Spin–orbit coupling and spin transport

Recent achievements in semiconductor spintronics are discussed. Special attention is paid to spin–orbit interaction, coupling of electron spins to external electric fields, and spin transport in media with spin–orbit coupling, including the mechanisms of spin-Hall effect. Importance of spin-transport parameters at spin-precession wave vector k_so is emphasized, and existence of an universal relation between spin currents and spin accumulation at the spatial scale of is conjectured.     

Spin–orbit induced magnetic phenomena in bulk metals and their surfaces and interfaces

First-principles electronic structure studies based on local spin density functional theory and performed on extremely complex simulations of ever increasingly realistic systems, play a very important role in explaining and predicting surface and interface magnetism. This review deals with what is a major issue for first-principles theory, namely the theoretical/computational treatment of the weak spin–orbit coupling in magnetic transition metals and their alloys and its important physical consequences: magneto-crystalline anisotropy, magnetostriction, magneto-optical Kerr effects and X-ray magnetic circular dichroism. As is demonstrated, extensive first-principles calculations and model analyses now provide simple physical insights and guidelines to search for new magnetic recording and sensor materials.     

Note on spin–orbit interactions in nuclei and hypernuclei

A detailed comparison is made between the spin–orbit interactions in Λ hypernuclei and ordinary nuclei. We argue that there are three major contributions to the spin–orbit interaction: (1) a short-range component involving scalar and vector mean fields; (2) a “wrong-sign” spin–orbit term generated by the pion exchange tensor force in second order; and (3) a three-body term induced by two-pion exchange with excitation of virtual Δ(1232)-isobars (à la Fujita–Miyazawa). For nucleons in nuclei the long-range pieces related to the pion-exchange dynamics tend to cancel, leaving room dominantly for spin–orbit mechanisms of short-range origin (parametrized, e.g., in terms of relativistic scalar and vector mean fields terms). In contrast, the absence of an analogous 2π-exchange three-body contribution for Λ hyperons in hypernuclei leads to an almost complete cancellation between the short-range (relativistic mean-field) component and the “wrong-sign” spin–orbit interaction generated by second order π-exchange with an intermediate Σ hyperon. These different balancing mechanisms between short- and long-range components are able to explain simultaneously the very strong spin–orbit interaction in ordinary nuclei and the remarkably weak spin–orbit splitting in Λ hypernuclei.     

Theoretical analysis of whispering-gallery mode ring dielectric resonator

A new type of whispering-gallery mode ring dielectric resonators are first proposed. Theoretical analysis and a method for determination of the resonant frequencies is presented by the mode matching method. The numerical results show good agreement with theoretical analysis.     

Exchange-enhanced spin-splitting in a two-dimensional electron gas in the presence of the Rashba spin–orbit interaction

We present a theoretical study on how many-body effects can affect the spin-splitting of a two-dimensional electron gas in the presence of the Rashba spin–orbit interaction. The standard Hartree–Fock approximation and Green's function approach are employed to calculate the energy spectrum and density of states of a spin-split two-dimensional electron gas (2DEG). We find that the presence of the exchange interaction can enhance significantly the spin-splitting of a 2DEG on top of the Rashba effect. The physical reasons behind this important phenomenon are discussed.     

Spin–orbit coupling in bulk GaAs

We study the spin–orbit coupling in the whole Brillouin zone for GaAs using both the sp³s^*d⁵ and sp³s^* nearest-neighbor tight-binding models. In the Γ-valley, the spin splitting obtained is in good agreement with experimental data. We then further explicitly present the coefficients of the spin splitting in GaAs L- and X-valleys. These results are important to the realization of spintronic device and the investigation of spin dynamics far away from equilibrium.     

Analysis of a fiber ring resonator as a multi-path light-wave circuit in white-light fiber-optic interferometric sensors

According to the phase shift response of a ring resonator, the role of a fiber-optic ring resonator as a multi-path light-wave circuit in white-light fiber-optic interferometric sensors is analyzed. Formulas related to the maximum intensity of the interference fringes and the system parameters are derived by exact mathematic deduction. The main factors affecting the multiplexing capability of the sensor array are discussed. The analysis method not only gives an explicit explanation for the enhancement of multiplexing capability but also can be applied to other structural white-light sensor systems, in which the ring resonator is used as a multi-path light-wave circuit.     

Gate voltage-dependent Aharanov–Bohm experiment in the presence of Rashba spin–orbit interaction

We measured gate voltage-dependent Aharonov–Bohm oscillations in an InGaAs-based two-dimensional electron gas ring with a gate on top of one of the branches. After ensemble averaging, the h/e oscillation spectrum showed smooth oscillatory behavior as a function of the gate voltage. This could be a manifestation of the spin–orbit interaction induced interference.     

Spin–orbit coupling and semiclassical electron dynamics in noncentrosymmetric metals

Spin–orbit coupling of electrons with the crystal lattice plays a crucial role in materials without inversion symmetry, lifting spin degeneracy of the Bloch states and endowing the resulting nondegenerate bands with complex spin textures and topologically nontrivial wavefunctions. We present a detailed symmetry-based analysis of the spin–orbit coupling and the band degeneracies in noncentrosymmetric metals. We systematically derive the semiclassical equations of motion for fermionic quasiparticles near the Fermi surface, taking into account both the spin–orbit coupling and the Zeeman interaction with an applied magnetic field. Some of the lowest-order quantum corrections to the equations of motions can be expressed in terms of a fictitious “magnetic field” in the momentum space, which is related to the Berry curvature of the band wavefunctions. The band degeneracy points or lines serve as sources of a topologically nontrivial Berry curvature. We discuss the observable effects of the wavefunction topology, focusing, in particular, on the modifications to the Lifshitz–Onsager semiclassical quantization condition and the de Haas-van Alphen effect in noncentrosymmetric metals.     

Spin–spin interaction in magnetic semiconductor quantum dots

Self-assembled Cd(Mn)Se/Zn(Mn)Se quantum dots have been investigated by means of spatially and time-resolved magneto-optical spectroscopy. In such quasi zero-dimensional diluted magnetic semiconductors, the exchange interaction couples the spins of optically generated charge carriers with localized magnetic ion spins. We demonstrate that this can be used on the one hand to monitor nanoscale magnetization with a resolution of <100 μ_B by a purely optical technique and on the other hand to optically manipulate the magnetization in a semiconductor quantum dot.     

Fano resonance and spectral compression in a ring resonator drop filter with feedback

We propose a ring resonator drop filter with feedback loop which can form the other ring cavity to produce an asymmetric Fano-resonance line shape and mode compression. By properly adjusting the feedback loop, the asymmetric line shapes of the transmission spectra can be controlled and selectively mode compression of the circuiting intensity in the feedback loop is achieved. Such characteristics are useful for applications in ring resonator-based photonic devices such as all-optical switches, sensors and intracavity frequency selection single-mode laser.     

Dynamics of One‐Dimensional Electrons With Broken Spin–Charge Separation

Spin–charge separation is known to be broken in many physically interesting one‐dimensional (1D) and quasi‐1D systems with spin–orbit interaction because of which spin and charge degrees of freedom are mixed in collective excitations. Mixed spin–charge modes carry an electric charge and therefore can be investigated by electrical means. We explore this possibility by studying the dynamic conductance of a 1D electron system with image‐potential‐induced spin–orbit interaction. The real part of the admittance reveals an oscillatory behavior versus frequency that reflects the collective excitation resonances for both modes at their respective transit frequencies. By analyzing the frequency dependence of the conductance the mode velocities can be found and their spin–charge structure can be determined quantitatively.     

Influence of nonlinear absorption effects on optical bistability in semiconductor ring resonators

We present a theoretical investigation of optical bistability in a nonlinear semiconductor ring resonator, by taking into account the two-photon absorption and the free-carrier absorption. By solving the intensity equation within the ring resonator, a parametric formulation is obtained for describing the bistability relation between the input and the output intensities. Numerical results show that the nonlinear absorption effects can affect the critical points and domain of the optical bistability.     

Spin-dependent magnetotransport through one or more rings in the presence of the Rashba and Dresselhaus terms of the spin–orbit interaction

Magnetotransport through one or several quasi-one-dimensional rings, in the presence of the Rashba (RSOI) and Dresselhaus (DSOI) terms of the spin–orbit interaction (SOI) and of a magnetic field B, is investigated. The RSOI field and an effective DSOI field are taken as E_R=E_R(sinγ₁e_r+cosγ₁e_z) and E_D=E_D(sinγ₂e_r+cosγ₂e_z), their strengths are denoted by α and β, respectively. The exact one-electron eigenvalues and eigenfunctions are obtained and used to evaluate the transmission as a function of α, β, and of the angles γ₁,γ₂. Because the RSOI term couples the electronic orbit (along the θ direction) with the Pauli matrices σ_z and σ_r while the DSOI term couples it with σ_θ, they affect the electronic spin transport through a ring in distinctly different ways. The resulting transmission shows a considerable structure as a function of the angles γ₁ or γ₂. The same holds for the transmission, versus α or β, with the SOI present only in one arm of the ring and for that through two rings with the same or different radii. Various results of the literature, valid for β=0, are readily recovered. For weak magnetic fields the influence of the Zeeman term on the transmission, assessed by perturbation theory, is negligible.     

Analysis of a second-order polarization-independent filter made of a single ring resonator and a Sagnac interferometer

A novel second-order polarization-independent filter made of a single ring resonator and a Sagnac interferometer (SRRSI) is proposed, and its filtering characteristics are investigated. By using birefringence in waveguide, a single ring resonator can be used to synthesize a filter with second-order response. Analytical formulas are derived for characteristics of the SRRSI varied with waveguide parameters, such as the coupling coefficient; and the critical condition of a second-order Butterworth filter is given. The influence of loss in the ring resonator is also analyzed.     

Localization corrections to charge and spin conductivity in ferromagnetic layered structures

Localization corrections to charge and spin conductivity of two-dimensional ferromagnetic systems with spin–orbit interaction are studied theoretically. The corrections lead to negative magnetoresistance — also in the presence of spin–orbit scattering. Magnitude of the corrections depends on the magnetization orientation with respect to the plane of the system. The corrections to spin conductivity are shown to be small.     

Spin–orbit stiffness of the spin‐polarized electron gas

In a spin‐polarized electron gas, Coulomb interaction couples the spin and motion degrees of freedom to build propagating spin waves. The spin wave stiffness S_sw quantifies the energy cost to trigger such excitation by perturbing the kinetic energy of the electron gas (i.e. putting it in motion). Here we introduce the concept of spin–orbit stiffness, S_so, as the energy necessary to excite a spin wave with a spin polarization induced by spin–orbit coupling. This quantity governs the Coulombic enhancement of the spin–orbit field acting of the spin wave. First‐principles calculations and electronic Raman scattering experiments carried out on a model spin‐polarized electron gas, embedded in a CdMnTe quantum well, demonstrate that S_so = S_sw. Through optical gating of the structure, we demonstrate the reproducible tuning of S_so by a factor of 3, highlighting the great potential of spin–orbit control of spin waves in view of spintronics applications. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Spin-polarization in a 3-terminal conductor induced by Rashba spin–orbit coupling

We investigate numerically the spin polarization of the current in the presence of Rashba spin–orbit interaction (RSOI) in a 3-terminal conductor. We use equation-of-motion method to simulate the time evolution of the wave packet and focus on single-channel transport. A T-shaped conductor with uniform RSOI proposed by Kiselev and Kim and a Y-shaped conductor with nonuniform RSOI are considered. In the T-shaped conductor, the strength of RSOI is assumed to be uniform. We have found that the spin polarization becomes nearly 100% with little loss of conductance for sufficiently strong spin–orbit coupling. This is due to the spin-dependent group velocity of electrons at the junction which causes the spin separation. In the Y-shaped conductor, the strength of RSOI is modulated perpendicular to the charge current. A spatial gradient of effective magnetic field due to the nonuniform RSOI causes the Stern–Gerlach type spin separation. The direction of the polarization is perpendicular to the current and parallel to the spatial gradient. Again almost 100% spin polarization can be realized by this spin separation.