Trigonal Field Research Articles

Suppression of antiferromagnetic order by strain-enhanced frustration in honeycomb cobaltate.

Layered honeycomb cobaltates are predicted as promising for realizing the Kitaev quantum spin liquid, a many-body quantum entangled ground state characterized by fractional excitations. However, they exhibit antiferromagnetic ordering at low temperatures, hindering the expected quantum state. We demonstrate that controlling the trigonal distortion of CoO6 octahedra is crucial to suppress antiferromagnetic order through enhancing frustration in layered honeycomb cobaltates. Using heterostructure engineering on Cu3Co2SbO6 thin films, we adjust the trigonal distortion of CoO6 octahedra and the resulting trigonal crystal field. The original Néel temperature of 16 kelvin in bulk Cu3Co2SbO6 decreases (increases) to 7.8 kelvin (22.7 kelvin) in strained Cu3Co2SbO6 films by decreasing (increasing) the magnitude of the trigonal crystal fields. The first-principles calculation suggests the enhancement of geometrical frustration as the origin of the suppression of antiferromagnetism. This finding supports the potential of layered honeycomb cobaltate heterostructures and strain engineering in realizing extremely elusive quantum phases of matter.

Temperature Induced Reversible Switching of the Magnetic Anisotropy in a Neodymium Complex Adsorbed on Graphite.

Controlling the magnetic anisotropy of molecular layers assembled on a surface is one of the challenges that needs to be addressed to create the next-generation spintronic devices. Recently, metal complexes that show a reversible solid-state switch of their magnetic anisotropy in response to physical stimuli, such as temperature and magnetic field, have been discovered. The complex Nd(trensal) (H3trensal=2,2',2''-tris(salicylideneimino)triethylamine) is predicted to exhibit such property. An ultra-thin film of Nd(trensal) is deposited on highly ordered pyrolytic graphite as a proof-of-concept system to show that this property can be retained at the nanoscale on a layered material. By combining single crystal magnetometric measurements and synchrotron X-ray-based absorption techniques, supported by multiplet ligand field simulations based on the trigonal crystal field surrounding the lanthanide centre, it is demonstrated that changing the temperature reverses the magnetic anisotropy of an ordered film of Nd(trensal), thus opening significant perspectives for the realization of a novel family of temperature-controlled molecular spintronic devices.

EPR parameters and optical spectrum of α-Al2O3:Ti3+ with dynamic Jahn-Teller effect

The quenching phenomenon of trigonal crystal field (CF), spin–orbit (SO) coupling operators, and orbital operators reflected in electron paramagnetic resonance (EPR) parameters and energy splitting intervals observed in experiments of α-Al2O3:Ti3+ is theoretically investigated by the calculation of EPR g factors and the energy differences of the lowest three levers E3/2, 1E1/2 and 2E1/2 with the formulas derived with high-order perturbation method. In the calculation, the coupling of 2T2g and 2Eg with e vibrational model of dynamic Jahn-Teller effect are considered. The calculated results are in agreement with the experimental values. The local defect structure around Ti3+ ions (bond lengths and angles of [TiO6]9-) and trigonal CF parameters ν and v′ are determinedand the covalence effects on SO coupling parameters ζ, ζ’ and orbital reduction parameters k、k’ are determined also.

Anisotropic hybridization probed by polarization dependent x-ray absorption spectroscopy in VI3 van der Waals Mott ferromagnet

Polarization dependent x-ray absorption spectroscopy was used to study the magnetic ground state and the orbital occupation in bulk-phase VI3 van der Waals crystals below and above the ferromagnetic and structural transitions. X-ray natural linear dichroism and x-ray magnetic circular dichroism spectra acquired at the V edges are compared against multiplet cluster calculations within the frame of the ligand field theory to quantify the intra-atomic electronic interactions at play and evaluate the effects of symmetry reduction occurring in a trigonally distorted VI6 unit. We observed a non zero linear dichroism proving the presence of an anisotropic charge density distribution around the V3+ ion due to the unbalanced hybridization between the vanadium and the ligand states. Such hybridization acts as an effective trigonal crystal field, slightly lifting the degeneracy of the ground state. However, the energy splitting associated to the distortion underestimates the experimental band gap, suggesting that the insulating ground state is stabilized by Mott correlation effects rather than via a Jahn–Teller mechanism. Our results clarify the role of the distortion in VI3 and establish a benchmark for the study of the spectroscopic properties of other van der Waals halides, including emerging 2D materials with mono and few-layers thickness, whose fundamental properties might be altered by reduced dimensions and interface proximity.

Identification of the compressive trigonal crystal field and orbital polarization in strained monolayer α-RuCl3 on graphite

α-RuCl3 is a tantalizing playground to search for the quantum spin liquid states with leading Kitaev term due to the conformation of Jackeli–Khaliullin mechanism. Suppressing the non-Kitaev interaction to approach the Kitaev limit is the major objective in the experimental design of Kitaev–Jackeli–Khaliullin materials, for which the practical feasibility rests on the manipulation of the exact crystalline structure. A tensile strain, leading to the further compressive trigonal field splitting which would alter the spin-orbital entangled character and tune the intrinsic hopping exchanges, has been widely proposed as the promising strategy to enhance the comparative Kitaev interaction. In this work, we preform in-depth Scan Tunneling Microscope study on the electronic patterns of strained α-RuCl3 monolayer on graphite substrate. Based on Chen’s derivative rule, a further trigonal field splitting is identified by analyzing the lateral-gradient imaging effect caused by an anisotropic tip. A spatial variation of the magnitude of trigonal crystal field due to the slight inhomogeneity of strain accords with the orbital polarization near the Mott gap. All evidences point to the facts that the compressive trigonal crystal field in the stretched α-RuCl3 monolayer lifts the degeneracy of t2g states with higher text{e}_{text{g}}' and lower a1g orbitals, and the Coulomb interactions of the text{e}_{text{g}}' orbitals take the main responsibility for the Mott effect.

Charge-transfer-enhanced d–d emission in antiferromagnetic NiPS3

The d electron plays a significant role in determining and controlling the properties of magnetic materials. However, the d electron transitions, especially d–d emission, have rarely been observed in magnetic materials due to the forbidden selection rules. Here, we report an observation of d–d emission in antiferromagnetic nickel phosphorus trisulfides (NiPS3) and its strong enhancement by stacking it with monolayer tungsten disulfide (WS2). We attribute the observation of the strong d–d emission enhancement to the charge transfer between NiPS3 and WS2 in the type-I heterostructure. The d–d emission peak splits into two peaks, D1 and D2, at low temperature below 150 K, from where an energy splitting due to the trigonal crystal field is measured as 105 meV. Moreover, we find that the d–d emissions in NiPS3 are nonpolarized lights, showing no dependence on the zigzag antiferromagnetic configuration. These results reveal rich fundamental information on the electronic and optical properties of emerging van der Waals antiferromagnetic NiPS3.

Magnetic anisotropy in two-orbital models

Motivated by the recent first-principle discovery of giant perpendicular magnetic anisotropy (PMA) in Fe/III–V nitride thin films, we theoretically study magnetic crystalline anisotropy(MCA) in a series of lattices with trigonal symmetry. Due to the trigonal crystal field, MCA in these lattices is dominated by first-order perturbation of the spin–orbit coupling (SOC) in the atomic limit, instead of second-order in conventional transition metal materials. In particular, the proportionality between MCA and SOC is robust in Kagome and pyrochlore lattices due to the flat bands therein. While in triangle lattice the second-order relation is restored under the bandwidth effect. These findings give rise to a new understanding of magnetic anisotropy and provide a guide for the future hunting of high PMA materials.

Resolution of zigzag magnetic correlations in Na-deficient NaxIrO3 without long-range ordering

The materials search for Kitaev quantum spin liquids led to the discovery of many honeycomb lattice materials. Much attention has been paid to materials without magnetic order down to the lowest temperatures. The newly synthesized Na-deficient ${\mathrm{Na}}_{x}{\mathrm{IrO}}_{3}$ has been found to bear no sign of long-range magnetic order above 1 K from physical property measurements. In this paper, we report momentum- and energy-resolved excitation spectra in Na-deficient ${\mathrm{Na}}_{x}{\mathrm{IrO}}_{3}$ measured using a resonant inelastic x-ray scattering spectrometer. Orbital excitation spectra show that the octahedral and trigonal crystal field splittings are larger in ${\mathrm{Na}}_{x}{\mathrm{IrO}}_{3}$ than in ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$. On the other hand, the low-energy spectrum at low temperature shows a wave-vector dispersion and a spectral weight distribution that are similar to those of ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$, revealing that the two-dimensional zigzag magnetic correlations in ${\mathrm{Na}}_{x}{\mathrm{IrO}}_{3}$ are similar to those in ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ in terms of the ordered magnetic moment direction and three dynamically fluctuating zigzag orders. The azimuth angle dependence of the low-energy spectrum corroborates these results. The two-dimensional zigzag magnetic correlations rapidly weaken until 50 K. At high temperatures, the spectral weight distribution of the low-energy excitation resembles that of the pure Kitaev model, indicating that the Kitaev interaction dominates the dynamic magnetic response at high temperature. We suggest that the larger crystal field and distortion and the weakened longer-range Heisenberg exchange interactions due to the Na deficiency in ${\mathrm{Na}}_{x}{\mathrm{IrO}}_{3}$ contribute to bring ${\mathrm{Na}}_{x}{\mathrm{IrO}}_{3}$ away from the zigzag long-range magnetic order phase.

Exchange interactions in d5 Kitaev materials: From Na2IrO3 to α−RuCl3

We present an analytical study of the exchange interactions between pseudospin one-half ${d}^{5}$ ions in honeycomb lattices with edge-shared octahedra. Various exchange channels involving Hubbard $U$, charge-transfer excitations, and cyclic exchange are considered. Hoppings within ${t}_{2g}$ orbitals as well as between ${t}_{2g}$ and ${e}_{g}$ orbitals are included. Special attention is paid to the trigonal crystal field $\mathrm{\ensuremath{\Delta}}$ effects on the exchange parameters. The obtained exchange Hamiltonian is dominated by ferromagnetic Kitaev interaction $K$ within a wide range of $\mathrm{\ensuremath{\Delta}}$. It is found that a parameter region close to the charge-transfer insulator regime and with a small $\mathrm{\ensuremath{\Delta}}$ is most promising to realize the Kitaev spin liquid phase. Two representative honeycomb materials ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ and $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ are discussed based on our theory. We have found that both materials share dominant ferromagnetic $K$ and positive nondiagonal $\mathrm{\ensuremath{\Gamma}}$ values. However, their Heisenberg $J$ terms have opposite signs: AFM $J>0$ in ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ and FM $J<0$ in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. This brings different magnetic fluctuations and results in their different magnetization behaviors and spin excitation spectra. Proximity to FM state due to the large FM $J$ is emphasized in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. The differences between the exchange couplings of these two materials originate from the opposite $\mathrm{\ensuremath{\Delta}}$ values, indicating that the crystal field can serve as an efficient control parameter to tune the magnetic properties of ${d}^{5}$ spin-orbit Mott insulators.

First demonstration of tuning between the Kitaev and Ising limits in a honeycomb lattice.

Recent observations of novel spin-orbit coupled states have generated interest in 4d/5d transition metal systems. A prime example is the state in iridate materials and α-RuCl3 that drives Kitaev interactions. Here, by tuning the competition between spin-orbit interaction (λSOC) and trigonal crystal field (ΔT), we restructure the spin-orbital wave functions into a previously unobserved state that drives Ising interactions. This is done via a topochemical reaction that converts Li2RhO3 to Ag3LiRh2O6. Using perturbation theory, we present an explicit expression for the state in the limit ΔT ≫ λSOC realized in Ag3LiRh2O6, different from the conventional state in the limit λSOC ≫ ΔT realized in Li2RhO3. The change of ground state is followed by a marked change of magnetism from a 6 K spin-glass in Li2RhO3 to a 94 K antiferromagnet in Ag3LiRh2O6.

Spectroscopic studies of Cr3+ ions in natural single crystal of magnesium aluminate spinel MgAl2O4

The natural spinel crystal MgAl2O4 containing the Cr3+ ions was studied experimentally and theoretically in this paper. The absorption and emission spectra at room and low temperatures were recorded. The experimental spectroscopic results were aided with the crystal field calculations, which returned the energy level schemes of the Cr3+ ions at the Al sites with the local D3d symmetry. Effects of the trigonal crystal field were clearly seen in the calculated results, which were compared with the experimental spectra to yield a good agreement between both data sets.

Towards Kitaev spin liquid in 3d transition metal compounds

This paper reviews the current progress on searching the Kitaev spin liquid state in 3[Formula: see text] electron systems. Honeycomb cobaltates were recently proposed as promising candidates to realize the Kitaev spin liquid state, due to the more localized wavefunctions of [Formula: see text] ions compared with that of [Formula: see text] and [Formula: see text] ions, and also the easy tunability of the exchange Hamiltonian in favor of Kitaev interaction. Several key parameters that have large impacts on the exchange constants, such as the charge-transfer gap and the trigonal crystal field, are identified and discussed. Specifically, tuning crystal field effect by means of strain or pressure is emphasized as an efficient phase control method driving the magnetically ordered cobaltates into the spin liquid state. Experimental results suggesting the existence of strong Kitaev interactions in layered honeycomb cobaltates are discussed. Finally, the future research directions are briefly outlined.

Large Orbital Magnetic Moment and Strong Perpendicular Magnetic Anisotropy in Heavily Intercalated FexTiS2

Titanium disulfide TiS$_2$, which is a member of the layered transition-metal dichalcogenides with the 1T-CdI$_2$-type crystal structure, is known to exhibit a wide variety of magnetism through intercalating various kinds of transition-metal atoms of different concentrations. Among them, Fe-intercalated titanium disulfide Fe$_x$TiS$_2$ is known to be ferromagnetic with strong perpendicular magnetic anisotropy (PMA) and large coercive fields ($H_\text{c}$). In order to study the microscopic origin of the magnetism of this compound, we have performed X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) measurements on single crystals of heavily intercalated Fe$_x$TiS$_2$ ($x\sim0.5$). The grown single crystals showed a strong PMA with a large $H_\text{c}$ of $\mu_0H_\text{c} \simeq 1.0\ \text{T}$. XAS and XMCD spectra showed that Fe is fully in the valence states of 2+ and that Ti is in an itinerant electronic state, indicating electron transfer from the intercalated Fe atoms to the host TiS$_2$ bands. The Fe$^{2+}$ ions were shown to have a large orbital magnetic moment of $\simeq 0.59\ \mu_\text{B}\text{/Fe}$, to which, combined with the spin-orbit interaction and the trigonal crystal field, we attribute the strong magnetic anisotropy of Fe$_x$TiS$_2$.

Disorder effects in LaAlO3 : Ho3+ single crystals revealed by optical spectra

High-resolution spectroscopic studies of $\mathrm{LaAl}{\mathrm{O}}_{3}$ single crystal doped with holmium ions are reported. Polarized and unpolarized absorption and luminescence spectra were measured in the broad spectral range from 2000 to $23\phantom{\rule{0.16em}{0ex}}000\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{--1}$ at temperatures of 4.5--5 K. Additional measurements were fulfilled using site-selective laser spectroscopy. Energies and symmetry properties of the corresponding wave functions of crystal-field levels of ${\mathrm{Ho}}^{3+}$ ions which substitute for ${\mathrm{La}}^{3+}$ ions in $\mathrm{LaAl}{\mathrm{O}}_{3}$ at sites with the ${D}_{3}$ symmetry were determined with high accuracy, and, on this basis, crystal-field calculations were performed. A thorough analysis of spectral line profiles with the fine doublet structure corresponding to singlet-doublet transitions in the trigonal crystal field was made, which showed the existence of the random deformation splitting phenomenon. The value of deformation splitting lies in the region $0.3--0.8\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{--1}$ that substantially exceeds the widths of the doublet hyperfine splitting. The observed line shapes were successfully modeled, assuming the interaction of the ${\mathrm{Ho}}^{3+}$ ions with random deformations of the crystal lattice induced by point defects and ferroelastic domain boundaries.

Energy scales in 4f1 delafossite magnets: Crystal-field splittings larger than the strength of spin-orbit coupling in KCeO2

Ytterbium-based delafossites with effective S=1/2 moments are investigated intensively as candidates for quantum spin-liquid ground states. While the synthesis of related cerium compounds has also been reported,many important details concerning their crystal, electronic, and magnetic structures are unclear. Here we analyze the S=1/2 system KCeO2, combining complementary theoretical methods. The lattice geometry was optimized and the band structure investigated using density functional theory extended to the level of a GGA+U calculation in order to reproduce the correct insulating behavior. The Ce 4f1 states were then analyzed in more detail with the help of ab initio wave-function-based computations. Unusually large effective crystal-field splittings of up to 320 meV are predicted, which puts KCeO2 in the strong field coupling regime. Our results reveal a subtle interplay between ligand-cage electrostatics and the trigonal field generated by the extended crystalline surroundings, relevant in the context of recent studies on tuning the nature of the ground-state wave function in 4f triangular-lattice and pyrochlore compounds. It also makes KCeO2 an interesting model system in relation to the effect of large crystal-field splittings on the anisotropy of intersite exchange in spin-orbit coupled quantum magnets.

Absorbance and energy levels for a Fe3+ ion in α-[formula omitted]. Optical pumping applied to a 31 GHz maser

The structure of 3d5 configuration ion in a trigonal field is theoretically determined on the basis of a 252×252 matrix of complete energy. The spectra of paramagnetic electron resonance and the optical absorption of the Fe3+ ion in sapphire crystal (α−Al2O3) have been calculated by diagonalizing the matrix of total energy. The obtained results are in good agreement with experimental observations. The strength of probability transitions between energy levels pairs are also established to show the possibility for achieving the inversion of the population in the fundamental state when applying the optical pumping mechanism to the crystal. The results based on the computed parameters of transition and on the maser effect equations show that a maser signal of a 31 GHz can be generated and that depends on the cryogenic design of the resonator.

Crystal-field Paschen-Back effect on ruby in ultrahigh magnetic fields

Zeeman spectra of the R lines of ruby (Cr$^{3+}$: $\alpha$-Al$_{2}$O$_{3}$) were studied in ultrahigh magnetic fields up to 230 T by magneto-photoluminescence measurements. The observed Zeeman patterns exhibit nonlinear behaviors above 100 T, evidencing the breakdown of the previously reported Paschen-Back effect for ${\bf B} \perp c$ geometry. We adopted the crystal-field multiplet theory including the cubic crystal field (${\mathcal H}_{\rm cubic}$), the trigonal crystal field (${\mathcal H}_{\rm trig}$), the spin-orbit interaction (${\mathcal H}_{\rm SO}$), and the Zeeman interaction (${\mathcal H}_{\rm Z}$). It is found that the nonlinear splitting of the R lines is owing to the hybridization between the $^{2}E$ and $^{2}T_{1}$ states, which leads to the quantization of these Zeeman levels with the orbital angular momentum. Our results suggest that the exquisite energy balance among ${\mathcal H}_{\rm cubic}$, ${\mathcal H}_{\rm trig}$, ${\mathcal H}_{\rm SO}$, and ${\mathcal H}_{\rm Z}$ realized in ruby offers a unique opportunity to observe the onset of the $crystal-field$ Paschen-Back effect toward the high-field extreme.

Kitaev Spin Liquid in 3d Transition Metal Compounds.

We study the exchange interactions and resulting magnetic phases in the honeycomb cobaltates. For a broad range of trigonal crystal fields acting on Co^{2+} ions, the low-energy pseudospin-1/2 Hamiltonian is dominated by bond-dependent Ising couplings that constitute the Kitaev model. The non-Kitaev terms nearly vanish at small values of trigonal field Δ, resulting in spin liquid ground state. Considering Na_{3}Co_{2}SbO_{6} as an example, we find that this compound is proximate to a Kitaev spin liquid phase, and can be driven into it by slightly reducing Δ by ∼20 meV, e.g., via strain or pressure control. We argue that, due to the more localized nature of the magnetic electrons in 3d compounds, cobaltates offer the most promising search area for Kitaev model physics.

Effects of defects and anions on the geometry, electronic structures and exchange interaction of Fe-doped 2H-MoSe2 monolayer

The stability, electronic structure and magnetic properties of Fe doped, Fe-VSe and Fe-NM (NM = B, N) codoped 2H-MoSe2 monolayers with a high concentration of 12.5% are systematically investigated using first-principles calculations. The results show that the Fe dopants are coupled ferromagnetically via p-d exchange mechanism with high d4 spin configuration in the zigzag direction, ascribing to the antiferromagnetic coupling between the localized Fe 3d orbitals and delocalized Se 4p orbitals. Due to large distortion around Fe dopants, the introducing of Se vacancy alters the trigonal prismatic coordination field and causes Hund’s exchange splitting of Fe 3d orbitals, further leading to obvious ferromagnetic coupling and high ferromagnetic stability (ΔEFM-AFM = −724.0 meV) for the Fe-VSe codoped MoSe2 configurations. The non-compensated Fe-NM (NM = B, N) codoping can largely enhance the total moments and structural stability of Fe-doped MoSe2 monolayer due to strong electrostatic attraction and synergistic interaction of anionic dopants. The Fe-doped MoSe2 monolayer is an attractive route to achieve stable room temperature spintronic devices by precise control of synthesis conditions, such as the introducing of Se vacancies and nonmagnetic elements.

VI3 : A two-dimensional Ising ferromagnet

Two-dimensional (2D) magnetic materials are of great current interest for their promising applications in spintronics. Here we propose the van der Waals (vdW) material VI3 to be a 2D Ising ferromagnet (FM), using density functional calculations, crystal field level diagrams, superexchange model analyses, and Monte Carlo simulations. The $a_{1g}$$^1$$e'_{-}$$^1$ ground state in the trigonal crystal field gives rise to the 2D Ising FM due to a significant single ion anisotropy (SIA) and enhanced FM superexchange both associated with the $S_z$=1 and $L_z$=--1 state of V3+ ions. We find that a tensile strain on the VI3 monolayer further stabilizes the $a_{1g}$$^1$$e'_{-}$$^1$ ground state, and its Curie temperature ($T_{\rm C}$) would increase from 70 K to 90-110 K under a 2.5-5\% tensile strain. Moreover, we suggest a group of spin-orbital states with a strong SIA which may help to search more 2D Ising magnets.