Intrinsic Spin-orbit Interaction Research Articles

Persistent current in a mesoscopic Holstein-Hubbard ring with Dresselhaus interaction

The effect of electron-phonon coupling, onsite repulsive Coulomb interaction and temperature on the persistent current in a quantum ring is studied in the presence of Dresselhaus spin-orbit interaction. The quantum ring threaded by the Aharonov-Bohm flux is modelled by the one-dimensional Holstein-Hubbard-Dresselhaus Hamiltonian. The electron-phonon interaction and Dresselhaus spin-orbit interaction are decoupled by employing the Lang-Firsov coherent transformation and a unitary transformation respectively. Thereafter, a self-consistent diagonalization technique is performed numerically at the Hartree-Fock level to obtain the effective electronic energy and current. It is shown that the intrinsic Dresselhaus spin-orbit interaction enhances the persistent charge and spin currents significantly. On the other hand, the persistent current is reduced by the onsite and nearest-neighbour electron-phonon interaction and Coulomb interaction. Also, the behaviour of the currents is modified by temperature. The spin-splitting of persistent spin current is enhanced considerably by Dresselhaus spin-orbit interaction and this splitting is tuneable in different regimes of magnetic flux, temperature, chemical potential and the interactions present in the system.

Effect of intrinsic & Rashba spin-orbit interactions (SOI) in case of bilayer graphene

In this study, we investigated how various SOI affect the properties of bilayer graphene’s energy band structure. We have considered intralayer interactions in this work. We focused on the system without biasing. We found that the intrinsic spin-orbit interaction (ISOI) can produce an energy band gap in bilayer graphene. On the other hand, in the case of an intralayer Rashba spin-orbit interaction (RSOI) different energy bands exist. The results shown depicts how the behaviour of the energy bands remains the same when we are increasing the number of atoms (N) in a unit cell of bilayer graphene.

Stabilizing the Inverted Phase of a WSe2/BLG/WSe2 Heterostructure via Hydrostatic Pressure.

Bilayer graphene (BLG) was recently shown to host a band-inverted phase with unconventional topology emerging from the Ising-type spin-orbit interaction (SOI) induced by the proximity of transition metal dichalcogenides with large intrinsic SOI. Here, we report the stabilization of this band-inverted phase in BLG symmetrically encapsulated in tungsten diselenide (WSe2) via hydrostatic pressure. Our observations from low temperature transport measurements are consistent with a single particle model with induced Ising SOI of opposite sign on the two graphene layers. To confirm the strengthening of the inverted phase, we present thermal activation measurements and show that the SOI-induced band gap increases by more than 100% due to the applied pressure. Finally, the investigation of Landau level spectra reveals the dependence of the level-crossings on the applied magnetic field, which further confirms the enhancement of SOI with pressure.

Magnetic edge states and edge current in honeycomb zigzag nanoribbons by Kane–Mele–Hubbard model

We investigate spin-dependent edge states of honeycomb zigzag nanoribbons with a focus on electron–electron interaction as the origin of the initial edge magnetism which is assumed to be anti-ferromagnetism order as a stable form. We study the effect of intrinsic spin–orbit interaction (SOI) and also applied in-plane transverse electric field on low energy spectrum and edge spin density. Tight-binding method in the framework of the self-consistent Kane–Mele–Hubbard model has been utilized for exploring electronic properties. Edge currents and electric dipole moments are also calculated. Results show electric field and SOI can dramatically affect the edge states and energy gaps. A transition from a magnetic edge state to a non-magnetic one occurs at critical values of SOI and electric field. Furthermore, the system goes into the topological insulator phase at sufficiently large SOI strengths. The results of edge spin density, electric dipole moment, and spin currents indicate that one can reach the favorite spin-dependent transport by manipulating the electric field and SOI in a zigzag nanoribbon. The outcome may pave the way to further control of spin-based transport in future devices.

Multiband character revealed from weak antilocalization in platinum thin films

Platinum (Pt) has been very much used for spin-charge conversion in spintronics research due to its large intrinsic spin-orbit interaction. Magnetoconductance originating from weak antilocalization in the quantum interference regime is used as a powerful tool to obtain the microscopic information of spin-orbit interaction and the coherence phase breaking scattering process among itinerant electrons. To acquire the knowledge of different types of scattering processes, we have performed a magnetoconductance study on Pt thin films which manifests multiband (multichannel) conduction. An extensive analysis of quantum-interference-originated weak antilocalization reveals the existence of strong (weak) interband scattering between two similar (different) orbitals. Coherence phase breaking lengths $({l}_{\ensuremath{\phi}})$ and their temperature dependence are found to be significantly different for these two conducting bands. The observed effects are consistent with the theoretical prediction that there exist three Fermi sheets with one $s$ and two $d$ orbital character. This study provides the evidence of two independent nonsimilar conducting channels and the presence of anisotropic spin-orbit interaction along with $e\text{\ensuremath{-}}e$ correlation in Pt thin films.

Modulation of Spin Dynamics in 2D Transition-Metal Dichalcogenide via Strain-Driven Symmetry Breaking.

Transition metal dichalcogenides (TMDs) possess intrinsic spin–orbit interaction (SOI) with high potential to be exploited for various quantum phenomena. SOI allows the manipulation of spin degree of freedom by controlling the carrier's orbital motion via mechanical strain. Here, strain modulated spin dynamics in bilayer MoS2 field‐effect transistors (FETs) fabricated on crested substrates are demonstrated. Weak antilocalization (WAL) is observed at moderate carrier concentrations, indicating additional spin relaxation path caused by strain fields arising from substrate crests. The spin lifetime is found to be inversely proportional to the momentum relaxation time, which follows the Dyakonov–Perel spin relaxation mechanism. Moreover, the spin–orbit splitting is obtained as 37.5 ± 1.4 meV, an order of magnitude larger than the theoretical prediction for monolayer MoS2, suggesting the strain enhanced spin‐lattice coupling. The work demonstrates strain engineering as a promising approach to manipulate spin degree of freedom toward new functional quantum devices.

Driving spin chirality by electron dynamics in laser-excited antiferromagnets

Despite recent successes in the area of ultrafast manipulation of magnetic order, optical generation and manipulation of complex spin textures is hindered by an insufficient theoretical understanding of underlying processes. In particular an important aspect of subtle connection between the electronic and magnetic degrees of freedom is not properly accounted for in existing theories. Here, we uncover a distinct physical mechanism for imprinting spin chirality into collinear magnets with short laser pulses. By simultaneously treating the laser-ignited evolution of electronic structure and magnetic order, we show that their intertwined dynamics can result in an emergence of quasi-stable chiral states. We find that laser-driven chirality does not require any auxiliary external fields or intrinsic spin–orbit interaction to exist, and it can survive on the time scale of nanoseconds even in the presence of thermal fluctuations, which makes the uncovered mechanism relevant for understanding various optical experiments on magnetic materials. Our findings provide a more detailed perspective of the complex interactions which occur between chiral magnetism and light.

Novel transport phenomena in graphene induced by strong spin-orbit interaction

Graphene is known to have small intrinsic spin-orbit Interaction (SOI). In this review, we demonstrate that SOIs in graphene can be strongly enhanced by proximity effect when graphene is deposited on the top of transition metal dichalcogenides. We discuss the symmetry of the induced SOIs and differences between TMD underlayers in the capacity of inducing strong SOIs in graphene. The strong SOIs contribute to bring novel phenomena to graphene, exemplified by robust supercurrents sustained even under tesla-range magnetic fields.

First-Principles Calculations Predict Tunable Large Magnetic Anisotropy Due to Spin-Polarized Quantum-Well Resonances in Nanometer-Thick SrRuO3 Films: Implications for Spintronic Devices

We demonstrate that the magnetic anisotropy in SrRuO3 (SRO) ultrathin films can be well controlled by thickness or electrical modulations: The easy axis (preferred magnetization direction) of a SRO ultrathin film can be switched between out-of-plane and in-plane magnetization either by altering the film thickness or by tuning the doping level through applying a gate voltage or chemical doping. Such a capability to manipulate the magnetocrystalline anisotropy energy (MCAE) is given by the spin–orbit coupling (SOC)-induced energy splitting in the spin-polarized quantum well states (QWSs) near the Fermi level. These QWSs are susceptible to the intrinsic spin–orbit interaction and thus drive a large energy discrepancy when an SRO ultrathin film rotates its magnetization direction. As a result of the MCAE nature, a SRO film has a magnetic anisotropy approximately an order of magnitude larger than those in 3d-ferromagnet ultrathin films and its easy-axis direction depends on the film thickness, gate voltage, and substrate. This tunable large magnetic anisotropy in SRO ultrathin films provides an excellent route toward advanced spintronic devices such as storage and memory devices.

Quantum spin Hall phase transition in the α−T3 lattice

We report a theoretic study of the topological properties of the $\ensuremath{\alpha}\text{\ensuremath{-}}{T}_{3}$ lattice by taking the intrinsic spin orbit interaction into account. It is shown that when $0<\ensuremath{\alpha}<1$, the electronic band structure is spin-valley split and the original flat band is distorted to display a nonzero dispersion that imparts the system to be metallic. The gapped valence or conduction band shows the quantum spin Hall phase and experiences a topological phase transition from the spin Chern number ${C}_{s}=1$ to ${C}_{s}=2$ at the critical point $\ensuremath{\alpha}=\frac{1}{2}$. When a staggered magnetization order is considered in the system, a bunch of topological phases appear such as the quantum spin quantum anomalous Hall phase with variation of $\ensuremath{\alpha}$ or the magnetization strength.

Effects of Anisotropic Strain on Spin-Orbit Torque Produced by the Dirac Nodal Line Semimetal IrO2.

We report spin-torque ferromagnetic resonance studies of the efficiency of the damping-like (ξDL) spin-orbit torque exerted on an adjacent ferromagnet film by current flowing in epitaxial (001) and (110) IrO2 thin films. IrO2 possesses Dirac nodal lines (DNLs) in the band structure that are gapped by spin-orbit coupling, which could enable a very high spin Hall conductivity, σSH. We find that the (001) films do exhibit exceptionally high ξDL ranging from 0.45 at 293 K to 0.65 at 30 K, which sets the lower bounds of σSH to be 1.9 × 105 and 3.75 × 105 Ω-1 m-1, respectively, 10 times higher and of opposite sign than the theoretical prediction. Furthermore, ξDL and σSH are substantially reduced in anisotropically strained (110) films. We suggest that this high sensitivity to anisotropic strain is because of changes in contributions to σSH near the DNLs.

Landau levels in spin-orbit coupling proximitized graphene: Bulk states

We study the magnetic-field dependence of Landau levels in graphene proximitized by large spin-orbit coupling materials, such as transition-metal dichalcogenides or topological insulators. In addition to the Rashba coupling, two types of intrinsic spin-orbit interactions, uniform (Kane-Mele type) and staggered (valley Zeeman type), are included, to resolve their interplay with magnetic orbital effects. Employing a continuum model approach, we derive analytic expressions for low-energy Landau levels, which can be used to extract local orbital and spin-orbit coupling parameters from scanning probe spectroscopy experiments. We compare different parameter regimes to identify fingerprints of relative and absolute magnitudes of intrinsic spin-orbit coupling in the spectra. The inverted band structure of graphene proximitized by WSe$_2$ leads to an interesting crossing of Landau states across the bulk gap at a crossover field, providing insights into the size of Rashba spin-orbit coupling. Landau level spectroscopy can help to resolve the type and signs of the intrinsic spin-orbit coupling by analyzing the symmetry in energy and number of crossings in the Landau fan chart. Finally, our results suggest that the strong response to the magnetic field of Dirac electrons in proximitized graphene can be associated with extremely large self-rotating magnetic moments.

Tunable spin-photovoltaic effect in zigzag MoS2 nanoribbons

This article introduces a method for generating spin-polarized photocurrent through light radiation on zigzag MoS2 nanoribbons. In this regard, we investigate local manipulation by exposing edge states to (i) a ferromagnetic, (ii) an antiferromagnetic exchange field, (iii) a parallel and an antiparallel electric field. These local manipulations at the edges with intrinsic spin-orbit interaction could produce a spin-polarized photocurrent and manipulate optical properties. Even at one edge of the nanoribbon, applying the exchange field could induce a fully spin polarization by light irradiation. Efficient quantum efficiency, significant optical spin polarization, and spin-polarized photocurrent make zigzag MoS2 nanoribbon an effective structure for improving the performance of spin-photovoltaic devices.

Band bending and zero-conductance resonances controlled by edge electric fields in zigzag silicene nanoribbons

We study the band structure and transport property of a zigzag silicene nanoribbon when electric fields are applied to the edges. It is found that band bending could be induced and controlled by the antisymmetric edge fields, which can be understood based on the wave functions of the edge states. The highest valence band and the lowest conduction band coexist in the band-bending region. With the narrowing of edge potentials, the bending increases gradually. When the edge fields become symmetric, an asymmetric band gap at the Dirac points can be obtained due to the intrinsic spin-orbit interaction, suggesting a valley-polarized quantum spin Hall state. The gap could reach a maximum value rapidly and then decrease slowly as the electric fields increase. Due to the combining effect of the band bending, band-selective rule, and resonant states, many zero-conductance resonances and resonance peaks appear in different regions, which could be described by the Fano resonance effect. Furthermore, the band bending and zero-conductance resonances are robust against the Hubbard interaction. The Hubbard interaction could work as a spin-dependent edge field, together with the edge electric fields, leading to a spin-dependent band gap and various quantum phases such as metal and half-metal.

Optimized micromagnet geometries for Majorana zero modes in low g -factor materials

Solid-state experimental realizations of Majorana bound states are based on materials with strong intrinsic spin-orbit interactions. In this paper, we explore an alternative approach where spin-orbit coupling is induced artificially through a nonuniform magnetic field that originates from an array of micromagnets. Using a recently developed optimization algorithm, we find suitable magnet geometries for the emergence of topological superconductivity in wires without intrinsic spin-orbit coupling. We confirm the robustness of Majorana bound states against disorder and periodic potentials whose amplitudes do not exceed the Zeeman energy. Furthermore, we identify low g-factor materials commonly used in mesoscopic physics experiments as viable candidates for Majorana devices.

Hyperfine-assisted decoherence of a phosphorus nuclear-spin qubit in silicon

The nuclear spin of a phosphorus atom in silicon has been used as a quantum bit in various quantum-information experiments. It has been proposed that this nuclear-spin qubit can be efficiently controlled by an ac electric field, when embedded in a two electron dot-donor setup subject to intrinsic or artificial spin-orbit interaction. Exposing the qubit to control electric fields in that setup exposes it to electric noise as well. In this work, we describe the effect of electric noise mechanisms, such as phonons and $1/f$ charge noise, and estimate the corresponding decoherence time scales of the nuclear-spin qubit. We identify a promising parameter range where the electrical single-qubit operations are at least an order of magnitude faster then the decoherence. In this regime, decoherence is dominated by dephasing due to $1/f$ charge noise. Our results facilitate the optimized design of nanostructures to demonstrate electrically driven nuclear spin resonance.

RKKY interaction in the zigzag-edge silicene-like nanoflake

Abstract By considering the Kane-Mele-Hubbard approximation on the honeycomb lattice, we investigate the spin-spin correlation for two magnetic impurities in zigzag edge silicene-like nanoflake (ZSiLF). The dependence of the spatial behaviors of RKKY interaction on the electron-electron (e-e), intrinsic spin-orbit interactions (ISOI) and, electric field are systematically investigated. Generally, the spatial behaviors of the RKKY interaction sensitively change by changing e-e interaction and electric field strengths in the presence of ISOI. The ISOI in a ZSiLF result in long-range in-plane and Ising interactions. Moreover, e-e interaction induces non-zero Dzyaloshinsky-Moriya (DM) term and nearly distance-independent Ising interaction (similar to graphene nanoflake) in the presence of ISOI. Furthermore, with considering e-e interaction, the in-plane DM interaction increases by increasing the strengths of the electric field and ISOI.

Spin–orbit coupling effects on the electronic properties of the pressure-induced superconductor CrAs

We present the effects of spin-orbit coupling on the low-energy bands and Fermi surface of the recently discovered pressure-induced superconductor CrAs. We apply the L\"owdin down-folding procedure to a tight-binding hamiltonian that includes the intrinsic spin-orbit interaction, originating from the Cr 3d electrons as well as from As 4p ones. Our results indicate that As contributions have negligible effects, whereas the modifications to the band structure and the Fermi surface can be mainly ascribed to the Cr contribution. We show that the inclusion of the spin-orbit interaction allows for a selective removal of the band degeneracy due to the crystal symmetries, along specific high symmetry lines. Such release of the band degeneracy naturally determines a reconstruction of the Fermi surface, including the possibility of changing the number of pockets.

Effects of the interplay between electron-electron interaction and intrinsic spin-orbit interaction on the indirect RKKY coupling in graphene nanoflakes.

The effects of electron-electron (e-e) interaction and intrinsic spin-orbit interaction (ISOI) on the maximum of the magnetization and the indirect RKKY (Ruderman-Kittel-Kasuya-Yosida) coupling between the magnetic impurities embedded in zig-zag graphene nanoflakes are investigated using the tight-binding Hamiltonian and the mean-field Hubbard model. The RKKY coupling energy values as a function of the e-e interaction strengths are plotted for different values of ISOI strength. The appearance of the e-e interaction and ISOI changes drastically the magnitude of the indirect coupling so that increasing or decreasing of the indirect coupling depends on strength of the e-e interaction and ISOI and the size of the nanoflake. The dependence of the RKKY coupling and the maximum of the magnetization on the positions of the magnetic impurities and the size of the system are studied. We find that the e-e interaction and the ISOI are responsible for changes of the magnetization along the zig-zag edges of the nanoflake.

Modified spin–orbit couplings in uniaxially strained graphene

Intrinsic and Rashba spin-orbit interactions in strained graphene is studied within the tight-binding (TB) approach. Dependence of Slater-Koster (SK) parameters of graphene on strain are extracted by fitting the \emph{ab initio} band structure to the TB results. A generalized low-energy effective Hamiltonian in the presence of spin-orbit couplings is proposed for strained graphene subjected to an external perpendicular electric field. Dependence of the modified Rashba strength and other parameters of effective Hamiltonian on the strain and electric field are calculated. In order to analyze the influence of the applied strain on the electronic properties of the graphene, one must take into account the lattice deformation, modifications of the hopping amplitudes and shift of the Dirac points. We find that using the strain it is possible to control the strength of Rashba and intrinsic spin-orbit couplings as well as energy gap at the shifted Dirac points. Meanwhile, the strain slightly modifies the topology of low-energy dispersion around the Dirac points. We describe the SOCs induced energy splitting as a function of strain.