Trigonal Field Research Articles

Almost pure Jeff=12 Mott state of In2Ir2O7 in the limit of reduced intersite hopping

The pyrochlore iridate In$_2$Ir$_2$O$_7$ is a strong $J_{\mathrm{eff}} = 1/2$ Mott insulator with frustrated magnetism. Despite the large trigonal crystal field, a small admixture of $J_{\mathrm{eff}} = 3/2$ component in the $J_{\mathrm{eff}} = 1/2$ bands and a small splitting of $J_{\mathrm{eff}} = 3/2$ bands are observed as compared with other pyrochlore iridates A$_2$Ir$_2$O$_7$ (A: trivalent cation). We argue that the reduced inter-site hopping between the $J_{\mathrm{eff}} = 1/2$ and the $J_{\mathrm{eff}} = 3/2$ manifold plays a predominant role in the distinct behavior of In$_2$Ir$_2$O$_7$ compared with other A$_2$Ir$_2$O$_7$. The effect of the intersite hopping should not be dismissed in the local physics of spin-orbital-entangled $J_{\mathrm{eff}} = 1/2$ Mott insulators.

Resonant inelastic x-ray scattering study of -RuCl3: a progress report

Ru M3-edge resonant inelastic x-ray scattering (RIXS) measurements of with 27 meV resolution reveals a spin–orbit exciton without noticeable splitting. We extract values for the spin–orbit coupling constant ( meV) and trigonal distortion field energy ( meV) which support the nature of . We demonstrate the feasibility of M-edge RIXS for 4d systems, which allows ultra high-resolution RIXS of 4d systems until instrumentation for L-edge RIXS improves.

Magnetism arising from Mexican-hat-like band dispersion in the WSe2/SnS2 heterostructure via interlayer strain.

Mexican-hat-like band dispersion is extremely critical to the realization of hole-doping-induced magnetism in monolayer metal monochalcogenides. However, it is absent from transition-metal dichalcogenides (TMDCs), i.e., WSe2. Herein, using first-principles calculations, we show that Mexican-hat-like band dispersion can be achieved by applying interlayer strain (ε) in the WSe2/SnS2 van der Waals (vdW) heterostructure when ε exceeds 15%. This is because in the strain-induced distorted trigonal prismatic crystal field, at the valence band edge, the W_dz2 orbitals shift upward around the Γ point, while the double-degenerate W_dxy/dx2-y2 orbitals shift downward at the K point, resulting in Mexican-hat-like band dispersion near the Γ point when the energy level of the Γ point surpasses that of the K point. On account of the appearance of the Mexican-hat-like band edge (MHBE), hole-doping in the strained WSe2/SnS2 heterostructure induces magnetization readily from the nonmagnetized phase. Our findings may provide a new strategy for the realization of magnetized TMDC-based vdW heterostructures.

Hibonite Blue: A New Class of Intense Inorganic Blue Colorants.

Commercially available spinel cobalt blue (CoAl2O4) utilizes a significant amount of carcinogenic Co2+, which makes its synthesis more hazardous and environmentally harmful. Considerable effort has been put into developing more environmentally benign and robust blue pigments to replace cobalt blue. A new class of blue pigments with tunable hue were prepared. The solid solution series, CaAl12–2xCoxTixO19 (0 < x ≤ 1), crystallizes in a hexagonal mineral hibonite (CaM12O19) structure with five distinct crystallographic sites for M cations (M = Al, Co, and Ti). The origin of intense blue color is attributed to a synergistic effect of allowed d–d transitions involving the chromophore Co2+ in both tetrahedral and trigonal bipyramidal crystal fields. Compared with commercial cobalt blue, these tunable hibonite blues possess a reddish hue that intensifies the blue color as observed in Y(In,Mn)O3 (YInMn) blues, with a significant reduction of Co2+ concentration from 33% to as low as 4% by mass. A significant advantage of hibonite blues over cobalt blue is the substantial reduction in carcinogenic cobalt content while enhancing the color properties at a reduced cost for raw materials.

Origin of Ising magnetism in Ca3Co2O6 unveiled by orbital imaging

The one-dimensional cobaltate Ca{}_{3}Co{}_{2}O{}_{6} is an intriguing material having an unconventional magnetic structure, displaying quantum tunneling phenomena in its magnetization. Using a newly developed experimental method, s-core-level non-resonant inelastic x-ray scattering (s-NIXS), we were able to image the atomic Co 3d orbital that is responsible for the Ising magnetism in this system. We can directly observe that corrections to the commonly accepted ideal prismatic trigonal crystal field scheme occur in Ca{}_{3}Co{}_{2}O{}_{6}, and it is the complex {d}_{2} orbital occupied by the sixth electron at the high-spin Co{}_{,text{trig},}^{3+} ({d}^{6}) sites that generates the Ising-like behavior. The ability to directly relate the orbital occupation with the local crystal structure is essential to model the magnetic properties of this system.

Spin-orbit coupling and crystal-field distortions for a low-spin 3d5 state in BaCoO3

We have studied the electronic structure of BaCoO$_3$ using soft x-ray absorption spectroscopy at the Co-$L_{2,3}$ and O-$K$ edges, magnetic circular dichroism at the Co-$L_{2,3}$ edges, as well as valence band hard x-ray photoelectron spectroscopy. The quantitative analysis of the spectra established that the Co ions are in the formal low-spin tetravalent 3$d^5$ state and that the system is a negative charge transfer Mott insulator. The spin-orbit coupling plays also an important role for the magnetism of the system. At the same time, a trigonal crystal field is present with sufficient strength to bring the 3$d^5$ ion away from the $J_{eff} = 1/2$ state. The sign of this crystal field is such that the $a_{1g}$ orbital is doubly occupied, explaining the absence of a Peierl's transition in this system which consists of chains of face-sharing CoO$_6$ octahedra. Moreover, with one hole residing in the $e_g^{\pi}$, the presence of an orbital moment and strong magneto-crystalline anisotropy can be understood. Yet, we also infer that crystal fields with lower symmetry must be present to reproduce the measured orbital moment quantitatively, thereby suggesting the possibility for orbital ordering to occur in BaCoO$_3$.

Achieving giant spin-orbit splitting in conduction band of monolayer WS2 via n-p co-doping

Large spin-orbit splitting in the conduction band minimum (CBM) of monolayer transition metal dichalcogenides (TMDs) is in great demand for suppressing the intervalley scattering. Here we propose a new scheme to significantly enhance the spin-orbit splitting at the K point in the CBM of WS2 monolayer, via the n-p co-doping of fluorine and group VA elements (N, P, As and Sb). Based on the first-principles calculations, a giant spin-orbit splitting of 101.86 meV is theorized in the F-Sb co-doped system. This is evidenced to originate from the enhanced spin-orbit interaction, intimately related to the strengthened trigonal prismatic ligand field and the increased asymmetric surface charge. The giant spin-orbit splitting in the CBM can strongly suppress the intervalley scattering, which will enhance the spin-valley coupling and is beneficial for longer spin and valley lifetimes. This theoretical work provides a key to designing the high-performance monolayer TMD-based spintronic devices.

Systematic analysis of the fine structure of energy levels and spin-Hamiltonian parameters of V3+ ion in corundum with dynamic Jahn-Teller effect

Systematic analysis of fine structure of the whole energy levels and spin-Hamiltonian parameters (zero-field splitting (ZFS) parameter D and g-factors g// and g⊥) for the ground state 3A2 (3T1) of V3+ ion in corundum are presented in detail with complete diagonalization method (CDM) of 45 × 45 energy matrix, in which the full configuration interactions are taken into account. The reduction of the splittings of excited electronic 3T2 (t2 ge) term with orbital triplet degenerate caused by spin-orbit (SO) and lower trigonal crystal field (CF) is studied by T2⊗e model dynamic Jahn-Teller theory, and Ham deduction factor, the Jahn-Teller energy EJT and Huang-Rhys factor S are estimated. The studies are performed within the strong-field scheme with molecular orbit (MO) approximation, in which the two SO coupling parameter model is used and the SO contributions from both the central 3d ion and ligands are taken in account. The calculated results are in good agreement with the experimental data, and the local structure of [VO6]9- cluster with C3 point group symmetry are determined quantitatively.

The Second and Third Crystal Field Splitting Moments in Verification of the Trigonal and Hexagonal Crystal Field Parametrizations

The paper, as the third in a series, presents the complete formulas for the crystal field splitting third moment of free ion states as functions of the relevant crystal field parameters in the case of the trigonal and hexagonal crystal fields. The additive structure of the expressions consists of 21 independent components for the trigonal symmetry, 12 for the hexagonal one and only 4 components for the ideal hexagonal coordination. The two scalar characteristics of the crystal field Hamiltonian HCF – the crystal field splitting second and third moments – enable us to verify the HCF parametrizations solely in an algebraic way. Such verification concerns the multipolar structure of the parametrizations as well as the signs of the crystal field parameters. Both the crystal field splitting moments can ensure us in what degree the comprehensive HCF parametrizations are adequate with respect to the individual ionic states of the electron configuration. As an example two chosen HCF parametrizations, one for the hexagonal system Nd3+:LaCl3 of the C3h symmetry, and the second for the trigonal system Tb3+:Y2O2S of the C3v symmetry are subjected to in depth analysis. The presented approach provides a critical insight into the crystal field parametrizations from a different point of view, i.e., omitting the conventional fitting procedure. After the extended verification the studied classical HCF parametrizations withstand, in principle, the test of time.

Theoretical Study of Electron Paramagnetic Resonance Spectra and Local Lattice Distortion for Mn2+ in Zn(ClO4)2·6(H2O)Mg(ClO4)2·6(H2O)

The electron paramagnetic resonance (EPR) spectra of trigonal Mn2+ centers in Zn(ClO4)2·6(H2O) and Mg(ClO4)2·6(H2O) crystals were studied on the basis of the complete energy matrices for a d5 configuration ion in a trigonal ligand field. It was demonstrated that the local lattice structure around a trigonal Mn2+ center has an compressed distortion along the crystalline c3 axis, and when Mn2+ is doped in the Zn(ClO4)2·6(H2O) and Mg(ClO4)2·6(H2O) crystals, there is a similar local distortion. From the EPR calculation, the local lattice structure parameters R=2.183 2 A, for Zn(ClO4)2·6(H2O), R=2.130 2 A, for Mg(ClO4)2·6(H2O) have been determined.

Large spin-orbit splitting in the conduction band of halogen (F, Cl, Br, and I) doped monolayer WS2 with spin-orbit coupling

Spin-orbit (SO) splitting in the conduction-band minimum (CBM) of monolayer $\mathrm{W}{\mathrm{S}}_{2}$ plays a pivotal role in spintronics for spin-valley coupled electron. Using first-principles calculation, a large SO splitting at the K point in the CBM is achieved in halogen doped monolayer $\mathrm{W}{\mathrm{S}}_{2}$ (83.55 meV for F doped 4 \ifmmode\times\else\texttimes\fi{} 4 \ifmmode\times\else\texttimes\fi{} 1 supercell) because of the strong spin-orbit coupling induced by the asymmetric electric field. We further clarify that the asymmetric electric field originates from the stronger trigonal prismatic ligand field and asymmetric surface charge distribution incurred by halogen doping. More importantly, halogen doping could be used to lift the degeneracy of K and K' valleys in the CBM of monolayer $\mathrm{W}{\mathrm{S}}_{2}$ by breaking the time-reversal symmetry. This research proposes a feasible method to enlarge the SO splitting in the CBM of transition-metal dichalcogenides, advancing their application in valley spintronic devices.

Ubiquitous formation of bulk Dirac cones and topological surface states from a single orbital manifold in transition-metal dichalcogenides.

Transition-metal dichalcogenides (TMDs) are renowned for their rich and varied bulk properties, while their single-layer variants have become one of the most prominent examples of two-dimensional materials beyond graphene. Their disparate ground states largely depend on transition metal d-electron-derived electronic states, on which the vast majority of attention has been concentrated to date. Here, we focus on the chalcogen-derived states. From density-functional theory calculations together with spin- and angle-resolved photoemission, we find that these generically host a co-existence of type-I and type-II three-dimensional bulk Dirac fermions as well as ladders of topological surface states and surface resonances. We demonstrate how these naturally arise within a single p-orbital manifold as a general consequence of a trigonal crystal field, and as such can be expected across a large number of compounds. Already, we demonstrate their existence in six separate TMDs, opening routes to tune, and ultimately exploit, their topological physics.

Studies of the optical and EPR spectral data for the trigonal strong field Cr3+ centers in Cr3+-doped Ca3Ga2Ge4O14 and Sr3Ga2Ge4O14 crystals

This paper represents the unified theoretical computations for the trigonal strong field Cr3+ centers (assigned to Cr3+ at octahedral Ga3+ sites) in Cr3+-doped Ca3Ga2Ge4O14 and Sr3Ga2Ge4O14 crystals. The computations adopt the complete diagonalization (of energy matrix) method based on the two-spin-orbit-parameter model where the contributions from both the spin-orbit parameter of central dn ion (in the classical crystal field theory) and that of ligand ion are contained. The calculated six optical bands and three spin-Hamiltonian parameters (g factors g//, g⊥ and zero-field splitting D) with only three adjustable parameters are reasonably coincident with the observed values. The very small local lattice relaxation in the Cr3+ centers in both crystals indicates the similarities of valence and ionic radius between Cr3+ ion and the replaced host ion. This supports the assignment that the trigonal strong field Cr3+ centers in both crystals are due to Cr3+ at octahedral Ga3+ site rather than octahedral Ge4+ site (the latter may be the weak field Cr3+ center).

Solution and solid state structures and magnetism of a series of linear trinuclear compounds with a hexacoordinate LnIII and two terminal NiII centers.

Reported are the syntheses, structures and magnetic properties, also by NMR spectroscopy in solution, of a series of 13 linear trinuclear 3d-4f compounds with a lanthanide(iii) surrounded by two NiII ions, NiLnIII, where the central LnIII is hexacoordinate. For three of the crystal structures, an additional H2O molecule is coordinated to the central LnIII ion, leading to a monocapped trigonal prismatic structure. However, NMR spectroscopy indicates that in solution, these complexes also have a hexacoordinate LnIII center. The solution magnetic anisotropies, determined by NMR spectroscopy, indicate that the axial components of the anisotropies are relatively small and that the DyIII derivative might therefore not exhibit single molecule magnetism. The axial anisotropies determined by NMR spectroscopy are in good agreement with the expectations based on the distorted trigonal prismatic ligand field.

Phase Diagram of Pyrochlore Iridates: All-in-All-out Magnetic Ordering and Non-Fermi-Liquid Properties.

We study the prototype 5d pyrochlore iridate Y_{2}Ir_{2}O_{7} from first principles using the local density approximation and dynamical mean-field theory (LDA+DMFT). We map out the phase diagram in the space of temperature, on-site Coulomb repulsion U, and filling. Consistent with experiments, we find that an all-in-all-out ordered insulating phase is stable for realistic values of U. The trigonal crystal field enhances the hybridization between the j_{eff}=1/2 and j_{eff}=3/2 states, and strong interband correlations are induced by the Coulomb interaction, which indicates that a three-band description is important. We demonstrate a substantial band narrowing in the paramagnetic metallic phase and non-Fermi-liquid behavior in the electron- or hole-doped system originating from long-lived quasi-spin-moments induced by nearly flat bands.

Large trigonal-field effect on spin-orbit coupled states in a pyrochlore iridate

The half-filled topmost valence band of ${\mathrm{Ir}}^{4+}$ in several iridates such as ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4},\phantom{\rule{0.16em}{0ex}}{\mathrm{IrO}}_{2}$, and ${\mathrm{CaIrO}}_{3}$ has been proposed to originate mainly from the spin-orbit coupled ${J}_{\mathrm{eff}}=1/2$ states. In pyrochlore iridates ${R}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$ ($R$: rare earth), some exotic electronic states are theoretically proposed by assuming ${J}_{\mathrm{eff}}=1/2$ states. However, the octahedral coordination around Ir is trigonally distorted, which may affect the energy level scheme of Ir $5d$ states. Here, we report spectra of resonant elastic and inelastic x-ray scattering in ${\mathrm{Eu}}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$ at the Ir $L$ edges. A large suppression of the magnetic scattering signal at the Ir ${L}_{\mathrm{II}}$ edge supports the ${J}_{\mathrm{eff}}=1/2$ picture rather than the $S=1/2$ one. The inelastic scattering spectrum indicates that the magnitude of the trigonal field on the ${\mathrm{Ir}}^{4+}$ states is evaluated to be comparable to the spin-orbit interaction. The energy diagram of the $5d$ state is proposed based on the simple cluster model.

EPR investigation of local structure for the [Mn(H2O)6]2+cluster in M(ClO4)2· 6H2O:Mn2+(M = Cd, Hg) systems at different temperatures

Local lattice structure distortion studies of the octahedral Mn 2+ center in M(ClO 4 ) 2 · 6H 2 O:Mn 2+ (M = Cd, Hg) systems have been performed systematically based on the diagonalization of the complete energy matrices of electron-electron repulsion, spin-orbit coupling and trigonal ligand-field interaction for a d 5 configuration ion in a trigonal ligand field. From the EPR calculation, the local structure distortion parameters R and θ are determined, respectively. Results show that the local lattice structure around a trigonal Mn 2+ center has a compressed distortion along the crystalline C 3 axis. The compression distortion may be ascribed to the fact that the radius of the Mn 2+ ion is smaller than that of the Hg 2+ ion and the Cd 2+ ion. The local lattice structure parameters for Mn 2+ in M(ClO 4 ) 2 · 6H 2 O:Mn 2+ (M = Cd, Hg) systems are determined at liquid-nitrogen temperature and room temperature.

Synthesis, crystal structure, and electronic properties of CeBiO3 oxide

Synthesis of CeBiO3 oxide is performed by a sol–gel method. Analysis of the powder X‐ray diffraction (XRD) pattern shows tetragonal unit cell with lattice parameters: a = 11.5030 Å, c = 5.4066 Å, space group P42/mnm, and Z = 4. Average crystallite sizes determined by Scherrer equation ∼14–47 nm show formation of nanoparticles in CeBiO3. On refinement of the unit‐cell structure, the agreement factors are lowered to: Rp = 0.98; Rwp = 0.99; Rexp = 0.006. Observed DC elctrical conductivity activation energy, Ea ∼ 0.62 eV shows the fairly strong semiconducting nature of CeBiO3. AC electrical conductivity results show electronic conductivity due to thermally activated hopping of Ce3+(4f1) electrons in CeBiO3. UV–VIS–NIR diffuse reflection absorption bands ∼200–440 nm are due to transitions from Ce3+(4f1) ground state 2F5/2 to five degeneracy lifted trigonal crystal field splitting of 5d levels of Ce3+ ions.

Coupling Ferroelectricity with Spin-Valley Physics in Oxide-Based Heterostructures.

The coupling of spin and valley physics is nowadays regarded as a promising route toward next-generation spintronic and valleytronic devices. In the aim of engineering functional properties for valleytronic applications, we focus on the ferroelectric heterostructure BiAlO3/BiIrO3, where the complex interplay among a trigonal crystal field, layer degrees of freedom, and spin-orbit coupling mediates a strong spin-valley coupling. Furthermore, we show that ferroelectricity provides a nonvolatile handle to manipulate and switch the emerging valley-contrasting spin polarization.

A Terminal N2 Complex of High-Spin Iron(I) in a Weak, Trigonal Ligand Field.

The role of Fe in biological and industrial N2 fixation has inspired the intense study of small molecule analogues of Fe-(NxHy) intermediates of potential relevance to these processes. Although a number of low-coordinate Fe-(N2) featuring varying degrees of fidelity to the nitrogenase active site are now known, these complexes frequently feature strongly donating ligands that either enforce low- or intermediate-spin states or result in linear Fe-(N2)-Fe bridging motifs. Given that the nitrogenase active site uses weak-field sulfide ligands to stabilize its reactive Fe center(s), N2 binding to high-spin Fe is of great interest. Herein, we report the synthesis and characterization of the first terminal N2 complex of high-spin (S = 3/2) Fe(I) as well as a bridging Fe-(N2)-Fe analogue. Electron paramagnetic resonance and solution magnetic moment determination confirm the high-spin state, and vibrational experiments indicate a substantial degree of activation of the N≡N bond in these complexes. Density functional theory calculations reveal an electronic structure for the terminal adduct featuring substantial delocalization of unpaired spin onto the N2 ligand.