Dresselhaus Fields Research Articles

Spin orbit torque switching of magnetization in the presence of two different orthogonal spin–orbit magnetic fields

Switching of magnetization by spin–orbit torque in the (Ga,Mn)(As,P) film was studied with currents along ⟨100⟩ crystal directions and an in-plane magnetic field bias. This geometry allowed us to identify the presence of two independent spin–orbit-induced magnetic fields: the Rashba field and the Dresselhaus field. Specifically, we observe that when the in-plane bias field is along the current (I ∥ Hbias), switching is dominated by the Rashba field, while the Dresselhaus field dominates magnetization reversal when the bias field is perpendicular to the current (I ⊥ Hbias). In our experiments, the magnitudes of the Rashba and Dresselhaus fields were determined to be 2.0 and 7.5 Oe, respectively, at a current density of 8.0 × 105 A/cm2.

Realizing Optical Persistent Spin Helix and Stern-Gerlach Deflection in an Anisotropic Liquid Crystal Microcavity.

Spin-orbit interactions which couple the spin of a particle with its momentum degrees of freedom lie at the center of spintronic applications. Of special interest in semiconductor physics are Rashba and Dresselhaus spin-orbit coupling. When equal in strength, the Rashba and Dresselhaus fields result in SU(2) spin rotation symmetry and emergence of the persistent spin helix only investigated for charge carriers in semiconductor quantum wells. Recently, a synthetic Rashba-Dresselhaus Hamiltonian was shown to describe cavity photons confined in a microcavity filled with optically anisotropic liquid crystal. In this Letter, we present a purely optical realization of two types of spin patterns corresponding to the persistent spin helix and the Stern-Gerlach experiment in such a cavity. We show how the symmetry of the Hamiltonian results in spatial oscillations of the spin orientation of photons traveling in the plane of the cavity.

Observation of Dresselhaus type spin splitting of zinc blende structure semiconductors by circular dichroic photoemission study

Material family of zinc blende structure semiconductors (ZBSSs) is important for novel technique such as spintronics. A study of the ZBSS spin-splitting structure in momentum space is essential when seeking to understand the exotic properties of the material. The Dresselhaus field predominates in the bulk, but the Rashba field plays important roles in states near the surface. Here, we used circular dichroism in angle-resolved photoemission spectroscopy (CD-ARPES) to explore the spin-splitting structure of bulk ZBSS in momentum space. The observed structure was well-explained by a Dresselhaus field attributable to the lack of inversion symmetry in ZBSS crystals. We show that CD-ARPES usefully reveals spin-splitting in momentum space. CD-ARPES combined with hard x-ray incident-beam would be useful to investigate the spin-splitting structures of the interface states in the ZBSS heterostructure.

Optical analogue of Dresselhaus spin–orbit interaction in photonic graphene

The concept of gauge fields plays a significant role in many areas of physics from particle physics and cosmology to condensed matter systems, where gauge potentials are a natural consequence of electromagnetic fields acting on charged particles and are of central importance in topological states of matter. Here, we report on the experimental realization of a synthetic non-Abelian gauge field for photons in a honeycomb microcavity lattice. We show that the effective magnetic field associated with TE-TM splitting has the symmetry of Dresselhaus spin-orbit interaction around Dirac points in the dispersion, and can be regarded as an SU(2) gauge field. The symmetry of the field is revealed in the optical spin Hall effect (OSHE), where under resonant excitation of the Dirac points precession of the photon pseudospin around the field direction leads to the formation of two spin domains. Furthermore, we observe that the Dresselhaus field changes its sign in the same Dirac valley on switching from s to p bands in good agreement with the tight binding modelling. Our work demonstrating a non-Abelian gauge field for light on the microscale paves the way towards manipulation of photons via spin on a chip.

Robustness of a persistent spin helix against a cubic Dresselhaus field in (001) and (110) oriented two-dimensional electron gases

The persistent spin helix (PSH) state in III--V semiconductor quantum wells (QWs) is a promising candidate for spin-based applications because the PSH state realizes controllable spin orientation with long spin lifetime. Although the cubic Dresselhaus spin-orbit (SO) interaction is known for breaking the PSH state in both (001)-oriented and (110)-oriented QWs, it is not well understood how the distinct symmetry of cubic Dresselhaus terms ${\ensuremath{\beta}}_{3}$ between (001) and (110) QWs affects the robustness of the PSH state. Here we investigate robustness of the PSH state between (001) and (110) QWs under various strengths of cubic Dresselhaus SO interaction based on numerical Monte Carlo approach and magnetoconductance simulation, respectively, representing optical spin excitation/detection and weak localization/weak antilocalization in magnetotransport. For electron spins initialized along $z\ensuremath{\parallel}[001]$ in a (001) QW and $x\ensuremath{\parallel}[001]\phantom{\rule{4pt}{0ex}}\mathrm{and}\phantom{\rule{4pt}{0ex}}y\ensuremath{\parallel}[1\overline{1}0]$ in a (110) QW, where the spin distribution is developed with the helical spin mode, a (001) QW shows a more robust PSH state against the increase of ${\ensuremath{\beta}}_{3}$ than does a (110) QW. This phenomenon is contrary to numerically computed magnetoconductance, where weak localization is maintained on the variation of ${\ensuremath{\beta}}_{3}$ in a (110) QW, whereas weak antilocalization appears in a (001) QW. By deriving the spin lifetime of the PSH state in a (110) QW from a diffusion equation using a random-walk approach, we demonstrate that such a difference arises directly from the magnitude and orientation of third angular harmonics in cubic Dresselhaus fields for (001) and (110) QWs.

Crystalline Direction Dependence of Spin Precession Angle and Its Application to Complementary Spin Logic Devices.

In a semiconductor channel, spin-orbit interaction is divided into two terms, Rashba and Dresselhaus effects, which are key phenomena for modulating spin precession angles. The direction of Rashba field is always perpendicular to the wavevector but that of Dresselhaus field depends on the crystal orientation. Based on the individual Rashba and Dresselhaus strengths, we calculate spin precession angles for various crystal orientations in an InAs quantum well structure. When the channel length is 1 μm, the precession angle is 550° for the [110] direction and 460° for the [1-10] direction, respectively. Using the two spin transistors with different crystal directions, which play roles of n- and p-type transistors in conventional charge transistors, we propose a complementary logic device.

Magnetic field effect on electron spin dynamics in (110) GaAs quantum wells

We study the electron spin relaxation in both symmetric and asymmetric GaAs/AlGaAs quantum wells (QWs) grown on (110) substrates in an external magnetic field B applied along the QW normal. The spin polarization is induced by circularly polarized light and is detected using the time-resolved Kerr rotation technique. In the asymmetric structure, where a δ-doped layer on one side of the QW produces the Rashba contribution to the conduction-band spin–orbit splitting, the lifetime of electron spins aligned along the growth axis exhibits an anomalous dependence on B in the range 0 < B < 0.5 T; this results from the interplay between the Dresselhaus and Rashba effective fields which are perpendicular to each other. For larger magnetic fields, the spin lifetime increases, which is a consequence of the cyclotron motion of the electrons and is also observed in (001)-grown quantum wells. The experimental results are in agreement with the calculation of the spin lifetimes in (110)-grown asymmetric quantum wells described by the point group Cs, where the growth direction is not the principal axis of the spin-relaxation-rate tensor.

Observation of the in-plane spin-dephasing anisotropy in [111]-grown GaAs/AlGaAs quantum well

The electron density and temperature dependent in-plane spin-dephasing anisotropy in [111]-grown GaAs quantum well (QW) has been investigated by time-resolved magneto-Kerr rotation technique. Due to the specific symmetry of [111]-grown quantum well, the in-plane Rashba and linear Dresselhaus effective spin-orbit magnetic field is parallel to each other for electron wave vectors in all directions. However, an obvious in-plane spin-dephasing anisotropy comparing [2¯11] with [01¯1] crystalline orientations has been observed and discussed in this work. Our results demonstrate the innegligible spin dephasing channel through inhomogeneous broadening induced by the out-of-plane non-linear Dresselhaus field, which arises naturally from the C3 symmetry of [111]-grown GaAs QW.

Separation of Rashba and Dresselhaus spin-orbit interactions using crystal direction dependent transport measurements

The Rashba spin-orbit interaction effective field is always in the plane of the two-dimensional electron gas and perpendicular to the carrier wavevector but the direction of the Dresselhaus field depends on the crystal orientation. These two spin-orbit interaction parameters can be determined separately by measuring and analyzing the Shubnikov-de Haas oscillations for various crystal directions. In the InAs quantum well system investigated, the Dresselhaus term is just 5% of the Rashba term. The gate dependence of the oscillation patterns clearly shows that only the Rashba term is modulated by an external electric field.

Effect of Dresselhaus spin-orbit coupling on spin dephasing in asymmetric and macroscopically symmetric (110)-grown quantum wells

We develop a microscopic theory of electron spin dephasing in (110)-grown quantum wells where the electron scattering time is comparable to or exceeds the period of spin precession in the effective magnetic field caused by spin-orbit coupling. Structures with a homogeneous and fluctuating Rashba field, which triggers the dephasing of electron spins aligned along the growth direction, are analyzed. We show that the Dresselhaus field, which is always present in zinc-blende-type quantum wells, suppresses the spin dephasing enabling a very long spin lifetime of conduction electrons. The dependence of the spin lifetime on the electron mobility is found to be nonmonotonic reaching the minimum in structures where the scattering time is comparable to the period of spin precession in the effective magnetic field.

Synchronous Spatial Oscillation of Electron- and Mn-Spin Polarizations in Dilute-Magnetic-Semiconductor Quantum Wells under Spin–Orbit Effective Magnetic Fields

In semiconductors, spin-orbit effective magnetic fields, i.e., the Rashba and Dresselhaus fields, are used to control electron-spin polarization. This operation, however, destroys the electron-spin coherence, and the spin polarization is limited to the vicinity of a ferromagnetic source electrode. In this paper, we propose the use of dilute magnetic semiconductors to improve the coherence of spatially oscillating electron-spin polarization. In dilute magnetic semiconductors, the electron-spin polarization near the source electrode dynamically induces the local spin polarization of magnetic impurities through s-d spin-flip scattering. This impurity-spin polarization improves, in turn, the coherence of the electron-spin polarization, and this improved electron-spin polarization induces impurity-spin polarization farther in the adjacent region. Because of this positive feedback, the coherent and synchronized spatial oscillations of electron- and impurity-spin polarizations grow cooperatively. A numerical calculation for a CdMnTe quantum well demonstrates the validity of this mechanism.

Detection of large in-plane spin-dephasing anisotropy in [1 0 0]-grown GaAs/AlGaAs quantum wells

The electron density-dependent in-plane spin dephasing anisotropy in GaAs/AlGaAs single quantum wells has been investigated by time-resolved magneto-Kerr rotation (TR-MOKE) measurements. Large anisotropy of in-plane spin dephasing time has been observed and compared for samples with different degrees of structural asymmetry. The breakdown of spin dephasing anisotropy with increase in electron density is ascribed to the combined effect of relative strength change in the Rashba and Dresselhaus fields and contribution of cubic Dresselhaus term at higher excitation electron density. It is revealed that Dresselhaus spin–orbit coupling strength is stronger than Rashba for all samples studied in our experiment. The measured anisotropy dependence on electron density and sample asymmetry agrees with previous theoretical studies.

Modeling of diffusion of injected electron spins in spin-orbit coupled microchannels

We report on a theoretical study of spin dynamics of an ensemble of spin-polarized electrons injected in a diffusive microchannel with linear Rashba and Dresselhaus spin-orbit coupling. We explore the dependence of the spin-precession and spin-diffusion lengths on the strengths of spin-orbit interaction and external magnetic fields, microchannel width, and orientation. Our results are based on numerical Monte Carlo simulations and on approximate analytical formulas both treating the spin-dynamics quantum mechanically. We conclude that spin-diffusion lengths comparable or larger than the precession length occur (i) in the vicinity of the persistent spin helix regime for arbitrary channel width and (ii) in channels of similar or smaller width than the precession length, independent of the ratio of Rashba and Dresselhaus fields. For similar strengths of the Rashba and Dresselhaus fields, the steady-state spin-density oscillates or remains constant along the channel for channels parallel to the in-plane diagonal crystal directions. An oscillatory spin-polarization pattern tilted by $45\ifmmode^\circ\else\textdegree\fi{}$ with respect to the channel axis is predicted for channels along the main cubic crystal directions. For typical experimental system parameters, magnetic fields on the order of tesla are required to affect the spin-diffusion and spin-precession lengths.

Controllable Dresselhaus field in microscopically inversion-symmetric quantum wells

We have investigated theoretically a method to control the Dresselhaus effective magnetic field, using crystallographically inversion-symmetric quantum wells, whose well layer consists of a compound semiconductor and a thin Ge layer at the centre of the well. The Dresselhaus field vanishes, because of the inversion symmetry of the crystal structure, and is induced by electric field applied perpendicular to the well. Sps* tight-binding calculation shows that the Dresselhaus field is proportional to the applied electric field, and is comparable to the Rashba field for wells with appropriate width. As a result, we can externally control the strength of the total effective magnetic field without changing its shape.

Spin-Dephasing Anisotropy for Electrons in a Diffusive Quasi-1D GaAs Wire

We present a numerical study of dephasing of electron spin ensembles in a diffusive quasi-one-dimensional GaAs wire due to the D’yakonov–Perel’ spin-dephasing mechanism. For widths of the wire below the spin precession length and for equal strength of Rashba and linear Dresselhaus spin–orbit fields a strong suppression of spin-dephasing is found. This suppression of spin-dephasing shows a strong dependence on the wire orientation with respect to the crystal lattice. The relevance for realistic cases is evaluated by studying how this effect degrades for deviating strength of Rashba and linear Dresselhaus fields, and with the inclusion of the cubic Dresselhaus term.

Measurement of Rashba and Dresselhaus spin–orbit magnetic fields

Spin–orbit coupling is a manifestation of special relativity. In the reference frame of a moving electron, electric fields transform into magnetic fields, which interact with the electron spin and lift the degeneracy of spin-up and spin-down states. In solid-state systems, the resulting spin–orbit fields are referred to as Dresselhaus and Rashba fields, depending on whether the electric fields originate from bulk or structure inversion asymmetry, respectively. Yet, it remains a challenge to determine the absolute value of both contributions in a single sample. Here, we show that both fields can be measured by optically monitoring the angular dependence of the electrons’ spin precession on their direction of motion with respect to the crystal lattice. Furthermore, we demonstrate spin resonance induced by the spin–orbit fields. We apply our method to GaAs/InGaAs quantum-well electrons, but it should be universally useful to characterize spin–orbit interactions in semiconductors, and therefore could facilitate the design of spintronic devices.

Spin precession, flips, and transmission through a ring: Relation between the spin–orbit interaction strengths and the final spin orientation

We study spin precession and transmission through a mesoscopic ring in the presence of the Rashba and Dresselhaus terms of the spin–orbit interaction (SOI), respectively, of strengths α and β , and of a magnetic field B. The Rashba field, the effective Dresselhaus field as well as B have perpendicular and radial components. The final spin orientations depend importantly on α , β , and B. In the absence of B the outgoing spins trace rings perpendicular to well-defined directions for β = 0 or α = 0 . For β = 0 ( α = 0 ) incident spins polarized along these well-defined directions exit the ring undeflected. For α ≠ β ≠ 0 the trace rings become spirals. The values of α and β are related to the final spin orientation. For weak magnetic fields this precession picture does not hold. Spin flips occur when α or β is varied as the angles describing the final spin orientation change drastically in a very narrow range of α or β values in which the total transmission vanishes.

SU(2) × U(1) unified theory for charge, orbit and spin currents

Spin and charge currents in systems with Rashba or Dresselhaus spin-orbit couplings are formulated in a unified version of four-dimensional SU(2)$\times$U(1) gauge theory, with U(1) the Maxwell field and SU(2) the Yang-Mills field. While the bare spin current is non-conserved, it is compensated by a contribution from the SU(2) gauge field, which gives rise to a spin torque in the spin transport, consistent with the semi-classical theory of Culcer et al. Orbit current is shown to be non-conserved in the presence of electromagnetic fields. Similar to the Maxwell field inducing forces on charge and charge current, we derive forces acting on spin and spin current induced by the Yang Mills fields such as the Rashba and Dresselhaus fields and the sheer strain field. The spin density and spin current may be considered as a source generating Yang-Mills field in certain condensed matter systems.