Spin-orbit Coupling Regime Research Articles

Room-temperature anisotropic in-plane spin dynamics in graphene induced by PdSe2 proximity.

van der Waals heterostructures provide a versatile platform for tailoring electrical, magnetic, optical and spin transport properties via proximity effects. Hexagonal transition metal dichalcogenides induce valley Zeeman spin-orbit coupling in graphene, creating spin lifetime anisotropy between in-plane and out-of-plane spin orientations. However, in-plane spin lifetimes remain isotropic due to the inherent heterostructure's three-fold symmetry. Here we demonstrate that pentagonal PdSe2, with its unique in-plane anisotropy, induces anisotropic gate-tunable spin-orbit coupling in graphene. This enables a tenfold modulation of spin lifetimes at room temperature, depending on the in-plane spin orientation. Moreover, the directional dependence of the spin lifetimes, along the three spatial directions, reveals a persistent in-plane spin texture component that governs the spin dynamics. These findings advance our understanding of spin physics in van der Waals heterostructures and pave the way for designing topological phases in graphene-based heterostructures in the strong spin-orbit coupling regime.

Dynamic Jahn-Teller effect in the strong spin-orbit coupling regime

Exotic quantum phases, arising from a complex interplay of charge, spin, lattice and orbital degrees of freedom, are of immense interest to a wide research community. A well-known example of such an entangled behavior is the Jahn-Teller effect, where the lifting of orbital degeneracy proceeds through lattice distortions. Here we demonstrate that a highly-symmetrical 5d1 double perovskite Ba2MgReO6, comprising a 3D array of isolated ReO6 octahedra, represents a rare example of a dynamic Jahn-Teller system in the strong spin-orbit coupling regime. Thermodynamic and resonant inelastic x-ray scattering experiments, supported by quantum chemistry calculations, undoubtedly show that the Jahn-Teller instability leads to a ground-state doublet, resolving a long-standing puzzle in this family of compounds. The dynamic state of ReO6 octahedra persists down to the lowest temperatures, where a multipolar order sets in, allowing for investigations of the interplay between a dynamic JT effect and strongly correlated electron behavior.

Physical origin of the anisotropic exchange tensor close to the first-order spin-orbit coupling regime and impact of the electric field on its magnitude.

This article follows earlier studies on the physical origin of magnetic anisotropy and the means of controlling it in polynuclear transition metal complexes. The difficulties encountered when focusing a magnetic field on a molecular object have led to consider the electric field as a more appropriate control tool. It is therefore fundamental to understand what governs the sensitivity of magnetic properties to the application of an electric field. We have already studied the impact of the electric field on the isotropic exchange coupling and on the Dzyaloshinskii-Moriya interaction (DMI). Here, we focus on the symmetric exchange anisotropy tensor. In order to obtain significant values of anisotropic interactions, we have carried out this study on a model complex that exhibits first-order spin-orbit coupling. We will show that (i) large values of the axial parameter of symmetric exchange can be reached when close to the first-order spin-orbit coupling regime, (ii) both correlated energies and wave functions must be used to achieve accurate values of the symmetric tensor components when the DMI is non-zero, and (iii) finally, an interferential effect between the DMI and the axial parameter of symmetric exchange occurs for a certain orientation of the electric field, i.e., the latter decreases in magnitude as the former increases. While DMI is often invoked as being involved in magneto-electric coupling, isotropic exchange and the symmetrical anisotropic tensor also contribute. Finally, we provide a recipe for generating significant anisotropic interactions and a significant change in magnetic properties under an electric field.

Intrinsic orbital and spin Hall effect in bismuth semimetal

We investigate the intrinsic orbital Hall conductivity (OHC) and spin Hall conductivity (SHC) in a bismuth semimetal, by employing an $sp$-orbital tight-binding model. We report a notable difference between the anisotropy of OHC and SHC whose orbital and spin polarizations lie within the basal plane. We do not observe a substantial correlation between the orbital and spin Berry curvatures with spin-orbit coupling (SOC) at the Fermi energy, disproving the correlation between OHC and SHC in a strong SOC regime. We argue the huge SHC in a Bi semimetal is attributed to its gigantic SOC which strongly affects the hybridization of the $p$ orbitals, despite its relatively small magnitude of OHC. We hope the distinct anisotropy of OHC and SHC provides a feasible means to differentiate between the two effects in experiments.

Correlated insulating states in carbon nanotubes controlled by magnetic field

Recent experiments have shown that nearly metallic nanotubes remain insulating throughout magnetic field sweeps, in which the magnetic flux through the nanotube is expected to pass through a critical point where the single-particle band gap closes in one valley. Here, the authors investigate correlated insulating states of zigzag carbon nanotubes, which emerge from the interplay of electron-electron interactions, magnetic flux, strain, and spin-orbit coupling. They find that the gap for charged excitations generically remains open near the critical flux value, and predict a novel mirror symmetry breaking phase that may arise in the experimentally relevant regime of spin-orbit coupling.

Extraction of giant Dzyaloshinskii-Moriya interaction from ab initio calculations: First-order spin-orbit coupling model and methodological study.

The Dzyaloshinskii-Moriya interaction is expected to be at the origin of interesting magnetic properties, such as multiferroicity, skyrmionic states, and exotic spin orders. Despite this, its theoretical determination is far from being established, neither from the pointof view of ab initio methodologies nor from that of the extraction technique to be used afterward. Recently, a very efficient way to increase its amplitude has been demonstrated near the first-order spin-orbit coupling regime. Within the first-order regime, the anisotropic spin Hamiltonian involving the Dzyaloshinskii-Moriya operator becomes inappropriate. Nevertheless, in order to approach this regime and identify the spin Hamiltonian limitations, it is necessary to characterize the underlying physics. To this end, we have developed a simple electronic and spin-orbit model describing the first-order regime and used ab initio calculations to conduct a thorough methodological study.

Evolution of Spin-Orbital Entanglement with Increasing Ising Spin-Orbit Coupling

Several realistic spin-orbital models for transition metal oxides go beyond the classical expectations and could be understood only by employing the quantum entanglement. Experiments on these materials confirm that spin-orbital entanglement has measurable consequences. Here, we capture the essential features of spin-orbital entanglement in complex quantum matter utilizing 1D spin-orbital model which accommodates SU(2)⊗SU(2) symmetric Kugel-Khomskii superexchange as well as the Ising on-site spin-orbit coupling. Building on the results obtained for full and effective models in the regime of strong spin-orbit coupling, we address the question whether the entanglement found on superexchange bonds always increases when the Ising spin-orbit coupling is added. We show that (i) quantum entanglement is amplified by strong spin-orbit coupling and, surprisingly, (ii) almost classical disentangled states are possible. We complete the latter case by analyzing how the entanglement existing for intermediate values of spin-orbit coupling can disappear for higher values of this coupling.

How spin-orbital entanglement depends on the spin-orbit coupling in a Mott insulator

The concept of the entanglement between spin and orbital degrees of freedom plays a crucial role in understanding various phases and exotic ground states in a broad class of materials, including orbitally ordered materials and spin liquids. We investigate how the spin-orbital entanglement in a Mott insulator depends on the value of the spin-orbit coupling of the relativistic origin. To this end, we numerically diagonalize a 1D spin-orbital model with the 'Kugel-Khomskii' exchange interactions between spins and orbitals on different sites supplemented by the on-site spin-orbit coupling. In the regime of small spin-orbit coupling w.r.t. the spin-orbital exchange, the ground state to a large extent resembles the one obtained in the limit of vanishing spin-orbit coupling. On the other hand, for large spin-orbit coupling the ground state can, depending on the model parameters, either still show negligible spin-orbital entanglement, or can evolve to a highly spin-orbitally entangled phase with completely distinct properties that are described by an effective XXZ model. The presented results suggest that: (i) the spin-orbital entanglement may be induced by large on-site spin-orbit coupling, as found in the 5d transition metal oxides, such as the iridates; (ii) for Mott insulators with weak spin-orbit coupling of Ising-type, such as e.g. the alkali hyperoxides, the effects of the spin-orbit coupling on the ground state can, in the first order of perturbation theory, be neglected.

Enhancing von Neumann entropy by chaos in spin–orbit entanglement**Project supported by the National Natural Science Foundation of China (Grant Nos. 11775101 and 11422541) and the US Office of Naval Research (Grant No. N00014-16-1-2828).

For a quantum system with multiple degrees of freedom or subspaces, loss of coherence in a certain subspace is intimately related to the enhancement of entanglement between this subspace and another one. We investigate intra-particle entanglement in two-dimensional mesoscopic systems, where an electron has both spin and orbital degrees of freedom and the interaction between them is enabled by Rashba type of spin–orbit coupling. The geometric shape of the scattering region can be adjusted to produce a continuous spectrum of classical dynamics with different degree of chaos. Focusing on the spin degree of freedom in the weak spin–orbit coupling regime, we find that classical chaos can significantly enhance spin–orbit entanglement at the expense of spin coherence. Our finding that classical chaos can be beneficial to intra-particle entanglement may have potential applications such as enhancing the bandwidth of quantum communications.

Toward the evaluation of intersystem crossing rates with variational relativistic methods.

The change in electronic state from one spin multiplicity to another, known as intersystem crossing, occurs in molecules via the relativistic phenomenon of spin-orbit coupling. Current means of estimating intersystem crossing rates rely on the perturbative evaluation of spin-orbit coupling effects. This perturbative approach, valid in lighter atoms where spin-orbit coupling is weaker, is expected to break down for heavier elements where relativistic effects become dominant. Methods which incorporate spin-orbit effects variationally, such as the exact-two-component (X2C) method, will be necessary to treat this strong-coupling regime. We present a novel procedure which produces a diabatic basis of spin-pure electronic states coupled by spin-orbit terms, generated from fully variational relativistic calculations. This method is implemented within X2C using time-dependent density-functional theory and is compared to results from a perturbative relativistic study in the weak spin-orbit coupling regime. Additional calculations on a more strongly spin-orbit-coupled [UO2Cl4]2- complex further illustrate the strengths of this method. This procedure will be valuable in the estimation of intersystem crossing rates within strongly spin-coupled species.

Toward the Optimized Spintronic Response of Sn‐Doped IrO2 Thin Films

AbstractAmorphous and polycrystalline Sn‐doped IrO2 thin films, Ir1‐xSnxO2, are grown for the first time. Their electrical response and strength of the spin–orbit coupling are studied in order to better understand and tailor its performance as spin current detector material. These experiments prove that the resistivity of IrO2 can be tuned over several orders of magnitude by controlling the doping content in both the amorphous and the polycrystalline state. In addition, growing amorphous samples increase the resistivity, thus improving the spin current to charge current conversion. As far as the spin–orbit coupling is concerned, the system not only remains in a strong spin–orbit coupling regime but it seems to undergo a slight enhancement in the amorphous state as well as in the Sn‐doped samples.

Microscopic theory of spin relaxation anisotropy in graphene with proximity-induced spin-orbit coupling

Inducing sizable spin--orbit interactions in graphene by proximity effect is establishing as a successful route to harnessing two-dimensional Dirac fermions for spintronics. Semiconducting transition metal dichalcogenides (TMDs) are an ideal complement to graphene because of their strong intrinsic spin--orbit coupling (SOC) and spin/valley-selective light absorption, which allows all-optical spin injection into graphene. In this study, we present a microscopic theory of spin dynamics in weakly disordered graphene samples subject to uniform proximity-induced SOC as realized in graphene/TMD bilayers. A time-dependent perturbative treatment is employed to derive spin Bloch equations governing the spin dynamics at high electronic density. Various scenarios are predicted, depending on a delicate competition between interface-induced Bychkov-Rashba and spin--valley (Zeeman-type) interactions and the ratio of intra- to inter-valley scattering rates. For weak SOC compared to the disorder-induced quasiparticle broadening, the anisotropy ratio of out-of-plane to in-plane spin lifetimes $\zeta=\tau_{s}^{\perp}/\tau_{s}^{\parallel}$ agrees qualitatively with a toy model of spins in a weak fluctuating SOC field recently proposed by Cummings and co-workers [PRL 119, 206601 (2017)]. In the opposite regime of well-resolved SOC, qualitatively different formulae are obtained, which can be tested in ultra-clean heterostructures characterized by uniform proximity-induced SOC in the graphene layer.

Spin-relaxation anisotropy in a nanowire quantum dot with strong spin-orbit coupling

We study the impacts of the magnetic field direction on the spin-manipulation and the spin-relaxation in a one-dimensional quantum dot with strong spin-orbit coupling. The energy spectrum and the corresponding eigenfunctions in the quantum dot are obtained exactly. We find that no matter how large the spin-orbit coupling is, the electric-dipole spin transition rate as a function of the magnetic field direction always has a π periodicity. However, the phonon-induced spin relaxation rate as a function of the magnetic field direction has a π periodicity only in the weak spin-orbit coupling regime, and the periodicity is prolonged to 2π in the strong spin-orbit coupling regime.

Interplay of covalency, spin-orbit coupling, and geometric frustration in the d3.5 system Ba3LiIr2O9

The electronic and magnetic properties of ${d}^{3.5}$ iridate ${\mathrm{Ba}}_{3}{\mathrm{LiIr}}_{2}{\mathrm{O}}_{9}$ have been studied using first-principles electronic structure calculations. The results of the calculations reveal that the system lies in an intermediate spin-orbit coupling (SOC) regime. There is strong covalency of $\mathrm{Ir}\ensuremath{-}5d$ and $\text{O}\ensuremath{-}2p$ orbitals. SOC, together with covalency, conspires to reduce the magnetic moment at the Ir site. By calculating the hopping interactions and exchange interactions, it is found that there is strong antiferromagnetic intradimer coupling within an ${\mathrm{Ir}}_{2}{\mathrm{O}}_{9}$ unit and other antiferromagnetic interdimer interactions make the system frustrated. The anisotropic magnetic interactions are also calculated. The calculations reveal that the magnitude of the Dzyaloshinskii-Moriya interactions parameter is small for this system. The magnetocrystalline anisotropy energy is large for this system and the easy axis lies on the $ab$ plane.

The impacts of the quantum-dot confining potential on the spin-orbit effect

For a nanowire quantum dot with the confining potential modeled by both the infinite and the finite square wells, we obtain exactly the energy spectrum and the wave functions in the strong spin-orbit coupling regime. We find that regardless of how small the well height is, there are at least two bound states in the finite square well: one has the σx{mathscr{P}} = −1 symmetry and the other has the σx{mathscr{P}} = 1 symmetry. When the well height is slowly tuned from large to small, the position of the maximal probability density of the first excited state moves from the center to x ≠ 0, while the position of the maximal probability density of the ground state is always at the center. A strong enhancement of the spin-orbit effect is demonstrated by tuning the well height. In particular, there exists a critical height {V}_{0}^{c}, at which the spin-orbit effect is enhanced to maximal.

Anisotropy of transport in bulk Rashba metals

The recent experimental discovery of three-dimensional (3D) materials hosting a strong Rashba spin-orbit coupling calls for the theoretical investigation of their transport properties. Here we study the zero temperature dc conductivity of a 3D Rashba metal in the presence of static diluted impurities. We show that, at variance with the two-dimensional case, in 3D systems spin-orbit coupling affects dc charge transport in all density regimes. We find in particular that the effect of spin-orbit interaction strongly depends on the direction of the current, and we show that this yields strongly anisotropic transport characteristics. In the dominant spin-orbit coupling regime where only the lowest band is occupied, the SO-induced conductivity anisotropy is governed entirely by the anomalous component of the renormalized current. We propose that measurements of the conductivity anisotropy in bulk Rashba metals may give a direct experimental assessment of the spin-orbit strength.

Induced interactions in the BCS-BEC crossover of two-dimensional Fermi gases with Rashba spin-orbit coupling

We investigate the Gorkov--Melik-Barkhudarov (GM) correction to superfluid transition temperature in two-dimensional Fermi gases with Rashba spin-orbit coupling (SOC) across the SOC-driven BCS-BEC crossover. In the calculation of the induced interaction, we find that the spin-component mixing due to SOC can induce both of the conventional screening and additional antiscreening contributions that interplay significantly in the strong SOC regime. While the GM correction generally lowers the estimate of transition temperature, it turns out that at a fixed weak interaction, the correction effect exhibits a crossover behavior where the ratio between the estimates without and with the correction first decreases with SOC and then becomes insensitive to SOC when it goes into the strong SOC regime. We demonstrate the applicability of the GM correction by comparing the zero-temperature condensate fraction with the recent quantum Monte Carlo results.

Excitation spectra of a Bose-Einstein condensate with an angular spin-orbit coupling

A theoretical model of a Bose-Einstein condensate with angular spin-orbit coupling has recently been proposed and it has been established that a half-skyrmion represents the ground state in a certain regime of spin-orbit coupling and interaction. Here we investigate low-lying excitations of this phase by using the Bogoliubov method and numerical simulations of the time-dependent Gross-Pitaevskii equation. We find that a sudden shift of the trap bottom results in a complex two-dimensional motion of the system's center of mass that is markedly different from the response of a competing phase, and comprises two dominant frequencies. Moreover, the breathing mode frequency of the half-skyrmion is set by both the spin-orbit coupling and the interaction strength, while in the competing state it takes a universal value. Effects of interactions are especially pronounced at the transition between the two phases.

Zeeman-field-induced nontrivial topological phases in a one-dimensional spin-orbit-coupled dimerized lattice

We study theoretically the interplay effect of Zeeman field and modulated spin-orbit coupling on topological properties of a one-dimensional dimerized lattice, known as Su-Schrieffer-Heeger model. We find that in the weak (strong) modulated spin-orbit coupling regime, trivial regions or nontrivial ones with two pairs of zero-energy states can be turned into nontrivial regions by applying a uniform (staggered) perpendicular Zeeman field through a topological phase transition. Furthermore, the resulting nontrivial phase hosting a pair of zero-energy boundary states can survive within a certain range of the perpendicular Zeeman field magnitude. Due to the effective time-reversal, particle-hole, chiral, and inversion symmetries, in the presence of either uniform or staggered perpendicular Zeeman field, the topological class of the system is BDI which can be characterized by $\mathbbm{Z}$ index. We also examine the robustness of the nontrivial phase by breaking the underlying symmetries giving rise that inversion symmetry plays an important role.

Three-dimensional quaternionic condensations, Hopf invariants, and skyrmion lattices with synthetic spin-orbit coupling

We study the topological configurations of the two-component condensates of bosons with the three-dimensional $(3\mathrm{D}) \stackrel{P\vec}{\ensuremath{\sigma}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{p}$ Weyl-type spin-orbit coupling subject to a harmonic trapping potential. The topology of the condensate wave functions manifests in the quaternionic representation. In comparison to the $\text{U}(1)$ complex phase, the quaternionic phase manifold is ${S}^{3}$ and the spin orientations form the ${S}^{2}$ Bloch sphere through the first Hopf mapping. The spatial distributions of the quaternionic phases exhibit the 3D skyrmion configurations, and the spin distributions possess nontrivial Hopf invariants. Spin textures evolve from the concentric distributions at the weak spin-orbit coupling regime to the rotation symmetry-breaking patterns at the intermediate spin-orbit coupling regime. In the strong spin-orbit coupling regime, the single-particle spectra exhibit the Landau-level-type quantization. In this regime, the three-dimensional skyrmion lattice structures are formed when interactions are below the energy scale of Landau-level mixings. Sufficiently strong interactions can change condensates into spin-polarized plane-wave states or superpositions of two plane waves exhibiting helical spin spirals.