated silica tubes, followed by annealing at 300 °C. Powder X-ray and single-crystal diffraction studies show that γ-“Au₅Zn₈” phases adopt a rhombohedrally distorted Cr₅Al₈ structure type rather than the cubic Cu₅Zn₈ type. The refined compositions from two single crystals extracted from the Zn- and Au-rich loadings are Au_4.27(3)Zn_8.26(3)□_0.47 (<b>I</b>) and Au_4.58(3)Zn_8.12(3)□_0.3 (<b>II</b>), respectively (□ = vacancy). These (<b>I</b> and <b>II</b>) refinements indicated both nonstatistical mixing of Au and Zn atoms as well as partially ordered vacancy distributions. The structures of these γ phases were solved in the acentric space group <i>R</i>3<i>m</i> (No. 160, <i>Z</i> = 6), and the observed lattice parameters from powder patterns were found to be <i>a</i> = 13.1029(6) and 13.1345(8) Å and <i>c</i> = 8.0410(4) and 8.1103(6) Å for crystals <b>I</b> and <b>II</b>, respectively. According to single-crystal refinements, the vacancies were found on the outer tetrahedron (OT) and octahedron (OH) of the 26-atom cluster. Single-crystal structural refinement clearly showed that the vacancy content per unit cell increases with increasing Zn, or valence-electron concentration. Electronic structure calculations, using the tight-binding linear muffin-tin orbital method with the atomic-sphere approximation (TB-LMTO-ASA) method, indicated the presence of a well-pronounced pseudogap at the Fermi level for “Au₅Zn₈” as the representative composition, an outcome that is consistent with the Hume–Rothery interpretation of γ brass

Turning Gold into “Diamond”: A Family of Hexagonal Diamond-Type Au-Frameworks Interconnected by Triangular Clusters in the Sr–Al–Au System

A new homologous series of intermetallic compounds containing three-dimensional (3-d) tetrahedral frameworks of gold atoms, akin to hexagonal diamond, have been discovered in four related Sr–Au–Al systems: (<b>I</b>) hexagonal SrAl_3–<i>x</i>Au_4+<i>x</i> (0.06(1) ≤ <i>x</i> ≤ 0.46(1), <i>P</i>6̅2<i>m</i>, <i>Z</i> = 3, <i>a</i> = 8.633(1)–8.664(1) Å, <i>c</i> = 7.083(2)–7.107(1) Å); (<b>II</b>) orthorhombic SrAl_2–<i>y</i>Au_5+<i>y</i> (<i>y</i> ≤ 0.05(1); <i>Pnma</i>, <i>Z</i> = 4, <i>a</i> = 8.942(1) Å, <i>b</i> = 7.2320(4) Å, <i>c</i> = 9.918(1) Å); (<b>III</b>) Sr₂Al_2–<i>z</i>Au_7+<i>z</i> (<i>z</i> = 0.32(2); <i>C</i>2<i>/c</i>, <i>Z</i> = 4, <i>a</i> = 14.956(4) Å, <i>b</i> = 8.564(2) Å, <i>c</i> = 8.682(1) Å, β = 123.86(1)°); and (<b>IV</b>) rhombohedral Sr₂Al_3–<i>w</i>Au_6+<i>w</i> (<i>w</i> ≈ 0.18(1); <i>R</i>3̅<i>c</i>, <i>Z</i> = 6, <i>a</i> = 8.448(1) Å, <i>c</i> = 21.735(4) Å). These remarkable compounds were obtained by fusion of the pure elements and were characterized by X-ray diffraction and electronic structure calculations. Phase <b>I</b> shows a narrow phase width and adopts the Ba₃Ag_14.6Al_6.4-type structure; phase <b>IV</b> is isostructural with Ba₂Au₆Zn₃, whereas phases <b>II</b> and <b>III</b> represent new structure types. This novel series can be formulated as Sr_<i>x</i>[M₃]_1–<i>x</i>Au₂, in which [M₃] (= [Al₃] or [Al₂Au]) triangles replace some Sr atoms in the hexagonal prismatic-like cavities of the Au network. The [M₃] triangles are either isolated or interconnected into zigzag chains or nets. According to tight-binding electronic structure calculations, the greatest overlap populations belong to the Al–Au bonds, whereas Au–Au interactions have a substantial nonbonding region surrounding the calculated Fermi levels. QTAIM analysis of the electron density reveals charge transfer from Sr to the Al–Au framework in all four systems. A study of chemical bonding by means of the electron-localizability indicator indicates two- and three-center interactions within the anionic Al–Au framework

Magnetic Ordering in Tetragonal 3d Metal Arsenides M₂As (M = Cr, Mn, Fe): An Ab Initio Investigation

The electronic and magnetic structures of the tetragonal Cu₂Sb-type 3d metal arsenides (M₂As, M = Cr, Mn, Fe) were examined using density functional theory to identify chemical influences on their respective patterns of magnetic order. Each compound adopts a different antiferromagnetic (AFM) ordering of local moments associated with the 3d metal sites, but every one involves a doubled crystallographic <i>c</i>-axis. These AFM ordering patterns are rationalized by the results of VASP calculations on several magnetically ordered models using <i>a</i> × <i>a</i> × 2<i>c</i> supercell. Effective exchange parameters obtained from SPRKKR calculations indicate that both direct and indirect exchange couplings play essential roles in understanding the different magnetic orderings observed. The nature of nearest-neighbor direct exchange couplings, that is, either ferromagnetic (FM) or AFM, were predicted by analysis of the corresponding crystal orbital Hamilton population (COHP) curves obtained by TB-LMTO calculations. Interestingly, the magnetic structures of Fe₂As and Mn₂As show tetragonal symmetry, but a magnetostrictive tetragonal-to-orthorhombic distortion could occur in Cr₂As through AFM Cr1–Cr2 coupling between symmetry inequivalent Cr atoms along the <i>a</i>-axis, but FM coupling along the <i>b</i>-axis. A LSDA+U approach is required to achieve magnetic moment values for Mn₂As in better agreement with experimental values, although computations always predict the moment at the M1 site to be lower than that at the M2 site. Finally, a rigid-band model applied to the calculated DOS curve of Mn₂As correctly assesses the magnetic ordering patterns in Cr₂As and Fe₂As