Anisotropic Spin-orbit Coupling Research Articles

Electrical manipulation of the spins in phosphorene double quantum dots

We investigate electric dipole spin resonance (EDSR) induced by an oscillating electric field within a system of double quantum dots formed electrostatically in monolayer phosphorene. Apart from the observed anisotropy of effective masses, phosphorene has been predicted to exhibit anisotropic spin-orbit coupling. Here, we examine a system consisting of two electrons confined in double quantum dots. A single-band effective Hamiltonian together with the configuration interaction theory is implemented to simulate the time evolution of the ground state. We examine spin flips resulting from singlet-triplet transitions driven by external AC electric fields, both near and away from the Pauli blockade regime, revealing fast sub-nanosecond transition times. Furthermore, we analyze the impact of anisotropy by comparing dots arranged along a different crystal axis. The sub-harmonic multi-photon transitions and Landau-Zener-Stückelberg-Majorana transitions are discussed. We show modulation of spin-like and charge-like characteristics of the qubit through potential detuning.

Effect of anisotropic spin-orbit coupling on condensation and superfluidity of a two-dimensional Fermi gases

Effect of anisotropic spin-orbit coupling on condensation and superfluidity of a two-dimensional Fermi gases

Giant anisotropic Gilbert damping and spin wave propagations in single-crystal magnetic insulator

Gilbert damping in magnetic systems describes the relaxation of magnetization. This term was phenomenologically introduced into the Landau–Lifschitz–Gilbert (LLG) equation to describe spin dynamics. In most studies, such as magnetic random access memory, spin-wave propagations, and microwave devices, it has been assumed that the Gilbert damping is an isotropic constant. In this study, we uncover a giant anisotropic Gilbert damping parameter of up to 431% in single-crystal thin films of epitaxial [100]-oriented yttrium iron garnet (YIG) using angle-dependent ferromagnetic resonance. In contrast, the Gilbert damping parameter of a [111]-oriented YIG film is almost isotropic. The observed anisotropic damping is shown to have a similar fourfold symmetry with magneto-crystalline anisotropy. The anisotropic spin-wave group velocity (vg), relaxation time (τ), and decay length (ld) were also experimentally evaluated through spin-wave spectra of [100]-oriented YIG thin film. We developed the LLG equation with the introduction of an anisotropic orbital Gilbert damping term. This anisotropic orbital damping originates from the crystal-field dominated anisotropic spin–orbit coupling and orbital-related magnon–phonon coupling. Our results extend the understanding of the mechanism of anisotropic Gilbert damping in single-crystal magnetic insulators with strong magneto-crystalline anisotropy.

Itinerant ferromagnetism entrenched by the anisotropy of spin–orbit coupling in a dipolar Fermi gas

We investigate the itinerant ferromagnetism in a dipolar Fermi atomic system with the anisotropic spin–orbit coupling (SOC), which is traditionally explored with isotropic contact interaction. We first study the ferromagnetism transition boundaries and the properties of the ground states through the density and spin-flip distribution in momentum space, and we find that both the anisotropy and the magnitude of the SOC play an important role in this process. We propose a helpful scheme and a quantum control method which can be applied to conquering the difficulties of previous experimental observation of itinerant ferromagnetism. Our further study reveals that exotic Fermi surfaces and an abnormal phase region can exist in this system by controlling the anisotropy of SOC, which can provide constructive suggestions for the research and the application of a dipolar Fermi gas. Furthermore, we also calculate the ferromagnetism transition temperature and novel distributions in momentum space at finite temperature beyond the ground states from the perspective of experiment.

The tunable anisotropic Rashba spin-orbit coupling effect in Pb-adsorbed Janus monolayer WSeTe.

The spin-splitting properties of Pb-adsorbed monolayer Janus WSeTe are investigated based on first-principles calculations. The adsorbed system shows large Rashba splitting (the Rashba parameter is up to 0.75 eV Å), and we find that different adsorption layers (Te/Se adsorption layers) exhibit different significant features under spin-orbit coupling. Zeeman splitting and Rashba splitting co-exist at the high symmetry Γ point of the Te adsorption layer, while the Se adsorption layer exhibits anisotropic Rashba spin-orbit coupling. It was determined using k·p perturbation theory that Pb atom adsorption reduces the initial symmetry of the 2H-WSeTe monolayer and induces a strong spin-orbit coupling effect, so as to induce the anisotropic Rashba effect. Furthermore, the tunability of Rashba splitting was demonstrated by varying the adsorption concentration, adjusting the adsorption distance, and applying biaxial strain. This predicted adsorption system has potential value in spintronic devices.

FORTRESS: FORTRAN programs to solve coupled Gross-Pitaevskii equations for spin-orbit coupled spin-f Bose-Einstein condensate with spin f = 1 or 2

We provide here the updated versions of OpenMP parallelized FORTRAN 90/95 programs to numerically study the ground states and/or the dynamics of homogeneous or trapped spin-1 or spin-2 Bose-Einstein condensates (BECs) with anisotropic spin-orbit (SO) coupling. The coupled sets of three or five Gross-Pitaevskii (GP) equations, respectively, for a spin-1 or a spin-2 Bose-Einstein condensate (BEC) are solved using a time-splitting Fourier spectral method. New version program summaryProgram Title: FORTRESSCPC Library link to program files:https://doi.org/10.17632/st7md3ss85.2Developer's repository link:https://github.com/arko87/FORTRESSLicensing provisions: MITProgramming language: OpenMP Fortran 90/95Supplementary material: The key details to solve the five coupled Gross-Pitaevskii equations for an SO-coupled spin-2 BEC are presented in the supplementary file. In addition, some sample numerically obtained ground state solutions of SO-coupled spin-2 BECs and OpenMP performance results of the software with spin f=2 are provided.Journal reference of previous version: Comput. Phys. Commun. 259 (2021) 107671Does the new version supersede the previous version?: YesReasons for the new version: The previous version can be used to numerically study an SO-coupled spin-1 BEC only, whereas the new version extends the applicability of the software to the SO-coupled spin-2 BECs.Summary of revisions: The new features and augmentations in the package are as follows:(i) Input parameters relevant to the problem under investigation are now read via an input file. Three sample input files corresponding to quasi-one-dimensional (q1D), quasi-two-dimensional (q2D), and three-dimensional (3D) spinor BECs have been provided. The user can edit these files as per the requirement of the problem. Details of the parameters in the sample input files are described in the README.md file provided with the software.(ii) The software has been augmented to solve the five coupled Gross-Pitaevskii equations for SO-coupled spin-2 BECs. The users can now employ the software to study SO-coupled spin-2 [1] as well as spin-1 [2,3] BECs by merely providing the integer ‘SPIN’ parameter equal to 1 for a spin-1 or 2 for a spin-2 BEC in the input file.(iii) A Makefile has been provided to compile the programs with multiple (intel, GNU, and f95) compiler options. Depending on the availability or the choice of user, any of the above compiler options can be used. The user can furthermore choose the variable DIMENSION = 1D, 2D or 3D in the Makefile to simulate, respectively, q1D, q2D or 3D spinor BECs. Depending on the value of DIMENSION, the relevant input file will be read. All the details about using the Makefile are given in the README.md file.(iv) The double precision reals and arrays have been declared in a processor-independent manner.(v) The various arrays have been declared with ALLOCATABLE attribute to assign the memory dynamically and thus more efficiently manage the memory requirement of the software. For a particular allocatable array, memory is allocated using an ALLOCATE statement and deallocated by using a DEALLOCATE statement.(vi) OpenMP parallelization has been improved further.(vii) A few other minor modifications to the codes, e.g. inclusion of convergence criterion based on energy in addition to the criterion based on the absolute value of the wavefunctions in the previous version, directing error messages to a file, etc.Nature of problem: To solve the coupled Gross-Pitaevskii equations (CGPEs) for an SO-spin-f BEC with f=1 or 2.Solution method: We use a time-splitting Fourier spectral method to solve the CGPEs. The resulting equations are evolved in imaginary time to obtain the ground state of the system or in real time to study the dynamics. Additional details of the solution method applicable to spin-2 BEC are provided in the supplementary material.

Vortex chains induced by anisotropic spin–orbit coupling and magnetic field in spin-2 Bose-Einstein condensates

We investigate the anisotropic spin–orbit coupled spin-2 Bose–Einstein condensates with Ioffe–Pritchard magnetic field. With nonzero magnetic field, anisotropic spin–orbit coupling will introduce several vortices and further generate a vortex chain. Inside the vortex chain, the vortices connect to each other, forming a line along the axis. The physical nature of the vortex chain can be explained by the particle current and the momentum distribution. The vortex number inside the vortex chain can be influenced via varying the magnetic field. Through adjusting the anisotropy of the spin–orbit coupling, the direction of the vortex chain is changed, and the vortex lattice can be triggered. Moreover, accompanied by the variation of the atomic interactions, the density and the momentum distribution of the vortex chain are affected. The realization and the detection of the vortex chain are compatible with current experimental techniques.

Electrical Control of Valley-Zeeman Spin-Orbit-Coupling-Induced Spin Precession at Room Temperature.

The ultimate goal of spintronics is achieving electrically controlled coherent manipulation of the electron spin at room temperature to enable devices such as spin field-effect transistors. With conventional materials, coherent spin precession has been observed in the ballistic regime and at low temperatures only. However, the strong spin anisotropy and the valley character of the electronic states in 2D materials provide unique control knobs to manipulate spin precession. Here, by manipulating the anisotropic spin-orbit coupling in bilayer graphene by the proximity effect to WSe_{2}, we achieve coherent spin precession in the absence of an external magnetic field, even in the diffusive regime. Remarkably, the sign of the precessing spin polarization can be tuned by a back gate voltage and by a drift current. Our realization of a spin field-effect transistor at room temperature is a cornerstone for the implementation of energy efficient spin-based logic.

Role of orbital off-diagonal spin and charge condensates in a three orbital model for Ca2RuO4 – Coulomb renormalized spin-orbit coupling, orbital moment, and tunable magnetic order

Strongly anisotropic spin-orbit coupling (SOC) renormalization and strongly enhanced orbital magnetic moments are obtained in the fully self consistent approach including the orbital off-diagonal spin and charge condensates. For moderate tetragonal distortion as in Ca2 RuO4, dominantly planar antiferromagnetic (AFM) order with small canting of moments in and about the crystal c axis are obtained. For reduced tetragonal distortion, we find a tunable regime wherein the magnetic order can be tuned (AFM or FM) by the bare SOC strength and octahedral tilting magnitude. In this regime, with decreasing tetragonal distortion, AFM order is maintained by progressively decreasing octahedral tilting, as observed in Ca2−xSrx RuO4. For purely planar order, the only self consistent solution is FM order along crystal b axis, which is relevant for the bilayer ruthenate compound Ca3 Ru2 O7.

Silver addition in polycrystalline La0.7Ca0.3MnO3: Large magnetoresistance and anisotropic magnetoresistance for manganite sensors

Perovskite manganite La1−yCayMnO3 has giant and tunable magnetoresistance (MR) and anisotropic magnetoresistance (AMR), still the following two challenges are of great concern: (i) large magnetic field is required for achieving excellent electromagnetic performance; and (ii) metal–insulator (M–I) transition temperature (TMI) significantly different from room temperature; both these factors limit its practical applications. In this study, polycrystalline La0.7Ca0.3MnO3:Agx composites were fabricated by sol–gel and solid–phase addition methods, and large MR and AMR (84.1% and 32%, respectively) were obtained at near room temperature in 1 T magnetic field when x = 0.2. Evidently, it was found that the grain boundary scattering effects were weakened due to Ag−addition, which resulted in an enhancement of MR. The tremendously high AMR value was attributed to the anisotropic spin–orbit coupling (SOC) effect. The electron–scattering and small–polaron hopping models were used to successfully fit the resistivity data, which support the SOC effect under different magnetic fields that enhance the AMR. These results support further development of the perovskite manganese oxide with potential applications in manganite devices.

FORTRESS: FORTRAN programs for solving coupled Gross–Pitaevskii equations for spin–orbit coupled spin-1 Bose–Einstein condensate

Here, we present simple and efficient numerical scheme to study static and dynamic properties of spin-1 Bose–Einstein condensates (BECs) with spin–orbit (SO) coupling by solving three coupled Gross–Pitaevskii equations (CGPEs) in three-, quasi-two and quasi-one dimensional systems. We provide a set of three codes developed in FORTRAN 90/95 programming language with user defined ‘option’ of imaginary and real-time propagation. We present the numerical results for energy, chemical potentials, and component densities for the ground state and compare with the available results from the literature. The results are presented for both the ferromagnetic and antiferromagnetic spin-1 BECs with and without SO coupling. To improve the computational speed, all the codes have the option of OpenMP parallelization. We have also presented the results for speedup and efficiency of OpenMP parallelization for the three codes with both imaginary and real-time propagation. Program summaryProgram Title: FORTRESSCPC Library link to program files:https://doi.org/10.17632/st7md3ss85.1Licensing provisions: MITProgramming language: (OpenMP) FORTRAN 90/95External routines/libraries: FFTW 3.3.8Nature of problem: To solve the coupled Gross–Pitaevskii equations for spin-1 BEC with anisotropic spin–orbit coupling using the time-splitting spectral method.Solution method: We use the time-splitting Fourier spectral method to solve the coupled Gross–Pitaevskii equations. The resulting equations are evolved in imaginary time to obtain the ground state of the system or in real-time to study the dynamics.

Magnetic reorientation transition in a three orbital model for Ca2RuO4—interplay of spin–orbit coupling, tetragonal distortion, and Coulomb interactions

Including the orbital off-diagonal spin and charge condensates in the self consistent determination of magnetic order within a realistic three-orbital model for the 4d4 compound Ca2RuO4, reveals a host of novel features including strong and anisotropic spin–orbit coupling (SOC) renormalization, coupling of strong orbital magnetic moments to orbital fields, and a magnetic reorientation transition. Highlighting the rich interplay between orbital geometry and overlap, SOC, Coulomb interactions, tetragonal distortion, and staggered octahedral tilting and rotation, our investigation yields a planar antiferromagnetic (AFM) order for moderate tetragonal distortion, with easy a–b plane and easy b axis anisotropies, along with small canting of the dominantly yz, xz orbital moments. With decreasing tetragonal distortion, we find a magnetic reorientation transition from the dominantly planar AFM order to a dominantly c axis ferromagnetic order with significant xy orbital moment.

Electronic and Optical Properties of Two-Dimensional Tellurene: From First-Principles Calculations.

Tellurene is a new-emerging two-dimensional anisotropic semiconductor, with fascinating electric and optical properties that differ dramatically from the bulk counterpart. In this work, the layer dependent electronic and optical properties of few-layer Tellurene has been calculated with the density functional theory (DFT). It shows that the band gap of the Tellurene changes from direct to indirect when layer number changes from monolayer (1 L) to few-layers (2 L–6 L) due to structural reconstruction. Tellurene also has an energy gap that can be tuned from 1.0 eV (1 L) to 0.3 eV (6 L). Furthermore, due to the interplay of spin–orbit coupling (SOC) and disappearance of inversion symmetry in odd-numbered layer structures resulting in the anisotropic SOC splitting, the decrease of the band gap with an increasing layer number is not monotonic but rather shows an odd-even quantum confinement effect. The optical results in Tellurene are layer dependent and different in E ⊥ C and E || C directions. The correlations between the structure, the electronic and optical properties of the Tellurene have been identified. Despite the weak nature of interlayer forces in their structure, their electronic and optical properties are highly dependent on the number of layers and highly anisotropic. These results are essential in the realization of its full potential and recommended for experimental exploration.

O2 atmospheric annealing-tunable defects in ionic oxide MgO nanoribbons

An isotropic lattice shrinkage (lattice volume ratio ∼−0.462%) structure was reported in cubic magnesium oxide (MgO) nanocrystals, favoring the enhanced electron correlation. Upon postannealing in an O2 atmosphere, significant changes in photoluminescence spectra were detected in pristine MgO nanoribbons (NRs): a substantial reduction in F+-type centers (Fc) and an increase in a previously unknown peak at 358 nm (3.46 eV) which we attribute to a small polaron (SP) complex as a deep acceptor. A reduced diluted magnetism was found in the O2-annealed MgO NRs. A room temperature electron paramagnetic resonance signal at g ∼ 2.0959 revealed the presence of an unpaired electron trapped in the MgO NRs and a weak broad signal shift at g ∼ 2.0888, suggesting a reduced anisotropic spin–orbit coupling in the O2-annealed MgO NRs. Finally, a view on competition between Fc and SP was proposed: the Fc defect favors FM, and the SP complex leads to reduced FM in MgO NRs. The findings provide new insight into the origin and defect engineering of d0 diluted magnetism in MgO (spin from MgO), and this physical mechanism would be generally applied to other ionic oxide family materials in the field.

Ultrafast Orbital-Oriented Control of Magnetization in Half-Metallic La0.7 Sr0.3 MnO3 Films.

Manipulating spins by ultrafast pulse laser provides a new avenue to switch the magnetization for spintronic applications. While the spin-orbit coupling is known to play a pivotal role in the ultrafast laser-induced demagnetization, the effect of the anisotropic spin-orbit coupling on the transient magnetization remains an open issue. This study uncovers the role of anisotropic spin-orbit coupling in the spin dynamics in a half-metallic La0.7 Sr0.3 MnO3 film by ultrafast pump-probe technique. The magnetic order is found to be transiently enhanced or attenuated within the initial sub-picosecond when the probe light is tuned to be s- or p-polarized, respectively. The subsequent slow demagnetization amplitude follows the fourfold symmetry of the orbitals as a function of the polarization angles of the probe light. A model based on the Elliott-Yafet spin-flip scatterings is proposed to reveal that the transient magnetization enhancement is related to the spin-mixed states arising from the anisotropic spin-orbit coupling. The findings provide new insights into the spin dynamics in magnetic systems with anisotropic spin-orbit coupling as well as perspectives for the ultrafast control of information process in spintronic devices.

Ring phases of spin-orbit coupled Bose-Einstein condensate in the radial optical lattices

We study the ground-state phases of two-dimensional spin-orbit coupled Bose-Einstein condensate loaded in the spin-dependent radial optical lattices. For strong depth of the spin-dependent radial optical lattice, three new types of the ring phases are found with isotropic spin-orbit coupling, i.e., the ring-stripe phase with the periodic density modulation along the radial direction, the ring-supersolid phase with the periodic density modulation both the radial and azimuthal directions and the windmill-supersolid phase with four vanes along the azimuthal direction. By increasing spin-orbit coupling, the system undergoes a sequence phase transitions from the ring-stripe phase to the ring-sueprsolid phase, and to the windmill-supersolid phase for the weak depth of radial optical lattice, however, the ring-stripe phase transforms to the windmill-supersolid phase directly for the strong depth of radial optical lattice. We also discuss the ground-state phases with anisotropic spin-orbit coupling, two-component Bose-Einstein condensates are easier condensed along the direction with larger spin-orbit coupling.

Ground state properties of a two-dimensional Fermi superfluid with anisotropic spin–orbit coupling

In this study, we performed a theoretical investigation of the ground state properties of a two-dimensional ultra-cold Fermi superfluid with anisotropic spin–orbit coupling (SOC). In the absence of the Zeeman field, the system evolved from a weak coupling BCS regime to a strongly interacting BEC regime (BCS–BEC crossover) with increases in either the two-particle interaction strength or the SOC parameters. We focused on the behaviors of the pairing parameter and density of states (DOS) when the anisotropic parameter of the SOC increased. Surprisingly, we discovered that the gap parameter decreased as the anisotropic parameters increased, but the DOS at the Fermi surface exhibited non-monotonic behavior as a function of the anisotropic parameter. In the presence of the Zeeman field, we considered a particular type of topological phase transition by obtaining the analytical result for the topological invariant and we related this directly to the quantum phase transition with a sudden change in the ground state wave-function. The effects of higher partial wave pairing terms on this topological phase transition were also considered in this study.

Vortex states and spin textures of rotating spin–orbit-coupled Bose–Einstein condensates in a toroidal trap

We consider the ground-state properties of Rashba spin–orbit-coupled pseudo-spin-1/2 Bose–Einstein condensates (BECs) in a rotating two-dimensional (2D) toroidal trap. In the absence of spin–orbit coupling (SOC), the increasing rotation frequency enhances the creation of giant vortices for the initially miscible BECs, while it can lead to the formation of semiring density patterns with irregular hidden vortex structures for the initially immiscible BECs. Without rotation, strong 2D isotropic SOC yields a heliciform-stripe phase for the initially immiscible BECs. Combined effects of rotation, SOC, and interatomic interactions on the vortex structures and typical spin textures of the ground state of the system are discussed systematically. In particular, for a fixed rotation frequency above the critical value, the increasing isotropic SOC favors a visible vortex necklace in each component which is accompanied by a hidden giant vortex plus a (several) hidden vortex necklace(s) in the central region. In the case of one-dimensional anisotropic SOC, large SOC strength results in the generation of hidden linear vortex string and the transition from initial component separation (component mixing) to component mixing (component separation). Furthermore, the peculiar spin textures including skyrmion lattice, skyrmion pair and skyrmion string are revealed in this system.

Hidden long-range order in a spin-orbit-coupled two-dimensional Bose gas

A spin-orbit coupled two-dimensional (2D) Bose gas is shown to simultaneously possess quasi and true long-range order in the total and relative phase sectors, respectively. The total phase undergoes a Berenzinskii- Kosterlitz-Thouless transition to a low temperature phase with quasi long-range order, as expected for a two- dimensional quantum gas. Additionally, the relative phase undergoes an Ising-type transition building up true long-range order, which is induced by the anisotropic spin-orbit coupling. Based on the Bogoliubov approach, expressions for the total- and relative-phase fluctuations are derived analytically for the low temperature regime. Numerical simulations of the stochastic projected Gross-Pitaevskii equation (SPGPE) give a good agreement with the analytical predictions.

Finite-temperature phases of two-dimensional spin-orbit-coupled bosons

We determine the finite temperature phase diagram of two dimensional bosons with two hyperfine (pseudo-spin) states coupled via Rashba-Dresselhaus spin-orbit interaction using classical field Monte Carlo calculations. For anisotropic spin-orbit coupling, we find a transition to a Berenzinskii-Kosterlitz-Thouless superfluid phase with quasi-long range order. We show that the spin-order of the quasi-condensate is driven by the anisotropy of interparticle interaction, favoring either a homogeneous plane wave state or stripe phase with broken translational symmetry. Both phases show characteristic behavior in the algebraically decaying spin density correlation function. For fully isotropic interparticle interaction, our calculations indicate a fractionalized quasi-condensate where the mean-field degeneracy of plane wave and stripe phase remains robust against critical fluctuations. In the case of fully isotropic spin-orbit coupling, the circular degeneracy of the single particle ground state destroys the algebraic ordered phase in the thermodynamic limit, but a cross-over remains for finite size systems.