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

Density Functional Analysis of the Spin Exchange Interactions and Charge Order Patterns in the Layered Magnetic Oxides YBaM₂O₅ (M = Mn, Fe, Co)

The spin and charge order phenomena of the layered magnetic oxides YBaM₂O₅ (M = Mn, Fe, Co) were analyzed on the basis of density functional calculations. We evaluated the spin exchange interactions of YBaM₂O₅ by performing energy-mapping analysis based on density functional calculations to find why they undergo a three-dimensional magnetic ordering at high temperature. We estimated the relative stabilities of the checkerboard and stripe charge order patterns of YBaM₂O₅ (M = Mn, Fe, Co) by optimizing their structures with density functional calculations to probe if the nature of the charge order pattern depends on whether their transition-metal ions are Jahn–Teller active

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

Computational Design of Rare-Earth-Free Magnets with the Ti₃Co₅B₂‑Type Structure

The prolific Ti₃Co₅B₂ structure type has produced exciting materials with tunable magnetic properties, ranging from soft magnetic Ti₂FeRh₅B₂, to semihard magnetic Ti₂FeRu₄RhB₂ and hard magnetic Sc₂FeRu₃Ir₂B₂. Density functional theory (DFT) was employed to investigate their spin–orbit coupling effect, spin exchange, and magnetic dipole–dipole interactions in order to understand their magnetic anisotropy and relate it to their various coercivities, with the objective of being able to predict new materials with large magnetic anisotropy. Our calculations show that the contribution of magnetic dipole–dipole interactions to the magnetocrystalline anisotropy energy (MAE) in Ti₃Co₅B₂-type compounds is much weaker than the spin–orbit coupling effect, and Sc₂FeRu₃Ir₂B₂ has, by far, the largest MAE and strong intrachain and interchain Fe–Fe spin exchange coupling, thus confirming its hard magnetic properties. We then targeted materials containing the more earth-abundant and less expensive Co, instead of Rh, Ru or Ir, so that our study started with Ti₃Co₅B₂, which we found to be nonmagnetic. In the next step, substitutions on the Ti sites in Ti₃Co₅B₂ led to new potential quaternary phases with the general formula T₂T′Co₅B₂ (T = Ti, Hf; T′ = Mn, Fe). For Hf₂MnCo₅B₂, we found a large MAE (+0.96 meV/f.u.) but relatively weak interchain Mn–Mn spin exchange interactions, whereas for Hf₂FeCo₅B₂, there is a relatively smaller MAE (+0.17 meV/f.u.) but strong Fe–Fe interchain and intrachain spin exchange interactions. Therefore, these two Co-rich phases are predicted to be new rare-earth-free, semihard to hard magnetic materials

Valence State Driven Site Preference in the Quaternary Compound Ca₅MgAgGe₅: An Electron-Deficient Phase with Optimized Bonding

The quaternary phase Ca₅Mg_0.95­Ag_1.05(1)Ge₅ (<b>3</b>) was synthesized by high-temperature solid-state techniques, and its crystal structure was determined by single-crystal diffraction methods in the orthorhombic space group <i>Pnma</i> – Wyckoff sequence <i>c</i>¹² with <i>a</i> = 23.1481(4) Å, <i>b</i> = 4.4736(1) Å, <i>c</i> = 11.0128(2) Å, <i>V</i> = 1140.43(4) ų, <i>Z</i> = 4. The crystal structure can be described as linear intergrowths of slabs cut from the CaGe (CrB-type) and the CaMGe (TiNiSi-type; M = Mg, Ag) structures. Hence, <b>3</b> is a <i>hettotype</i> of the hitherto missing <i>n</i> = 3 member of the structure series with the general formula R_2+<i>n</i>T₂­X_2+<i>n</i>, previously described with <i>n</i> = 1, 2, and 4. The member with <i>n</i> = 3 was predicted in the space group <i>Cmcm</i> – Wyckoff sequence <i>f</i>⁵<i>c</i>². The experimental space group <i>Pnma</i> (in the nonstandard setting <i>Pmcn</i>) corresponds to a <i>klassengleiche</i> symmetry reduction of index two of the predicted space group <i>Cmcm</i>. This transition originates from the switching of one Ge and one Ag position in the TiNiSi-related slab, a process that triggers an uncoupling of each of the five 8<i>f</i> sites in <i>Cmcm</i> into two 4<i>c</i> sites in <i>Pnma</i>. The Mg/Ag site preference was investigated using VASP calculations and revealed a remarkable example of an intermetallic compound for which the electrostatic valency principle is a critical structure-directing force. The compound is deficient by one valence electron according to the Zintl concept, but LMTO electronic structure calculations indicate electronic stabilization and overall bonding optimization in the polyanionic network. Other stability factors beyond the Zintl concept that may account for the electronic stabilization are discussed

Linear Metal Chains in Ca₂M₂X (M = Pd, Pt; X = Al, Ge): Origin of the Pairwise Distortion and Its Role in the Structure Stability

A series of four new analogue phases Ca₂M₂X (M = Pd, Pt and X = Al, Ge) were prepared by direct combination of the respective elements in stoichiometric mixtures at high temperature in order to analyze the impact of valence electron count (vec) and electronegativity differences (Δχ) on the structure selection and stability. Their crystal structures, as determined from single-crystal X-ray diffraction data, correspond to two different but closely related structure types. The first compound, Ca₂Pd₂Ge (<b>I</b>), is an unprecedented ternary ordered variant of the Zr₂Al₃-type (orthorhombic, <i>Fdd</i>2). The three other phases, Ca₂Pt₂Ge (<b>II</b>), Ca₂Pd₂Al (<b>III</b>) and Ca₂Pt₂Al (<b>IV</b>), adopt the Gd₂Ge₂Al-type structure (monoclinic, <i>C</i>2/<i>c</i>). All title structures feature linear chains of the noble metals (Pd or Pt). The Pd linear chains in <b>I</b> are undistorted with equidistant Pd···Pd atoms, whereas the metal chains in <b>II–IV</b> are <i>pairwise</i> distorted, resulting in short connected {Pd₂} or {Pt₂} dumbbells that are separated by longer M···M contacts. The occurrence and magnitude of the pairing distortion in these chains are controlled by the <i>vec</i> and the Δχ between the constituent elements, a result which is supported by analysis of the calculated <i>Bader</i> effective charges. The metal chains act as charge modulation units, critical for the stability and the electronic flexibility of the structures by an adequate adjustment of the metal–metal bond order to both the <i>vec</i> and the degree of charge transfer. Thus, Ca₂Pd₂Ge (28 ve/f.u) is a Zintl-like, charge optimized phase with formally zerovalent Pd atoms forming the undistorted metal chains; semimetallic properties are predicted by TB-LMTO calculations. In contrast, the isoelectronic Ca₂Pt₂Ge is predicted to be a good metal with the Fermi level located at a local maximum of the DOS, a fingerprint of potential electronic instability. This is due to greater charge transfer to the more electronegative Pt atoms forming the metal chains and probably to packing frustration in the well packed structure that may prevent a larger distortion of the Pt chains. However, the instability is suppressed in the aliovalent but isostructural phases Ca₂M₂Al (27 ve/f.u) with an enhancement of the pairing distortion within the metal chains but lower M–M bond order. Further reduction of the <i>vec</i> as in Ca₂M₂Cd (26 ve/f.u) may induce a transition toward the more geometrically flexible W₂CoB₂-type with a low dimensional structure, to create more room for a larger distortion of the metal chain as dictated by the shortage of valence electrons

Spin Frustration and Magnetic Ordering from One-Dimensional Stacking of Cr₃ Triangles in TiCrIr₂B₂

Spin-frustrated chains of Cr₃ triangles are found in the new metal boride TiCrIr₂B₂ by synergistic experimental and theoretical investigations. Although magnetic ordering is found at 275 K, competing ferro- and anti-ferromagnetic interactions coupled with spin frustration induce a rather small total magnetic moment (0.05 μ_B at 5 T), and density functional theory (DFT) calculations propose a canted, nonlinear magnetic ground-state ordering in the new phase. TiCrIr₂B₂ crystallizes in the hexagonal Ti_1+<i>x</i>Os_2–<i>x</i>RuB₂ structure type (space group <i>P</i>6̅2<i>m</i>, No. 189, Pearson symbol <i>hP</i>18). The structure contains trigonal planar B₄ boron fragments with B–B distances of 1.76(3) Å alternating along the <i>c</i>-direction with Cr₃ triangles with intra- and intertriangle Cr–Cr distances of 2.642(9) and 3.185(1) Å, respectively. Magnetization measurements of TiCrIr₂B₂ reveal ferrimagnetic behavior and a large, negative Weiss constant of −750 K. DFT calculations demonstrate a strong site preference of Cr for the triangle sites, as well as magnetic frustration due to indirect anti-ferromagnetic interactions within the Cr₃ triangles

Unexpected Competition between Antiferromagnetic and Ferromagnetic States in Hf₂MnRu₅B₂: Predicted and Realized

Materials “design” is increasingly gaining importance in the solid-state materials community in general and in the field of magnetic materials in particular. Density functional theory (DFT) predicted the competition between ferromagnetic (FM) and antiferromagnetic (AFM) ground states in a ruthenium-rich Ti₃Co₅B₂-type boride (Hf₂MnRu₅B₂) for the first time. Vienna ab initio simulation package (VASP) total energy calculations indicated that the FM model was marginally more stable than one of the AFM models (AFM1), indicating very weak interactions between magnetic 1D Mn chains that can be easily perturbated by external means (magnetic field or composition). The predicted phase was then synthesized by arc-melting and characterized as Hf₂Mn_1–<i>x</i>Ru_5+<i>x</i>B₂ (<i>x</i> = 0.27). Vibrating-scanning magnetometry shows an AFM ground state with <i>T</i>_N ≈ 20 K under low magnetic field (0.005 T). At moderate-to-higher fields, AFM ordering vanishes while FM ordering emerges with a Curie temperature of 115 K. These experimental outcomes confirm the weak nature of the interchain interactions, as predicted by DFT calculations

Spin Frustration and Magnetic Ordering from One-Dimensional Stacking of Cr₃ Triangles in TiCrIr₂B₂

Spin-frustrated chains of Cr₃ triangles are found in the new metal boride TiCrIr₂B₂ by synergistic experimental and theoretical investigations. Although magnetic ordering is found at 275 K, competing ferro- and anti-ferromagnetic interactions coupled with spin frustration induce a rather small total magnetic moment (0.05 μ_B at 5 T), and density functional theory (DFT) calculations propose a canted, nonlinear magnetic ground-state ordering in the new phase. TiCrIr₂B₂ crystallizes in the hexagonal Ti_1+<i>x</i>Os_2–<i>x</i>RuB₂ structure type (space group <i>P</i>6̅2<i>m</i>, No. 189, Pearson symbol <i>hP</i>18). The structure contains trigonal planar B₄ boron fragments with B–B distances of 1.76(3) Å alternating along the <i>c</i>-direction with Cr₃ triangles with intra- and intertriangle Cr–Cr distances of 2.642(9) and 3.185(1) Å, respectively. Magnetization measurements of TiCrIr₂B₂ reveal ferrimagnetic behavior and a large, negative Weiss constant of −750 K. DFT calculations demonstrate a strong site preference of Cr for the triangle sites, as well as magnetic frustration due to indirect anti-ferromagnetic interactions within the Cr₃ triangles

MOESM1 of Association between homocysteine level and the risk of diabetic retinopathy: a systematic review and meta-analysis

Additional file 1. Meta-regression