Competing Magnetic Interactions in the Antiferromagnetic Topological Insulator MnBi_{2}Te_{4}.

The antiferromagnetic (AFM) compound MnBi_{2}Te_{4} is suggested to be the first realization of an AFM topological insulator. We report on inelastic neutron scattering studies of the magnetic interactions in MnBi_{2}Te_{4} that possess ferromagnetic triangular layers with AFM interlayer coupling. The spin waves display a large spin gap and pairwise exchange interactions within the triangular layer are long ranged and frustrated by large next-nearest neighbor AFM exchange. The degree of frustration suggests proximity to a variety of magnetic phases, potentially including skyrmion phases, which could be accessed in chemically tuned compounds or upon the application of symmetry-breaking fields.

Electronic and Structural Factors Controlling the Spin Orientations of Magnetic Ions.

Magnetic ions M in discrete molecules and extended solids form MLn complexes with their first-coordinate ligand atoms L. The spin moment of M in a complex MLn prefers a certain direction in coordinate space because of spin-orbit coupling (SOC). In this minireview, we examine the structural and electronic factors governing the preferred spin orientations. Elaborate experimental measurements and/or sophisticated computational efforts are required to find the preferred spin orientations of magnetic ions, largely because the energy scale of SOC is very small. The latter is also the very reason why one can readily predict the preferred spin orientation of M by analyzing the SOC-induced highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) interactions of the MLn complexes in terms of qualitative perturbation theory. The strength of this HOMO-LUMO interaction depends on the spin orientation, which is governed by the selection rules based on the minimum |ΔLz| value (i.e., the minimum difference in the magnetic quantum numbers) between the HOMO and LUMO. With the local z axis of MLn chosen as its n-fold rotational axis, the preferred spin orientation is parallel to the z axis (∥z) when |ΔLz| = 0 but perpendicular to the z axis (⊥z) when |ΔLz| = 1.

Spin-Density Wave as a Superposition of Two Magnetic States of Opposite Chirality and Its Implications.

A magnetic solid with weak spin frustration tends to adopt a noncollinear magnetic structure such as a cycloidal structure below a certain temperature and a spin-density wave (SDW) slightly above this temperature. The causes for these observations were explored by studying the magnetic structure of BaYFeO4, which undergoes a SDW and a cycloidal phase transition below 48 and 36 K, respectively, in terms of the density functional theory calculations. We show that a SDW structure arises from a superposition of two magnetic states of opposite chirality, an SDW state precedes a chiral magnetic state because of the lattice relaxation, and whether a SDW is transversal or longitudinal is governed by the magnetic anisotropy of magnetic ions.

Nonequivalent Spin Exchanges of the Hexagonal Spin Lattice Affecting the Low-Temperature Magnetic Properties of RInO3 (R = Gd, Tb, Dy): Importance of Spin-Orbit Coupling for Spin Exchanges between Rare-Earth Cations with Nonzero Orbital Moments.

Rare-earth indium oxides RInO3 (R = Gd, Tb, Dy) consist of spin-frustrated hexagonal spin lattices made up of rare-earth ions R3+, where R3+ = Gd3+ (f7, L = 0), Tb3+ (f8, L = 3), and Dy3+ (f9, L = 5). We carried out DFT calculations for RInO3, including on-site repulsion U with/without spin-orbit coupling (SOC), to explore if their low-temperature magnetic properties are related to the two nonequivalent nearest-neighbor (NN) spin exchanges of their hexagonal spin lattices. Our DFT + U + SOC calculations predict that the orbital moments of the Tb3+ and Dy3+ ions are smaller than their free-ion values by ∼2µB while the Tb3+ spins have an in-plane magnetic anisotropy, in agreement with the experiments. This suggests that the f orbitals of each R3+ (R = Tb, Dy) ion are engaged, though weakly, in bonding with the surrounding ligand atoms. The magnetic properties of GdInO3 with the zero orbital moment are adequately described by the spin exchanges extracted by DFT + U calculations. In describing the magnetic properties of TbInO3 and DyInO3 with nonzero orbital moments, however, the spin exchanges extracted by DFT + U + SOC calculations are necessary. The spin exchanges of RInO3 (R = Gd, Tb, Dy) are dominated by the two NN spin exchanges J1 and J2 of their hexagonal spin lattice, in which the honeycomb lattice of J2 forms spin-frustrated ( J1, J1, J2) triangles. The J2/ J1 ratios are calculated to be ∼3, ∼1.7, and ∼1 for GdInO3, TbInO3, and DyInO3, respectively. This suggests that the antiferromagnetic (AFM) ordering of GdInO3 below 1.8 K is most likely an AFM ordering of its honeycomb spin lattice and that TbInO3 would exhibit low-temperature magnetic properties similar to those of GdInO3 while DyInO3 would not.

A2MnXO4 Family (A = Li, Na, Ag; X = Si, Ge): Structural and Magnetic Properties.

Four new manganese germanates and silicates, A2MnGeO4 (A = Li, Na) and A2MnSiO4 (A = Na, Ag), were prepared, and their crystal structures were determined using the X-ray Rietveld method. All of them contain all components in tetrahedral coordination. Li2MnGeO4 is orthorhombic (Pmn21) layered, isostructural with Li2CdGeO4, and the three other compounds are monoclinic (Pn) cristobalite-related frameworks. As in other stuffed cristobalites of various symmetry (Pn A2MXO4, Pna21 and Pbca AMO2), average bond angles on bridging oxygens (here, Mn-O-X) increase with increasing A/X and/or A/M radius ratios, indicating the trend to the ideal cubic (Fd3̅m) structure typified by CsAlO2. The sublattices of the magnetic Mn2+ ions in both structure types under study (Pmn21 and Pn) are essentially the same; namely, they are pseudocubic eutaxy with 12 nearest neighbors. The magnetic properties of the four new phases plus Li2MnSiO4 were characterized by carrying out magnetic susceptibility, specific heat, magnetization, and electron spin resonance measurements and also by performing energy-mapping analysis to evaluate their spin exchange constants. Ag2MnSiO4 remains paramagnetic down to 2 K, but A2MnXO4 (A = Li, Na; X = Si, Ge) undergo a three-dimensional antiferromagnetic ordering. All five phases exhibit short-range AFM ordering correlations, hence showing them to be low-dimensional magnets and a magnetic field induced spin-reorientation transition at T < TN for all AFM phases. We constructed the magnetic phase diagrams for A2MnXO4 (A = Li, Na; X = Si, Ge) on the basis of the thermodynamic data in magnetic fields up to 9 T. The magnetic properties of all five phases experimentally determined are well explained by their spin exchange constants evaluated by performing energy-mapping analysis.

Group of Quantum Bits Acting as a Bit Using a Single-Domain Ferromagnet of Uniaxial Magnetic Ions.

Read/write operations with individual quantum bits (i.e., qbits) are a challenging problem to solve in quantum computing. To alleviate this difficulty, we considered the possibility of using a group of qbits that act collectively as a bit (hereafter, a group bit or a gbit, in short). A promising candidate for a gbit is a single-domain ferromagnet (SDF) independent of its size, which can be prepared as a magnet of well-separated uniaxial magnetic ions (UMIs) at sites of no electric dipole moment with their uniaxial axes aligned along one common direction. When magnetized, the UMIs of such a magnet have a ferromagnetic (FM) arrangement and the resulting SDF becomes a gbit with its two opposite moment orientations representing the |0⟩ and |1⟩ states of a bit. We probed the requirements for such magnets and identified several 2H-perovskites as materials satisfying these requirements.

Single-Domain Ferromagnet of Noncentrosymmetric Uniaxial Magnetic Ions and Magnetoelectric Interaction.

The feasibility of a single-domain ferromagnet based on uniaxial magnetic ions was examined. For a noncentrosymmetric uniaxial magnetic ion of magnetic moment µ at a site of local electric dipole moment p, it is unknown to date whether µ prefers to be parallel or antiparallel to µ. The nature of this magnetoelectric interaction was probed in terms of analogical reasoning based on the Rashba effect and density functional theory (DFT) calculations. We show that µ and p prefer an antiparallel arrangement, predict that Fe-doped CaZnOS is a single-domain ferromagnet like a bar magnet, and find the probable cause for the ferromagnetism and weak magnetization hysteresis in Fe-doped hexagonal ZnO and ZnS at very low dopant concentrations.

Superconductivity Induced by Oxygen Doping in Y2 O2 Bi.

When doped with oxygen, the layered Y2 O2 Bi phase becomes a superconductor. This finding raises questions about the sites for doped oxygen, the mechanism of superconductivity, and practical guidelines for discovering new superconductors. We probed these questions in terms of first-principles calculations for undoped and O-doped Y2 O2 Bi. The preferred sites for doped O atoms are the centers of Bi4 squares in the Bi square net. Several Bi 6p x/y bands of Y2 O2 Bi are raised in energy by oxygen doping because the 2p x/y orbitals of the doped oxygen make antibonding possible with the 6p x/y orbitals of surrounding Bi atoms. Consequently, the condition necessary for the "flat/steep" band model for superconductivity is satisfied in O-doped Y2 O2 Bi.

A small bandgap semiconductor, p-type MnV2O6, active for photocatalytic hydrogen and oxygen production.

Extensive research has been conducted with the goal to find a single bandgap material that can absorb visible light and efficiently drive the catalysis of water to both hydrogen and oxygen. The p-type MnV2O6 (C2/m, Z = 2, a = 9.289 Å, b = 3.535 Å, and c = 6.763 Å, ß = 112.64°), synthesized via solid-state techniques, was investigated for its potential use in the visible-light photocatalysis of water. Mott-Schottky analysis was used to experimentally determine the energetic positions of the valence and conduction bands as +0.985 V and -0.464 V, respectively, at pH 5.68 vs. RHE. These are found to be suitable potentials to drive the reduction and oxidation of water under irradiation. The bandgap transitions, probed using spin-polarized density functional calculations, consist of the excitation of electrons from the half-filled Mn 3d5 orbitals to the empty V 3d0 orbitals. Both hydrogen and oxygen gas were observed as products during suspended-particle photocatalysis experiments under visible-light irradiation. The rate and total moles of gas produced were found to increase with the reaction temperature. As the temperature was raised from 30 °C to 37 °C and 44 °C, the moles of hydrogen produced over 6 hours increased by ∼1.5 and ∼2.5 times. Only oxygen is produced in pure water, showing that methanol is needed to drive hydrogen production.

Fine-Tuning the Properties of Doped Multifunctional Materials by Controlled Reduction of Dopants.

The physical properties of doped multifunctional compounds are commonly tuned by controlling the amount of dopants, but this control is limited because all the properties are influenced simultaneously by this single parameter. Here, we present a strategy that enables the fine-tuning of a specific combination of properties by controlling the reduction of dopants. The feasibility of this approach was demonstrated by optimizing the near-IR photoluminescence of strontium titanate SrTiO3 :Ni for potential applications in biomedicine for a range of absorbance in the visible/near-IR region. We discussed how material properties, such as luminescence, conductivity, or photocatalytic properties can be designed by carefully controlling the ratio of dopants in different oxidation states.

Condensed-matter equation of states covering a wide region of pressure studied experimentally.

The relationships among the pressure P, volume V, and temperature T of solid-state materials are described by their equations of state (EOSs), which are often derived from the consideration of the finite-strain energy or the interatomic potential. These EOSs consist of typically three parameters to determine from experimental P-V-T data by fitting analyses. In the empirical approach to EOSs, one either refines such fitting parameters or improves the mathematical functions to better simulate the experimental data. Despite over seven decades of studies on EOSs, none has been found to be accurate for all types of solids over the whole temperature and pressure ranges studied experimentally. Here we show that the simple empirical EOS, P = α1(PV) + α2(PV)2 + α3(PV)3, in which the pressure P is indirectly related to the volume V through a cubic polynomial of the energy term PV with three fitting parameters α1 − α3, provides accurate descriptions for the P-vs-V data of condensed matter in a wide region of pressure studied experimentally even in the presence of phase transitions.

Spin orientations of the spin-half Ir(4+) ions in Sr3NiIrO6, Sr2IrO4, and Na2IrO3: Density functional, perturbation theory, and Madelung potential analyses.

The spins of the low-spin Ir(4+) (S = 1/2, d(5)) ions at the octahedral sites of the oxides Sr3NiIrO6, Sr2IrO4, and Na2IrO3 exhibit preferred orientations with respect to their IrO6 octahedra. We evaluated the magnetic anisotropies of these S = 1/2 ions on the basis of density functional theory (DFT) calculations including spin-orbit coupling (SOC), and probed their origin by performing perturbation theory analyses with SOC as perturbation within the LS coupling scheme. The observed spin orientations of Sr3NiIrO6 and Sr2IrO4 are correctly predicted by DFT calculations, and are accounted for by the perturbation theory analysis. As for the spin orientation of Na2IrO3, both experimental studies and DFT calculations have not been unequivocal. Our analysis reveals that the Ir(4+) spin orientation of Na2IrO3 should have nonzero components along the c- and a-axis directions. The spin orientations determined by DFT calculations are sensitive to the accuracy of the crystal structures employed, which is explained by perturbation theory analyses when interactions between adjacent Ir(4+) ions are taken into consideration. There are indications implying that the 5d electrons of Na2IrO3 are less strongly localized compared with those of Sr3NiIrO6 and Sr2IrO4. This implication was confirmed by showing that the Madelung potentials of the Ir(4+) ions are less negative in Na2IrO3 than in Sr3NiIrO6 and Sr2IrO4. Most transition-metal S = 1/2 ions do have magnetic anisotropies because the SOC induces interactions among their crystal-field split d-states, and the associated mixing of the states modifies only the orbital parts of the states. This finding cannot be mimicked by a spin Hamiltonian because this model Hamiltonian lacks the orbital degree of freedom, thereby leading to the spin-half syndrome. The spin-orbital entanglement for the 5d spin-half ions Ir(4+) is not as strong as has been assumed.

Structure and Composition of the 200†K-Superconducting Phase of H2 S at Ultrahigh Pressure: The Perovskite (SH(-) )(H3 S(+) ).

At ultrahigh pressure (>110 GPa), H2 S is converted into a metallic phase that becomes superconducting with a record Tc of approximately 200 K. It has been proposed that the superconducting phase is body-centered cubic H3 S (Im3‾ m, a=3.089 Å) resulting from the decomposition reaction 3 H2 S→2 H3 S+S. The analogy between H2 S and H2 O led us to a very different conclusion. The well-known dissociation of water into H3 O(+) and OH(-) increases by orders of magnitude under pressure. H2 S is anticipated to behave similarly under pressure, with the dissociation process 2 H2 S→H3 S(+) +SH(-) leading to the perovskite structure (SH(-) )(H3 S(+) ). This phase consists of corner-sharing SH6 octahedra with SH(-) ions at each A site (the centers of the S8 cubes). DFT calculations show that the perovskite (SH(-) )(H3 S(+) ) is thermodynamically more stable than the Im3‾ m structure of H3 S, and suggest that the A site hydrogen atoms are most likely fluxional even at Tc .

Ionic Liquid Character of Zinc Chloride Hydrates Define Solvent Characteristics that Afford the Solubility of Cellulose.

The recently described ionic liquid structure of the three equivalent hydrate of zinc chloride (ZnCl2·R H2O, R = 3, existing as [Zn(OH2)6][ZnCl4]) explains the solubility of cellulose in this medium. Only hydrate compositions in the narrow range of 3 - x < R < 3 + x with x ≈ 1 dissolve cellulose. Once dissolved, the cellulose remains in solution up to the R = 9 hydrate. Neutron diffraction and differential pair distribution function analysis of cellulose and model compound solutions (1 wt % cellulose in the R = 3 hydrate and 1 wt % ethanol in the R = 3 hydrate and the ZnCl2·3 ethanol liquid) coupled with detailed solubility measurements suggest that cellulose solubility occurs via coordination of the primary OH to the hydrated zinc cation with ring hydroxyls forming part of a second coordination shell around the cation of the ionic liquid.

Prediction of Spin Orientations in Terms of HOMO-LUMO Interactions Using Spin-Orbit Coupling as Perturbation.

For most chemists and physicists, electron spin is merely a means needed to satisfy the Pauli principle in electronic structure description. However, the absolute orientations of spins in coordinate space can be crucial in understanding the magnetic properties of materials with unpaired electrons. At low temperature, the spins of a magnetic solid may undergo long-range magnetic ordering, which allows one to determine the directions and magnitudes of spin moments by neutron diffraction refinements. The preferred spin orientation of a magnetic ion can be predicted on the basis of density functional theory (DFT) calculations including electron correlation and spin-orbit coupling (SOC). However, most chemists and physicists are unaware of how the observed and/or calculated spin orientations are related to the local electronic structures of the magnetic ions. This is true even for most crystallographers who determine the directions and magnitudes of spin moments because, for them, they are merely the parameters needed for the diffraction refinements. The objective of this article is to provide a conceptual framework of thinking about and predicting the preferred spin orientation of a magnetic ion by examining the relationship between the spin orientation and the local electronic structure of the ion. In general, a magnetic ion M (i.e., an ion possessing unpaired spins) in a solid or a molecule is surrounded with main-group ligand atoms L to form an MLn polyhedron, where n is typically 4-6, and the d states of MLn are split because the antibonding interactions of the metal d orbitals with the p orbitals of the surrounding ligands L depend on the symmetries of the orbitals involved.1 The magnetic ion M of MLn has a certain preferred spin direction because its split d states interact among themselves under SOC.2,3 The preferred spin direction can be readily predicted on the basis of perturbation theory in which the SOC is taken as perturbation and the split d states as unperturbed states by inspecting the magnetic quantum numbers of its d orbitals present in the HOMO and LUMO of the MLn polyhedron. This is quite analogous to how chemists predict whether a chemical reaction is symmetry-allowed or symmetry-forbidden in terms of the HOMO-LUMO interactions by simply inspecting the symmetries of the frontier orbitals.4,5 Experimentally, the determination of the preferred spin orientations of magnetic ions requires a sophisticated level of experiments, for example, neutron diffraction measurements for magnetic solids with an ordered spin state at a very low temperature. Theoretically, it requires an elaborate level of electronic structure calculations, namely, DFT calculations including electron correlation and SOC. We show that the outcomes of such intricate experimental measurements and theoretical calculations can be predicted by a simple perturbation theory analysis.

Synthesis of the Layered Quaternary Uranium-Containing Oxide Cs2Mn3U6O22 and Characterization of its Magnetic Properties.

A layered quaternary uranium-containing oxide, Cs2Mn3U6O22, was crystallized from a cesium chloride flux. The crystal structure was determined to consist of α-U3O8 topological layers that are separated by alternating cesium and manganese layers. This ordered arrangement creates a separation between manganese layers of 13 Å, leading to complex low-dimensional magnetic properties. The compound crystallizes in a new structure type in the monoclinic space group, C2/m, with a = 6.8730(10) Å, b = 11.7717(17) Å, c = 13.374(2) Å, and ß = 99.673(5)°. The magnetic properties were measured and analyzed by first-principles density functional theory calculations.