Electronic and Structural Factors Controlling the Spin Orientations of Magnetic Ions

Tunable valley polarization effect and second-order topological state in monolayer FeClSH

In two-dimensional (2D) materials, breaking the inversion symmetry plays an important role in valleytronics. Ferrovalley (FV) materials can achieve spontaneous valley polarization (VP) without additional modulation due to the magnetic exchange interaction and strong spin-orbit coupling. Using first-principles calculations, we predict a new 2D material, Janus FeClSH, which exhibits a large spontaneous VP. This monolayer is a perfect FV material, where the valence band maximum and conduction band minimum are located at the K/K' point. A large VP of 102.95 meV is spontaneously generated for the case of out-of-plane magnetization. Additionally, we propose that the irradiating circularly polarized light can be used to realize VP for the case of in-plane magnetization. Remarkably, a triangular nanoflake of FeClSH with armchair edges can show nontrivial corner states, exhibiting a second-order topological insulator (SOTI) state. The VP effect and SOTI state are tunable with the Hubbard U parameter, making the FeClSH monolayer promising for the study of the coupling between VP and SOTI.

Spectroscopic and Magnetic Studies of Co(II) Scorpionate Complexes: Is There a Halide Effect on Magnetic Anisotropy?

The observation of single-molecule magnetism in transition-metal complexes relies on the phenomenon of zero-field splitting (ZFS), which arises from the interplay of spin-orbit coupling (SOC) with ligand-field-induced symmetry lowering. Previous studies have demonstrated that the magnitude of ZFS in complexes with 3d metal ions is sometimes enhanced through coordination with heavy halide ligands (Br and I) that possess large free-atom SOC constants. In this study, we systematically probe this "heavy-atom effect" in high-spin cobalt(II)-halide complexes supported by substituted hydrotris(pyrazol-1-yl)borate ligands (Tp^tBu,Me and Tp^Ph,Me). Two series of complexes were prepared: [Co^IIX(Tp^tBu,Me)] (1-X; X = F, Cl, Br, and I) and [Co^IIX(Tp^Ph,Me)(Hpz^Ph,Me)] (2-X; X = Cl, Br, and I), where Hpz^Ph,Me is a monodentate pyrazole ligand. Examination with dc magnetometry, high-frequency and -field electron paramagnetic resonance, and far-infrared magnetic spectroscopy yielded axial (D) and rhombic (E) ZFS parameters for each complex. With the exception of 1-F, complexes in the four-coordinate 1-X series exhibit positive D-values between 10 and 13 cm^-1, with no dependence on halide size. The five-coordinate 2-X series exhibit large and negative D-values between -60 and -90 cm^-1. Interpretation of the magnetic parameters with the aid of ligand-field theory and ab initio calculations elucidated the roles of molecular geometry, ligand-field effects, and metal-ligand covalency in controlling the magnitude of ZFS in cobalt-halide complexes.

Enhanced Intrinsic Anomalous Valley Hall Effect Induced by Spin-Orbit Coupling in MXene Monolayer M3N2O2 (M = Y, La)

The limitation of suitable anomalous valley Hall effect (AVHE) materials has seriously hindered the booming development and the widespread application of valleytronics. Here, through the first-principles calculations, we propose a MXene monolayer Y₃N₂O₂ with spontaneous valley polarization (VP) of 21.3 meV, which induces intrinsic AVHE. The VP can be modulated linearly, which provides a route of effective control of the valley signals. Importantly, VP can be enhanced by adjusting up the spin-orbit coupling (SOC) based on a SOC Hamiltonian model and the first-principles calculations. From this physics underlying, we substitute the Y atom with the La atom and further propose the monolayer La₃N₂O₂, in which the heavy atom La will provide stronger SOC than Y atom. The spontaneous VP in La₃N₂O₂ is enhanced to 100.4 meV, so AVHE can be easily achieved. Our work not only provides compelling candidates for AVHE materials but also offers a novel mindset for finding suitable valleytronic devices.

Spontaneous Valley Polarization in a Ferromagnetic Fe(OH)2 Monolayer

At present, creating sizable spontaneous valley polarization is at the center of the study of valleytronics, which, however, is still a huge challenge. In this work, we determined that the ferromagnetic Fe(OH)₂ monolayer of the hexagonal lattice is a highly appealing candidate for valleytronics by using first-principles calculations in conjunction with tight-binding model analysis. In light of the simultaneous inversion symmetry breaking and time-reversal symmetry breaking, we illustrated that the strong spin-orbit coupling and robust ferromagnetic exchange interaction cause a spontaneous valley polarization as large as 67 meV for Fe(OH)₂, indicative of room-temperature application. In addition, the physics of valley-selective circular dichroism, spin/valley Hall effects, and topological phase transition were also discussed.

2D electrene LaH2monolayer: an ideal ferrovalley direct semiconductor with room-temperature ferromagnetic stability

In developing nonvolatile valleytronic devices, ferromagnetic (FM) ferrovalley semiconductors are critically needed due to the existence of spontaneous valley polarization. At present, however, the known real materials have various drawbacks towards practical applications, including the in-plane FM ground state, low Curie temperature (TC), small valley polarization, narrow energy window with clean polarized valley, and indirect bandgap. From first-principles calculations, here we predict anideal ferrovalley semiconductor, honeycomb LaH₂monolayer (ML), whose intrinsic properties can overcome all these shortcomings. We demonstrate that LaH₂ML, having satisfied structural stability, is a FM half-semiconducting electrene (La3+2H-⋅e-) with its magnetic moments localized at the lattice interstitial sites rather than La atoms. At the same time, LaH₂ML holds the following desired attributes: a robust out-of-plane FM ground state with a highTC(334 K), a sizable valley polarization (166 meV), a wide energy window (137 meV) harboring clean single-valley carriers, and a direct bandgap. These results identify a much needed ideal ferrovalley semiconductor candidate, holding the promising application potential in valleytronics and spintronics devices.

Spontaneous Valley Polarization and Electrical Control of Valley Physics in Single-Layer TcIrGe2S6

The modulation of valley polarization in one single system is of important fundamental and practical importance in quantum information technology. Here, through the first-principles calculations, we identify single-layer TcIrGe₂S₆ as a tantalizing candidate for realizing the modulation of valley polarization. Arising from the combination of inversion symmetry breaking and intrinsic magnetic exchange interaction, single-layer TcIrGe₂S₆ exhibits spontaneous valley polarization. The value of valley polarization in the conduction band is 161 meV, favorable for achieving the intriguing anomalous valley Hall effect. Furthermore, single-layer TcIrGe₂S₆ possesses ferroelectric order. More remarkably, its ferroelectric and valley physics can be strongly coupled, namely, the valley properties can be switched off and on electrically. These findings not only provide a compelling candidate for two-dimensional valleytronic research but also open a new avenue for modulating valley physics.

Skin-Deep Aspect of Thermopower in Bi2Q3, PbQ, and BiCuQO (Q = Se, Te): Hidden One-Dimensional Character of Their Band Edges Leading to High Thermopower

ConspectusThermoelectric (TE) materials have received much attention because of their ability to convert heat energy to electrical energy. At a given temperature T, the efficiency of a TE material for this energy conversion is measured by the figure of merit zT, which is related to the thermopower (or Seebeck coefficient) S, the thermal conductivity κ, and the electrical conductivity σ of the TE material as zT = (S²σT)/κ. Bi₂Q₃ and PbQ (Q = Se, Te) are efficient TE materials with high zT, although they are not ecofriendly and their stability is poor at high temperature. In principle, a TE material can have a high zT if it has a low thermal conductivity and a high electrical conductivity, but the latter condition is hardly met in a real material because the parameters S, σ and κ have a conflicting dependence on material properties. The difficulty in searching for TE materials of high zT is even more exasperated because the relationship between the thermopower S and the carrier density n (hereafter, the S-vs-n relationship) for the well-known hole-doped samples of BiCuSeO showed that the hole carriers responsible for their thermopower are associated largely with the electronic states lying within ∼0.5 eV of its valence band maximum (VBM). Thus, the states governing the TE properties lie in the "skin-deep" region from the VBM. For electron-doped TE systems, the electron carriers responsible for their thermopower should also be associated with the electronic states lying within ∼0.5 eV of the conduction band minimum (CBM). This makes it difficult to predict TE materials of high zT. One faces a similar skin-deep phenomenon in searching for superconductors of high transition temperature because the transition from a normal metallic to a superconducting state involves the normal metallic states in the vicinity of the Fermi level E_F. Other skin-deep phenomena in metallic compounds include the formation of charge density wave (CDW), which involves the electronic states in the vicinity of their Fermi levels. For magnetic materials of transition-metal ions, the preferred orientation of their spin moments is a skin-deep phenomenon because it is governed by the interaction between the highest-occupied and the lowest unoccupied d-states of these ions. In the present work we probe the issues concerning how to find the possible range of thermopower expected for a given TE material and hence how to recognize what experimental values of thermopower are expected or unusual. For these purposes, we analyze the accumulated S and n data on the three well-studied TE materials, Bi₂Q₃, PbQ, and BiCuQO (Q = Se, Te), as representative examples, in terms of the ideal theoretical S-vs-n relationships, which we determine for their defect-free Bi₂Q₃, PbQ, and BiCuQO structures using density functional theory (DFT) calculations under the rigid band approximation. We find that the general trends in the experimental S-vs-n relationships are reasonably well explained by the calculated S-vs-n relationships, and the carrier densities covering these relationships are associated with the states lying within ∼0.5 eV from their band edges confirming the skin-deep nature of their thermoelectric properties. Despite the fact that these TE materials are not one-dimensional (1D) in structure, they mostly possess sharp density-of-state peaks around their band edges because their band dispersions have a hidden 1D character so their thermopower is generally high in magnitude.

Large easy-axis magnetic anisotropy in a series of trigonal prismatic mononuclear cobalt (II) complexes with zero-field hidden single-molecule magnet behaviour: The important role of the distortion of the coordination sphere and intermolecular interactions on the slow relaxation

The complexes [Co(L)]X·S (X = CoCl42- , S = CH3CN (1); X = ZnCl42- , S = CH3OH (2)), [Co(L)]X2·S (X = ClO4-, S = 2CH3OH (3) and X =...

Unusual Spin Exchanges Mediated by the Molecular Anion P2S64-: Theoretical Analyses of the Magnetic Ground States, Magnetic Anisotropy and Spin Exchanges of MPS3 (M = Mn, Fe, Co, Ni)

We examined the magnetic ground states, the preferred spin orientations and the spin exchanges of four layered phases MPS3 (M = Mn, Fe, Co, Ni) by first principles density functional theory plus onsite repulsion (DFT + U) calculations. The magnetic ground states predicted for MPS3 by DFT + U calculations using their optimized crystal structures are in agreement with experiment for M = Mn, Co and Ni, but not for FePS3. DFT + U calculations including spin-orbit coupling correctly predict the observed spin orientations for FePS3, CoPS3 and NiPS3, but not for MnPS3. Further analyses suggest that the ||z spin direction observed for the Mn2+ ions of MnPS3 is caused by the magnetic dipole-dipole interaction in its magnetic ground state. Noting that the spin exchanges are determined by the ligand p-orbital tails of magnetic orbitals, we formulated qualitative rules governing spin exchanges as the guidelines for discussing and estimating the spin exchanges of magnetic solids. Use of these rules allowed us to recognize several unusual exchanges of MPS3, which are mediated by the symmetry-adapted group orbitals of P2S64- and exhibit unusual features unknown from other types of spin exchanges.

Orbital Magnetic Moments of the High-Spin Co2+ Ions at Axially-Elongated Octahedral Sites: Unquenched as Reported from Experiment or Quenched as Predicted by Theory?

Neutron diffraction studies on magnetic solids composed of axially elongated CoO₄X₂ (X = Cl, Br, S, Se) octahedra show that the ordered magnetic moments of their high-spin Co²⁺ (d⁷, S = ³/₂) ions are greater than 3 μ_B, i.e., the spin moment expected for S = ³/₂ ions, and increase almost linearly from 3.22 to 4.45 μ_B as the bond-length ratio r_Co-X/r_Co-O increases from 1.347 to 1.659 where r_Co-X and r_Co-O are the Co-X and Co-O bond lengths, respectively. These observations imply that the orbital moments of the Co²⁺ ions increase linearly from 0.22 to 1.45 μ_B with increasing the r_Co-X/r_Co-O ratio from 1.347 to 1.659. We probed this implication by examining the condition for unquenched orbital moment and also by evaluating the magnetic moments of the Co²⁺ ions based on DFT+U+SOC calculations for those systems of the CoO₄X₂ octahedra. Our work shows that the orbital moments of the Co²⁺ ions are essentially quenched and, hence, that the observations of the neutron diffraction studies are not explained by the current theory of magnetic moments. This discrepancy between experiment and theory urges one to check the foundations of the current theory of magnetic moments as well as the current method of neutron diffraction refinements for ordered magnetic structures.

Physical Properties of Molecules and Condensed Materials Governed by Onsite Repulsion, Spin-Orbit Coupling and Polarizability of Their Constituent Atoms

The onsite repulsion, spin-orbit coupling and polarizability of elements and their ions play important roles in controlling the physical properties of molecules and condensed materials. In celebration of the 150th birthday of the periodic table this year, we briefly review how these parameters affect the physical properties and are interrelated.

Effect of Nonmagnetic Ion Deficiency on Magnetic Structure: Density Functional Study of Sr2MnO2Cu2-xTe2, Sr2MO2Cu2Te2 (M = Co, Mn), and the Oxide-Hydrides Sr2VO3H, Sr3V2O5H2, and SrVO2H

Two seemingly puzzling observations on two magnetic systems were analyzed. For the oxide-hydrides Sr₂VO₃H, Sr₃V₂O₅H₂, and SrVO₂H, made up of VO₄H₂ octahedra, the spin orientations of the V³⁺ (d², S = 1) ions were reported to be different, namely, perpendicular to the H-V-H bond in Sr₂VO₃H but parallel to the H-V-H bond in Sr₃V₂O₅H₂ and SrVO₂H, despite that the d-state split patterns of the VO₄H₂ octahedra are similar in the three oxide-hydrides. Another puzzling observation is the contrasting magnetic structures of Sr₂CoO₂Cu₂Te₂ and Sr₂MnO₂Cu_1.58Te₂, consisting of the layers made up of corner-sharing MO₄Te₂ (M = Co, Mn) octahedra. The Co²⁺ spins in each CoO₂Te₂ layer are antiferromagnetically coupled with spins perpendicular to the Te-Co-Te bond, whereas the Mn³⁺/Mn²⁺ ions of each MnO₂Te₂ layer are ferromagnetically coupled with spins parallel to the Te-Mn-Te bonds. We investigated the cause for these observations by performing first-principles density functional theory (DFT) calculations for stoichiometric phases Sr₂VO₃H, Sr₃V₂O₅H₂, SrVO₂H, Sr₂CoO₂Cu₂Te₂, and Sr₂MnO₂Cu₂Te₂, as well as nonstoichiometric phase Sr₂MnO₂Cu_1.5Te₂. Our study reveals that the V³⁺ ions in all three oxide-hydrides should have the spin orientation parallel to the H-V-H bond. The unusual magnetic structure of the MnO₂Te₂ layers of Sr₂MnO₂Cu_1.52Te₂ arises from the preference of a Mn³⁺ spin to be parallel to the Te-Mn-Te bond, the ferromagnetic spin exchange between adjacent Mn³⁺ and Mn²⁺ ions, and the nearly equal numbers of Mn³⁺ and Mn²⁺ ions in each MnO₂Te₂ layer. We show that the spin orientation of the magnetic ions in an antiferromagnetically coupled perovskite layer, expected in the absence of nonmagnetic ion vacancies, cannot be altered by the magnetic ions of higher oxidation that result from trace vacancies at the nonmagnetic ion sites.