Spin-orbit Coupling Research Articles

Nonrelativistic ferromagnetotriakontadipolar order and spin splitting in hematite

We show that hematite, α−Fe2O3, below its Morin transition, has a ferroic ordering of rank-5 magnetic triakontadipoles on the Fe ions. In the absence of spin-orbit coupling, these are the lowest-order ferroically aligned magnetic multipoles, and they give rise to the g-wave nonrelativistic spin splitting in hematite. We find that the ferroically ordered magnetic triakontadipoles result from the simultaneous antiferroic ordering of the charge hexadecapoles and the magnetic dipoles, providing a route to manipulating the magnitude and the sign of the magnetic triakontadipoles as well as the spin splitting. Furthermore, we find that both the ferroic ordering of the magnetic triakontadipoles and many of the spin-split features persist in the weak ferromagnetic phase above the Morin transition temperature. Published by the American Physical Society 2024

Interlayer and interfacial Dzyaloshinskii-Moriya interaction in magnetic trilayers: First-principles calculations

We determine the Dzyaloshinskii-Moriya interaction within and between two magnetic cobalt layers separated by a nonmagnetic spacer through calculations. We investigate different materials for the nonmagnetic layer, focusing on the experimentally realized Co/Ag/Co system. We laterally shift the atoms in the nonmagnetic layer to achieve the symmetry breaking required for the interlayer Dzyaloshinskii-Moriya interaction. We compare the resulting interactions with the Levy-Fert model and observe a good overall agreement between the model and the calculations for the dependence on the atomic positions. Additionally, we derive a formula for the strength of the interlayer isotropic exchange interaction depending on the position of the atoms in the nonmagnetic layer and compare it to the first-principles results. We investigate the limitations of the Levy-Fert model by turning off the spin-orbit coupling separately on the nonmagnetic and magnetic atoms and by studying the effect of band filling. Our work advances the understanding of the microscopic mechanisms of the interlayer Dzyaloshinskii-Moriya interaction and gives insight into possible new material combinations with strong interlayer Dzyaloshinskii-Moriya interaction. Published by the American Physical Society 2024

Interband optical absorption coefficient of the diluted magnetic semiconductor ellipsoid quantum dot with Rashba spin orbit interaction

Interband optical absorption coefficient of the diluted magnetic semiconductor ellipsoid quantum dot with Rashba spin orbit interaction

Chirality-induced phonon spin selectivity by elastic spin–orbit interaction

Spin and orbital degrees of freedom are crucial in not only fundamental particles but also classical waves such as optical systems, wherein the spin-orbit interaction (SOI) of light provides new perspectives for manipulating electromagnetic waves. Elastic waves possess similar spin angular momentum (SAM) and orbital angular momentum (OAM). However, the elastic counterpart of SOI remains unexplored, even for ubiquitous elastic waveguides (WG). Here, we demonstrate the existence of elastic SOI in helical WG. We prove that the torsion and curvature of helical WG induces synthetic gauge potentials in describing the elastic vibrations. Through analytical theory and simulations, we unveil the interplay among elastic SAM, intrinsic OAM, and extrinsic OAM, impacted by the elastic SOI. Importantly, results show that elastic SOI can introduce the Chirality-Induced Phonon Spin Selectivity. These findings advance our understanding of angular momentum physics in elastic waves and enable practical strategies for wave manipulation.

Electron-Spin Relaxation in Boron-Doped Graphene Nanoribbons.

Boron-doped graphene nanoribbons are promising platforms for developing organic materials with magnetic properties. Boron dopants can be used to create localized magnetic states in nanoribbons with tunable interactions. Controlling the coherence times of these magnetic states is the very first step in designing materials for quantum computation or information storage. In this work, we address the connection between the relaxation time and the position of the dopants for a series of boron-doped graphene nanofragments. We combine Redfield theory and ab initio calculations of magnetic properties to unveil the mechanism that governs spin relaxation in solution. We demonstrate that relaxation times can be in the order of 1 ms for the selected graphene nanofragments. A detailed analysis of the relaxation mechanism reveals that the spin decoherence is fundamentally driven by fluctuations of the spin-orbit coupling, and the hyperfine interaction facilitated by the thermal motion of the graphene nanofragments. The close connection between relaxation time, hyperfine interaction and the spin-orbit coupling offers the perspective of designing attractive materials with long-lived spin states.

Strain-Induced Antiferroelectric-Ferroelectric-Antiferroelectric Phase Transitions in Epitaxial LaTaO4 Films.

We employed first-principles to delve into the strain-induced structural phase transitions in epitaxial LaTaO4 films. The ground state of bulk LaTaO4 adopts a monoclinic antiferroelectric phase, characterized by the antiphase rotation of two adjacent oxygen octahedra layers. Under epitaxial tensile strain, LaTaO4 thin films undergo a consecutive phase transition, namely, antiferroelectric-ferroelectric-antiferroelectric phase transitions. The ferroelectricity in the orthorhombic phase under tensile strain originates from the in-phase rotation of two adjacent oxygen octahedra layers, in contrast to the case of perovskite systems, in which octahedra rotation suppresses the conventional proper ferroelectricity. With spin-orbit coupling effects, a pronounced Rashba effect at the Brillouin zone center naturally leads to the formation of opposite directions of spin texture. Moreover, the tensile strain also synergistically enhances the corresponding Rashba parameters. Our findings may provide novel insights for controlling oxygen octahedra rotation to achieve control over the ferroelectricity and Rashba effect, which holds promising implications for applications in electronics and spintronics.

Erratum: Spin-Group Symmetry in Magnetic Materials with Negligible Spin-Orbit Coupling [Phys. Rev. X 12 , 021016 (2022)

Erratum: Spin-Group Symmetry in Magnetic Materials with Negligible Spin-Orbit Coupling [Phys. Rev. X <b>12</b> , 021016 (2022)

Rotating nonlinear states in trapped binary Bose-Einstein condensates under the action of the spin-orbit coupling

Abstract We report results of systematic analysis of confined steadily rotating patterns in the two-component BEC including the spin-orbit coupling (SOC) of the Rashba type, which acts in the interplay with the attractive or repulsive intra-component and inter-component nonlinear interactions and confining potential. The analysis is based on the system of the Gross-Pitaevskii equations (GPEs) written in the rotating coordinates. The resulting GPE system includes effective Zeeman splitting. In the case of the attractive nonlinearity, the analysis, performed by means of the imaginary-time simulations, produces deformation of the known two-dimensional SOC solitons (semi-vortices and mixed-modes). Essentially novel findings are reported in the case of the repulsive nonlinearity. They demonstrate patterns arranged as chains of unitary vortices which, at smaller values of the rotation velocity $\Omega $, assume the straight (single-string) form. At larger $\Omega $, the straight chains become unstable, being spontaneously replaced by a trilete star-shaped array of&amp;#xD;vortices. At still large values of $\Omega $, the trilete pattern rebuilds itself into a star-shaped one formed of five and, then, seven strings. The transitions between the different patterns are accounted for by comparison of their energy. It is shown that the straight chains of vortices, which form the star-shaped structures, are aligned with boundaries between domains populated by plane waves with different wave vectors. A transition from an axisymmetric higher-order (multiple) vortex state to the trilete pattern is investigated too.

Impact of Cr doping on Hall resistivity and magnetic anisotropy in SrRuO3 thin films.

Hall effects, including anomalous and topological types, in correlated ferromagnetic oxides provide an intriguing framework to investigate emergent phenomena arising from the interaction between spin-orbit coupling and magnetic fields. SrRuO3 is a widely studied itinerant ferromagnetic system with intriguing electronic and magnetic characteristics. The electronic transport of SrRuO3 is highly susceptible to the defects (O/Ru vacancy, chemical doping, ion implantation), and interfacial strain. In this regard, we investigate the impact of Cr doping on the magnetic anisotropy and the Hall effect in SrRuO3 thin films. The work encompasses a comprehensive analysis of the structural, spectroscopic, magnetic, and magnetotransport properties of Cr-doped SrRuO3 films grown on SrTiO3(001) substrates. Cross-sectional transmission electron microscopy reveals a sharp and coherent interface between the layers. Notably, perpendicular magnetic anisotropy is preserved in doped films with thicknesses up to 113 nm. The resistivity exhibits a T^2 dependence below the Curie temperature, reflecting the influence of disorder and correlation-induced localization effects. Interestingly, in contrast to the undoped parent compound SrRuO3, an anomaly in the Hall signal has been observed up to a large thickness (56 nm) attributed to the random Cr doping and Ru vacancy. Based on our measurements, a field-temperature (H -T) phase diagram of anomalous Hall resistivity is constructed.

Thermal quantum coherence: A Comparative Study of Molybdenum Disulfide vs. Graphene

Abstract This study examines quantum coherence in molybdenum disulfide $MoS_2$ by considering thermal fluctuations and the spin-orbit coupling of molybdenum's $d$ orbitals. Our results reveal that at the ground state, the system exhibits significant coherence, particularly for high values of the wave vector $k$. Interestingly, this coherence improves with increasing temperature before asymptotically decreasing towards zero. In conclusion, we have shown that graphene generally outperforms molybdenum due to its perfect two-dimensional structure thanks to the high mobility of electrons in its conduction bands. Moreover, these findings enable predictions about the behavior of other materials with similar band structures based on their crystal lattice interactions.

Non-adiabatic coupling matrix elements in a magnetic field: Geometric gauge dependence and Berry phase.

Non-adiabatic coupling matrix elements (NACMEs) are important in quantum chemistry, particularly for molecular dynamics methods such as surface hopping. However, NACMEs are gauge dependent. This presents a difficulty for their calculation in general, where there are no restrictions on the gauge function except that it be differentiable. These cases are relevant for complex-valued electronic wave functions, such as those that arise in the presence of a magnetic field or spin-orbit coupling. In addition, the Berry curvature and Berry force play an important role in molecular dynamics in a magnetic field and are also relevant in the context of spin-orbit coupling. For methods such as surface hopping, excited-state Berry curvatures will also be of interest. With this in mind, we have developed a scheme for the calculation of continuous, differentiable NACMEs as a function of the molecular geometry for complex-valued wave functions. We demonstrate the efficacy of the method using the H2 molecule at the full configuration-interaction (FCI) level of theory. In addition, ground- and excited-state Berry curvatures are computed for the first time using FCI theory. Finally, Berry phases are computed directly in terms of diagonal NACMEs.

Conformation and Bonding of Lanthanide(III) Trihalides LnX3 (Ln = La-Lu; X = F, Cl, Br): A Relativistic Local Vibrational Mode Study.

This study employed relativistic methods to investigate the connection between the conformation and bonding properties of 45 lanthanide trihalides LnX3 (Ln: La-Lu; X:F, Cl, Br). Our findings reveal several insights. The proper symmetry exhibited by open-shell LnX3 requires the inclusion of spin-orbit coupling, achieved with 2-component relativistic Hamiltonians. Fluorines (LnF3) primarily exhibit pyramidal structures, while chlorides and bromides tend to yield planar conformations. For a given halide, the strength of Ln-X bonds increases across the lanthanide series, another outcome of the lanthanide contraction. Both strength and covalency of Ln-X bonds decrease upon the halide, i.e., LnF3 > LnCl3 > LnBr3. We introduced a novel parameter, the local force constant associated with the dihedral β(X-Ln-X-X), ka(β), which quantifies the resistance of these molecules to conformational changes. We observed a correlation between ka(β) and the covalency of the Ln-X bond, with higher ka(β) values indicating a stronger covalent character. Finally, the degree of pyramidalization in the LnX3 structures is connected to (i) the extent of charge donation within the molecule and (ii) the greater covalency of the Ln-X bond. These findings provide valuable insights into the interplay between the electronic structure and molecular geometry in LnX3.

Creation of Two-Dimensional Electron Gas at the Heterointerface of CaZrO3/KTaO3 with Tunable Rashba Spin–Orbit Coupling

Creation of Two-Dimensional Electron Gas at the Heterointerface of CaZrO₃/KTaO₃ with Tunable Rashba Spin–Orbit Coupling

First principles investigations on structural, electronic, optical, and thermodynamical properties of bulk and surfaces of In2CO

This study reports first-principles investigations of the structural, electronic, thermal, and optical properties of a novel material In2CO in bulk phase and slab models in (001), (100), (101), and (011) orientations to develop a fundamental understanding of its characteristics. The material appeared structurally as well as dynamically stable in the orthorhombic phase. The thermal properties demonstrated that the material's heat capacity is more temperature-sensitive than entropy and enthalpy. The electronic band structure analysis revealed that the orthorhombic phase material is a semiconductor with a narrow indirect band gap. The electronic structures modeled using the spin-orbit coupling yielded the metallic phase of the slabs except for (001) orientation. The electromagnetic absorption characteristics of the compound are also investigated to explore the material's potential in optoelectronic applications. The direction-dependent study of optical characteristics revealed that the (001) slab of the material can be an efficient infrared detector. The survey findings provide instrumental outcomes in utilizing In2CO in electronic and optoelectronic applications.

Room-Temperature Ferromagnetism with Strong Spin-Orbit Coupling Achieved in CaRuO3 Interfacial Phase via Magnetic Proximity Effect.

Recently, theoretical and experimental research predicted that ferromagnets with strong spin-orbit coupling (SOC) could serve as spin sources with dramatically enhanced spin-orbit torque (SOT) efficiency due to the combination of spin Hall effect and anomalous Hall effect (AHE), presenting potential advantages over conventional nonmagnetic heavy metals. However, materials with a strong SOC and room-temperature ferromagnetism are rare. Here, we report on a ferromagnetic (FM) interfacial phase with Curie temperature exceeding 300 K in the heavy transition-metal oxide CaRuO3, in proximity to La0.67Sr0.33MnO3. Electron energy loss and polarized neutron reflectometry spectra reveal the strong charge transfer from Ru to Mn at the interface, triggering antiferromagnetic exchange interactions between interfacial Ru/Mn ions and thus transferring magnetic order from La0.67Sr0.33MnO3 to CaRuO3. An obvious advantage of such interfacial phase is the enhanced anomalous Hall effect at temperatures from 150 to 300 K. Compared to the most promising room-temperature ferromagnetic oxide La0.67Sr0.33MnO3, the anomalous Hall conductivity σxyAHE (or anomalous Hall angle θH) of CaRuO3/La0.67Sr0.33MnO3 superlattices is increased by 30 (or 31) times at 150 K and 10 (or 3) times at 300 K. This work demonstrates a special approach for inducing ferromagnetism in heavy transition-metal oxides with strong SOC, offering promising prospects for all-oxide-based spintronic applications.

Embedding Plate‐Like Pyrochlore in Perovskite Phase to Enhance Energy Storage Performance of BNT‐Based Ceramic Capacitors

AbstractNext‐generation electrical and electronic systems rely on the development of efficient energy‐storage dielectric ceramic capacitors. However, achieving a synergistic enhancement in the polarization and in the breakdown field strength (Eb) presents a considerable challenge. Herein, a heterogeneous combination strategy involving embedding a high Eb plate‐like pyrochlore phase in a high‐polarization perovskite phase is proposed. The embedded plate‐like pyrochlore increases the breakdown field strength and promotes the dynamic polarization response. Meanwhile, the strong spin–orbit coupling effect of the 5d electrons is conducive to the maintenance of the high polarization value of the perovskite. Consequently, the prepared multilayer ceramic capacitor (MLCC) exhibits an ultrahigh Eb and a high polarization. More specifically, an energy storage density (Wrec) of 14.9 J cm−3 with an efficiency of up to 93.4% is achieved for the optimized pyrochlore/perovskite phase. Furthermore, the MLCCs also exhibits an Wrec of ≈ 7.7 J cm−3 ± 4.5% in the temperature range of −50–180 °C. Therefore, this heterogeneous combination strategy therefore provides a simple and effective method for improving the energy‐storage performances of dielectric ceramic capacitors.

Spin–orbit enabled unconventional Stoner magnetism

The Stoner instability remains a cornerstone for understanding metallic ferromagnets. This instability captures the interplay of Coulomb repulsion, Pauli exclusion, and twofold fermionic spin degeneracy. In materials with spin-orbit coupling, this fermionic spin is generalized to a twofold degenerate pseudospin which is typically believed to have symmetry properties as spin. Here, we identify a distinct symmetry of this pseudospin that forbids it to couple to a Zeeman field. This "spinless" property is required to exist in five nonsymmorphic space groups and has nontrivial implications for superconductivity and magnetism. With Coulomb repulsion, Fermi surfaces composed primarily of this spinless pseudospin property give rise to Stoner instabilities into magnetic states that are qualitatively different than ferromagnets. These spinless-pseudospin ferromagnets break time-reversal symmetry, have a vanishing magnetization, are noncollinear, and exhibit momentum-dependent energy band spin-splittings. In superconductors, for all pairing symmetries and field orientations, this spinless pseudospin extinguishes paramagnetic limiting. We discuss applications to superconducting UCoGe and magnetic NiS[Formula: see text]Se[Formula: see text].

Electromagnetically tunable spin-valley-polarized current via anomalous Nernst effect in monolayer of jacutingaite.

Monolayer jacutingaite (Pt2HgSe3) exhibits remarkable properties, including significant spin-orbit coupling and a tunable band gap, attributed to its buckled honeycomb geometry and the presence of heavy atoms. In this study, we explore the spin- and valley-dependent anomalous Nernst effect (ANE) in jacutingaite under the influence of a vertical electric field, off-resonance circularly polarized light (OCPL), and an antiferromagnetic exchange field. Our findings, within the low-energy approximation, reveal the emergence of a perfectly spin-polarized ANE with the application of appropriate OCPL and a perfectly valley-polarized ANE under an antiferromagnetic exchange field. Leveraging the robust spin-orbit coupling inherent in monolayer jacutingaite, our study highlights the potential to attain perfectly spin-valley-polarized Nernst currents across a wide range of Fermi energy levels by combining these fields in pairs with a suitable strength. The findings can be used for the development of spin-valley-based optoelectronic devices.&#xD.

Revisiting the global minimum of Au10 clusters.

This study employs high-level quantum chemical calculations to determine the global minimum structure of Au10 clusters definitively. Contrary to previous reports, coupled-cluster singles and doubles with perturbative triples [CCSD(T)] calculations with sizable quadruple-ζ basis sets incorporating the spin-orbit (SO) effect reveal that the planar 10.b structure is the true global minimum for Au10, not the three-dimensional 10.a structure. Two-component spin-orbit density functional theory calculations demonstrate that the SO effect is minimal for most Au10 isomers, except for the 10.f structure. A straightforward diagnostic tool is proposed for identifying Au cluster structures with strong spin-orbit coupling based on 6p orbital occupation. The calculated IR spectra based on Boltzmann averaging the six Au10 isomers show good agreement with recent experimental spectra although minor discrepancies are noted potentially due to interactions with Kr. The results suggest that the transition point to non-planar global minimum structures for Au clusters lies beyond Au10 but is nearby.

Exact-Two-Component Complete Active Space Method with Variational Treatment of Magnetic Field and Spin-Orbit Coupling: Application to X-ray Magnetic Circular Dichroism Spectroscopy.

We introduce an exact-two-component complete active space self-consistent-field (X2C-CASSCF) method formulated under the restricted-magnetic-balance condition. This framework allows for the nonperturbative treatment of static magnetic fields using gauge-including atomic orbitals (GIAOs). The GIAO-X2C-CASSCF methodology effectively captures all microstates within the same 2J + 1-degenerate manifold and their splitting in a static magnetic field, which are not accessible through single-reference-based methods. We also present mathematical recursive expressions for evaluating one-electron relativistic integrals by using GIAOs in the presence of a finite magnetic field. Benchmark studies include oxygen and nitrogen K-edge X-ray magnetic circular dichroism spectroscopy (XMCD) for closed-shell organic compounds, as well as L-edge XMCD spectroscopy for the high-spin open-shell transition metal ion Mn2+ and the tetrahedral Mn(II)O46- complex.