Effect Of Rashba Spin-orbit Coupling Research Articles

Spin-wave-induced spin torque in Rashba ferromagnets

We study the effects of Rashba spin-orbit coupling on the spin torque induced by spin waves, which are the plane wave dynamics of magnetization. The spin torque is derived from linear response theory, and we calculate the dynamic spin torque by considering the impurity-ladder-sum vertex corrections. This dynamic spin torque is divided into three terms: a damping term, a $distortion$ term, and a correction term for the equation of motion. The $distorting$ torque describes a phenomenon unique to the Rashba spin-orbit coupling system, where the distorted motion of magnetization precession is subjected to the anisotropic force from the Rashba coupling. The oscillation mode of the precession exhibits an elliptical trajectory, and the ellipticity depends on the strength of the nesting effects, which could be reduced by decreasing the electron lifetime.

Disorder driven transition beyond two-component, single-flavor Dirac physics in silicene

We consider the topological insulator (TI) phase of silicenein the presence of an applied electric field Ez perpendicular to its plane. These are assembly of Dirac fermions on a low-buckled 2D hexagonal lattice. The buckled structure generates a staggered sub-lattice potential between silicon atoms at A sites and B sites for the applied field. The starting point of our investigation is the Hamiltonian involving the Dirac kinetic energy, a mass gap term, and the spin-orbit coupling. Tuning of Ez allows for rich behaviour starting from a TI state to a band insulator(BI)with a valley-spin-polarized metal (VSPM) at a critical value in between. As long as the impurity potential strength V0 is of the same order as the intrinsic spin-orbit coupling (SOC) tso(∼ 4 meV), VSPM phase is protected. The effective “two-component, single-flavorDirac physics” remains valid in this phase.Theincrease in V0, however, leads to the disappearance of this phase due to enhanced scattering processes, i.e. the out-of-plane electric field driven topological insulator to metal transition, being predicted for our system, will not be observable when the impurity potential is very high. The enhancement in SOC (tso) or the Rashbaspin-orbit coupling effect (t2), however, does not lead to such a scenario.

Effect of disorder in the transition from topological insulator to valley-spin polarized state in silicene and Germanene

We work with the reduced silicene/germanene single-particle Hamiltonian in buckled 2D hexagonal lattice expressed in terms of Pauli matrices associated with the pseudo-spin. The Hamiltonian of these systems comprises of the Dirac kinetic energy, a mass term and the spin–orbit coupling. The mass term breaks the sub-lattice symmetry of the system’s honey-comb structure and generates spin-split band gap with the help of the spin–orbit coupling. The buckled lattice generates a staggered sub-lattice potential between silicon atoms at A sites and B sites for an applied electric field E z perpendicular to its plane. The physics of the system is determined by two Dirac-like cones at K and K′ points. By tuning E z , one attains a critical value at which the system at the topological insulating phase goes to a semi-metal state, where the ‘spin-down’ upon the ‘spin-up’ band gap ratio (r) ≪ 1 for the valley K and r ≫ 1 for the valley K′. This state is termed as the ‘valley-spin-polarized-metal’ due to the opposite spin-polarization of the K and K′ valleys. Upon increasing E z further, the system turns into a trivial insulator. This event is associated with the valley magnetic moment reversal. Our preliminary investigation have shown that, as long as the (non-magnetic) impurity scattering strength V 0 is moderate, i.e. V 0 is of the same order as the intrinsic spin–orbit coupling t so (~4 meV), the ‘valley-spin-polarized-metal’ phase is protected. The substantial enhancement in V 0, however, leads to the disappearance of this phase due to accentuated intra- and inter-valley scattering processes. This disappearance does not occur due to the increase in Rashba spin–orbit coupling effect.

Influence of magnetic field and Rashba spin–orbit coupling on strong-coupling magnetopolarons in quantum disks

On the basis of Lee–Low–Pines (LLP) unitary transformation, the influence of external magnetic field, Rashba spin–orbit coupling and quantum size effect on the ground-state interaction energy of strong-coupling magnetopolarons in quantum disks (QDs) is studied by using the Tokuda improved linear combine operator method. The results show that the ground-state interaction energy of magnetopolarons consists of four parts: the energy caused by the confinement potential of QDs, interaction energy between the electron and external magnetic field, electron and longitudinal-optical (LO) phonon interaction energy and additional term of Rashba effect originating from phonons. The electron–LO phonon interaction energy Ee- ph and additional term of Rashba effect are always negative; the absolute value |Ee- ph | increases with increasing transverse confinement strength ω0, cyclotron frequency of external magnetic field ωc and electron–LO phonon coupling strength α, but decreases with increasing the thickness of QDs L; the state properties of magnetopolarons are closely linked with the sign of the ground-state interaction energy of magnetopolarons E int and change of E int with ωc, ω0, α and L. In addition, the vibration frequency of magnetopolarons λ increases with increasing ωc, ω0 and α, but decreases with increasing L. For the ground state of magnetopolarons in QDs, the electron–LO phonon interaction plays a significant role, meanwhile, the influence of Rashba spin–orbit coupling effect cannot be ignored.

Rashba spin-orbit coupling in the Kane-Mele-Hubbard model

Spin-orbit (SO) coupling is the crucial parameter to drive topological insulating phases in electronic band models. In particular, the generic emergence of SO coupling involves the Rashba term which fully breaks the SU(2) spin symmetry. As soon as interactions are taken into account, however, many theoretical studies have to content themselves with the analysis of a simplified U(1) conserving SO term without Rashba coupling. We intend to fill this gap by studying the Kane-Mele-Hubbard (KMH) model in the presence of Rashba SO coupling and present the first systematic analysis of the effect of Rashba SO coupling in a correlated two-dimensional topological insulator. We apply the variational cluster approach (VCA) to determine the interacting phase diagram by computing local density of states, magnetization, single particle spectral function, and edge states. Preceded by a detailed VCA analysis of the KMH model in the presence of U(1) conserving SO coupling, we find that the additional Rashba SO coupling drives new electronic phases such as a metallic regime and a direct-gap only topological insulating phase which persist in the presence of interactions.

Polarization of a quasi-two-dimensional repulsive Fermi gas with Rashba spin-orbit coupling: A variational study

Motivated by the remarkable experimental control of synthetic gauge fields in ultracold atomic systems, we investigate the effect of an artificial Rashba spin-orbit coupling on the spin polarization of a two-dimensional repulsive Fermi gas. By using a variational many-body wave function, based on a suitable spinorial structure, we find that the polarization properties of the system are indeed controlled by the interplay between spin-orbit coupling and repulsive interaction. In particular, two main effects are found: (1) The Rashba coupling determines a gradual increase of the degree of polarization beyond the critical repulsive interaction strength, at variance with conventional two-dimensional Stoner instability. (2) The critical interaction strength, above which finite polarization is developed, shows a dependence on the Rashba coupling, i.e., it is enhanced in case the Rashba coupling exceeds a critical value. A simple analytic expression for the critical interaction strength is further derived in the context of our variational formulation, which allows for a straightforward and insightful analysis of the present problem.

Effects of Rashba spin–orbit coupling and a magnetic field on a polygonal quantum ring

Using standard quantum network method, we analytically investigate the effect of Rashba spin-orbit coupling (RSOC) and a magnetic field on the spin transport properties of a polygonal quantum ring. Using Landauer-Buttiker formula, we have found that the polarization direction and phase of transmitted electrons can be controlled by both the magnetic field and RSOC. A device to generate a spin-polarized conductance in a polygon with an arbitrary number of sides is discussed. This device would permit precise control of spin and selectively provide spin filtering for either spin up or spin down simply by interchanging the source and drain.

Study of the properties of strong-coupling magnetopolaron in quantum disks induced by the Rashba spin-orbit interaction

On the basis of Lee-Low-Pines unitary transformation, the properties of strong-coupling magnetopolarons in quantum disks (QDs) induced by the Rashba spin-orbit interaction are studied using the Tokuda improved linearly combined operator method. Results show that the state properties of magnetopolarons are closely linked with the sign of the interaction energy Eint, and the Eint of magnetopolarons changes with the transverse confinement strength 0, the cyclotron frequency of the external magnetic field c, the electron-LO phonon coupling strength , and the thickness L of QDs. The average number N of phonons increases with increasing c, 0 and , but the oscillation decreases with increasing thickness L of QDs. The effective mass m0* of magnetopolarons splits into two (m+*, m-*), induced by the Rashba spin-orbit interaction, and the values of them increase with increasing c, 0 and , but the oscillation decreases with increasing thickness L of QDs. For the ground state of magnetopolarons in QDs, the electron-LO phonon interaction plays a significant role, meanwhile, the Rashba spin-orbit coupling effect cannot be ignored. Only for the lower volocity of the electrons, can the polaron effect and the Rashba spin-orbit interaction effect on the magnetopolaron be obvious.

Effects of external magnetic fields and Rashba spin-orbit coupling on spin conductance in graphene

The present article is concerned with spin conductance in graphene (SCG) when both the application of an external magnetic field and Rashba spin-orbit coupling (RSOC) are taken into account. Introducing a Casimir operator, we analyze the structure of total Hamiltonian and demonstrate how the matrix elements along with the summations involved in the suitably adopted Kubo’s formula, may be analytically calculated. From the results so-obtained one finds that, in addition to discrete and symmetric behavior of SCG against the external field, it exhibits large peaks as high as six times that in ordinary two dimensional electron gases. Moreover, it is shown that for any Fermi energy the SCG asymptotically approaches a value three times larger than the standard unit of (e/4π), for large magnetic fields. Effects of the magnetic field, RSOC and Fermi energy on the characteristics of SCG are also discussed. The material presented in this article thus provides novel means of controlling the SCG by external agents.

Single ferromagnetic layer magnetic random access memory

We propose a magnetic random access memory (MRAM) device in which both the writing and reading processes are realized within a single ferromagnetic (FM) layer. The FM layer is sandwiched between layers of heavy element and oxide to enhance the Rashba spin-orbit coupling (RSOC). When the in-plane FM moments are oriented at some intermediate angle to the current direction, the RSOC effect induces a spin accumulation in the FM layer, which in turn generates a Rashba spin torque field via the s-d exchange interaction. This field acts as the writing field of the memory device. The RSOC also induces a charge accumulation in the transverse direction via the inverse spin Hall effect (ISHE), which can be used to realize the memory read-out. The writing and read-out processes of the proposed memory are modeled numerically via the non-equilibrium Green's function technique. Besides the advantages of Rashba spin torque writing, i.e., no spin injection and symmetrical data-writing process, this single FM layer MRAM design does away with having a giant magnetoresistive or magnetic tunnel junction multilayer structure by utilizing the ISHE for the read-out process.

Spin transition rates in nanowire superlattices: Rashba spin–orbit coupling effects

We investigate the influence of Rashba spin–orbit coupling in a parabolic nanowire modulated by longitudinal periodic potential. The modulation potential can be obtained from realistically grown superlattices (SLs). Our study shows that the Rashba spin–orbit interaction induces the level crossing point in the parabolic nanowire SLs. We estimate large anticrossing width (approximately 117 µeV) between singlet–triplet states. We study the phonon and electromagnetic field mediated spin transition rates in the parabolic nanowire SLs. We report that the phonon mediated spin transition rate is several order of magnitude larger than the electromagnetic field mediated spin transition rate. Based on the Feynman disentangling technique, we find the exact spin transition probability. For the case wave vector k = 0, we report that the transition probability can be tuned in the form of resonance at fixed time interval. For the general case (k ≠ 0), we solve the Riccati equation and find that the arbitrary values of k induces the damping in the transition probability. At large value of Rashba spin–orbit coupling coefficients for (k ≠ 0), spin transition probability freezes.

Spin interference in Rashba metal ring in a time-dependent magnetic field

We investigate spin transport in a metal square ring with a strong Rashba spin orbit coupling (RSOC) effect, in the presence of a time-dependent magnetic field. We show that RSOC can be regarded as a spin-dependent gauge field which imparts a spin-dependent geometric phase (Aharonov-Casher phase) to conduction electrons in the ring. Combining the Aharonov-Bohm phase due to the time-dependent magnetic field with the able Aharonov-Casher phase due to RSOC, we are able to construct a spin interference condition, which modulates spin transport in the ring. The spin transport in the system is calculated via the tight-binding non-equilibrium Green's function formalism. Based on our transport calculations, we proposed a potential application of the Rashba square ring system as an alternating spin current generator.

Topological phases in gated bilayer graphene: Effects of Rashba spin-orbit coupling and exchange field

We present a systematic study on the influence of Rashba spin-orbit coupling, interlayer potential difference and exchange field on the topological properties of bilayer graphene. In the presence of only Rashba spin-orbit coupling and interlayer potential difference, the band gap opening due to broken out-of-plane inversion symmetry offers new possibilities of realizing tunable topological phase transitions by varying an external gate voltage. We find a two-dimensional $Z_2$ topological insulator phase and a quantum valley Hall phase in $AB$-stacked bilayer graphene and obtain their effective low-energy Hamiltonians near the Dirac points. For $AA$ stacking, we do not find any topological insulator phase in the presence of large Rashba spin-orbit coupling. When the exchange field is also turned on, the bilayer system exhibits a rich variety of topological phases including a quantum anomalous Hall phase, and we obtain the phase diagram as a function of the Rashba spin-orbit coupling, interlayer potential difference, and exchange field.

Transport properties in a multi-terminal regular polygonal quantum ring with Rashba spin—orbit coupling

Transport properties in a multi-terminal regular polygonal quantum ring with Rashba spin—orbit coupling (SOC) are investigated analytically using quantum networks and the transport matrix method. The results show that conductances remain at exactly the same values when the output leads are located at axisymmetric positions. However, for the nonaxisymmetrical case, there is a phase difference between the upper and lower arm, which leads to zero conductances appearing periodically. An isotropy of the conductance is destroyed by the Rashba SOC effect in the axisymmetric case. In addition, the position of zero conductance is regulated with the strength of the Rashba SOC.

Non-equilibrium spatial distribution of Rashba spin torque in ferromagnetic metal layer

We study the spatial distribution of spin torque induced by a strong Rashba spin-orbit coupling (RSOC) in a ferromagnetic (FM) metal layer, using the Keldysh non-equilibrium Green's function method. In the presence of the s-d interaction between the non-equilibrium conduction electrons and the local magnetic moments, the RSOC effect induces a torque on the moments, which we term the Rashba spin torque. A correlation between the Rashba spin torque and the spatial spin current is presented in this work, clearly mapping the spatial distribution of Rashba spin torque in a nano-sized ferromagnetic device. When local magnetism is turned on, the out-of-plane (Sz) Spin Hall effect (SHE) is disrupted, but rather unexpectedly an in-plane (Sy) SHE is detected. We also study the effect of Rashba strength (αR) and splitting exchange (Δ) on the non-equilibrium Rashba spin torque averaged over the device. Rashba spin torque allows an efficient transfer of spin momentum such that a typical switching field of 20 mT can be attained with a low current density of less than 107A/cm2.

Strain enhanced spin polarization in graphene with Rashba spin-orbit coupling and exchange effects

We investigate spin polarization and valley-dependent transport in bulk graphene in the presence of the exchange splitting field, the pseudo magnetic field, and Rashba spin-orbit coupling (SOC). It is demonstrated that Rashba SOC and the pseudo magnetic field cannot produce a spin polarization component perpendicular to the graphene sheet, but the exchange field can. However, the Rashba SOC leads to a finite in-plane spin polarization, which can be modulated by the pseudo magnetic field. Furthermore, it is also demonstrated that the valley polarization current cannot be produced in the considered system due to the mirror symmetry property of transmission probability for valley K and K′.

Rashba spin–orbit coupling effects on a current-induced domain wall motion

A current-induced domain wall motion in magnetic nanowires with a strong structural inversion asymmetry [I.M. Miron, T. Moore, H. Szambolics, L.D. Buda-Prejbeanu, S. Auffret, B. Rodmacq, S. Pizzini, J. Vogel, M. Bonfim, A. Schuhl, G. Gaudin, Nat. Mat. 10 (2011) 419] seems to have novel features such as the domain wall motion along the current direction or the delay of the onset of the Walker breakdown. In such a highly asymmetric system, the Rashba spin–orbit coupling (RSOC) may affect a domain wall motion. We studied theoretically the RSOC effects on a domain wall motion and found that the RSOC, indeed, can induce the domain wall motion along the current direction in certain situations. It also delays the Walker breakdown and for a strong RSOC, the Walker breakdown does not occur at all. The RSOC effects are sensitive to the magnetic anisotropy of nanowires and also to the ratio between the Gilbert damping parameter α and the non-adiabaticity parameter β.

Spin-Orbit Coupled Bose-Einstein Condensate Under Rotation

We examine the combined effects of Rashba spin-orbit (SO) coupling and rotation on trapped spinor Bose-Einstein condensates. The nature of single particle states is thoroughly examined in the Landau level basis and is shown to support the formation of a half-quantum vortex. In the presence of weak s-wave interactions, the ground state at strong SO coupling develops ringlike structures with domains whose number shows step behavior with increasing rotation. For the fast rotation case, the vortex pattern favors a triangular lattice, accompanied by density depletion in the central region and a weakened Skyrmionic character as the SO coupling is enhanced. Giant vortex formation is facilitated when SO coupling and rotation are both strong.

Electrical Manipulation and Measurement of Spin Properties of Quantum Spin Hall Edge States

We study the effects of a gate-controlled Rashba spin-orbit coupling to quantum spin Hall edge states in HgTe quantum wells. A uniform Rashba coupling can be employed in tuning the spin orientation of the edge states while preserving the time-reversal symmetry. We introduce a sample geometry where the Rashba coupling can be used in probing helicity by purely electrical means without requiring spin detection, application of magnetic materials or magnetic fields. In the considered setup a tilt of the spin orientation with respect to the normal of the sample leads to a reduction in the two-terminal conductance with current-voltage characteristics and temperature dependence typical of Luttinger liquid constrictions.

Spin-polarized current separator based on a fork-shaped Rashba nanostructure

A scheme for a spin-polarized current separator is investigated by studying the spin-dependent electron transport of a fork-shaped nanostructure with Rashba spin-orbit coupling (SOC), connected to three leads with the same width. It is found that two spin-polarized currents are of the same magnitude but opposite polarizations can be generated simultaneously in the two output leads when the spin-unpolarized electrons injected from the input lead. The underlying physics is revealed to originate from the different spin-dependent conductance caused by the effects of Rashba SOC and the geometrical structure of the system. Further study shows that the spin-polarized current with a strong robustness against disorder, demonstrates the feasibility of the proposed nanostructure for a real application.