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.     

Spin Hall effect and spin current generation in two-dimensional systems with random Rashba spin–orbit coupling

We consider a new effect induced by spin–orbit coupling in a two-dimensional electron gas confined in a semiconductor quantum well, i.e. the possibility of spin current generation by fluctuating random Rashba spin–orbit interaction, with the corresponding mean value of the interaction being equal to zero. Our main results suggest that – in contrast to the spatially uniform Rashba spin–orbit interaction – the spin Hall effect does not vanish for typical disorder strengths. We also point out some other possibilities of using such a random Rashba coupling for the generation of spin density and spin current in two-dimensional nonmagnetic structures.     

Mechanical analogues of spin Hamiltonians and dynamics

Bloch et al. mapped the precession of the spin-half in a magnetic field of variable magnitude and direction to the rotations of a rigid sphere rolling on a curved surface utilizing SU(2)–SO(3)$\mathit{SU}(2)\text{–}\mathit{SO}(3)$ isomorphism. This formalism is extended to study the behaviour of spin–orbit interactions and the mechanical analogy for Rashba–Dresselhauss spin–orbit interaction in two dimensions is presented by making its spin states isomorphic to the rotations of a rigid sphere rolling on a ring. The change in phase of spin is represented by the angle of rotation of sphere after a complete revolution. In order to develop the mechanical analogy for the spin filter, we find that perfect spin filtration of down spin makes the sphere to rotate at some unique angles and the perfect spin filtration of up spin causes the rotations with certain discrete frequencies.     

Effect of in-plane magnetic field on spin polarization in the presence of the Dresselhaus spin–orbit effect

In this paper, we theoretically study the effect of the in-plane magnetic field on spin polarization in the presence of the Dresselhaus spin–orbit effect. It is shown that the large spin polarization can be achieved in such a nanostructure due to the effects of both the Dresselhaus spin–orbit term and the in-plane magnetic field, but the latter plays a main role in the tunneling process. It is also shown that with the increase of in-plane magnetic field, the degree of spin splitting obviously becomes larger.     

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–Büttiker 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.     

Spin transport in graphene spin–orbit barrier structure

We studied spin-dependent transport in monolayer graphene with a spin–orbit barrier, a narrow strip in which the spin–orbit interaction is not zero. When the Fermi energy is between the two spin-split bands, the structure can be used to generate spin-polarized current. For a strong enough Rashba strength, a thick enough barrier or a low enough Fermi energy, highly spin-polarized current is generated (polarization ∼0.7–0.85$\sim 0.7\text{–}0.85$). Under these conditions, the spin direction of the transmitted electron is approximately perpendicular to the direction of motion. This shows that graphene spin–orbit nanostructures are useful for the development of graphene spintronic devices.     

Influence of the spin–orbit interaction in the impurity-band states of n-doped semiconductors

We study numerically the effects of an extrinsic spin–orbit interaction on the model of electrons in n-doped semiconductors of Matsubara and Toyozawa (MT). We focus on the analysis of the density of states (DOS) and the inverse participation ratio (IPR) of the spin–orbit perturbed states in the MT set of energy eigenstates in order to characterize the eigenstates with respect to their extended or localized nature. The finite sizes that we are able to consider necessitate an enhancement of the spin–orbit coupling strength in order to obtain a meaningful perturbation. The IPR and DOS are then studied as a function of the enhancement parameter.     

Characteristics of persistent spin current components in a quasi-periodic Fibonacci ring with spin–orbit interactions: Prediction of spin–orbit coupling and on-site energy

In the present work we investigate the behavior of all three components of persistent spin current in a quasi-periodic Fibonacci ring subjected to Rashba and Dresselhaus spin–orbit interactions. Analogous to persistent charge current in a conducting ring where electrons gain a Berry phase in presence of magnetic flux, spin Berry phase is associated during the motion of electrons in presence of a spin–orbit field which is responsible for the generation of spin current. The interplay between two spin–orbit fields along with quasi-periodic Fibonacci sequence on persistent spin current is described elaborately, and from our analysis, we can estimate the strength of any one of two spin–orbit couplings together with on-site energy, provided the other is known.     

Equal coupling strength approach to spin precession effects concerning Rashba and Dresselhaus spin–orbit interactions in the presence of in-plane magnetic fields

The influence of Rashba and Dresselhaus spin–orbit interactions on the electronic properties of quasi one-dimensional systems like InAs quantum wires is discussed in the presence of in-plane magnetic fields. One shows that equal coupling strength conditions are provided specifically by the commutativity of two-dimensional constituents of velocity and current operators. The interesting point is that equal strength spin–orbit couplings one deals with proceed in conjunction with related spin conservations, which amounts to account for selected orientations of the magnetic field. Accordingly, the in-plane magnetic fields should be directed solely along the bisectrices. Other angles may be conceivable, but in this case spin conservations alluded to above are lost. Such results open the way to a consistent derivation of the equal coupling strength limit of the energy, which leads in turn to the derivation of novel spin-precession effects. A related effective gyromagnetic factor has also been established.     

The effect of inertia on the Dirac electron,the spin Hall current and the momentum space Berry curvature

We have studied the spin dependent force and the associated momentum space Berry curvature in an accelerating system. The results are derived by taking into consideration the non-relativistic limit of a generally covariant Dirac equation with an electromagnetic field present, where the methodology of the Foldy–Wouthuysen transformation is applied to achieve the non-relativistic limit. Spin currents appear due to the combined action of the external electric field, the crystal field and the induced inertial electric field via the total effective spin–orbit interaction. In an accelerating frame, the crucial role of momentum space Berry curvature in the spin dynamics has also been addressed from the perspective of spin Hall conductivity. For time dependent acceleration, the expression for the spin polarization has been derived.     

Theory of spin polarization in mesoscopic spin–orbit coupling systems

We establish a general formalism of the bulk spin polarization (BSP) and the current-based spin polarization (CSP) for mesoscopic ferromagnetic and spin–orbit interaction (SOI) semiconducting systems. Based on this formalism, we reveal the basic properties of BSP and CSP and their relationships. The BSP describes the intrinsic spin polarized properties of devices. The CSP depends on both intrinsic parameters of device and the incident current. For the non-spin-polarized incident current with the in-phase spin-phase coherence, CSP equals to BSP. We give analytically the BSP and CSP of several typical nanodevice models, ferromagnetic nanowire, Rashba nanowire and rings. These results provide basic physical behaviors of BSP and CSP and their relationships.     

Rashba–Dresselhaus double refraction in a two-dimensional electron gas

We investigate the ballistic transport properties of an electron traversing through a two-dimensional electron gas with the Rashba and Dresselhaus spin–orbit coupling (R–D SOC) coexistent. A nonzero incident angle is considered. The relation between the transmission and the incident angle, the interfacial scattering strength, the length of the SOC region and the SOC intensity are revealed. The transmission strength decays when the incident angle is larger than a critical angle. The transport spin polarization is remarkably modulated by the coaction of the two types of SOC.     

Electrical control of ferromagnetic state

We report experiments where magnetization in GaMnAs ferromagnetic semiconductor is manipulated via strain or electric current. In both cases, charge carrier holes become partially polarized due to the anisotropic modification of holes spectra caused by spin–orbit interactions, and this polarization exerts spin torque sufficient to rotate ferromagnetic domains.     

Mesoscopic Fano effect modulated by Rashba spin–orbit coupling and external magnetic field

By employing non-equilibrium Green's function method, the mesoscopic Fano effect modulated by Rashba spin–orbit (SO) coupling and external magnetic field has been elucidated for electron transport through a hybrid system composed of a quantum dot (QD) and an Aharonov–Bohm (AB) ring. The results show that the orientation of the Fano line shape is modulated by the Rashba spin–orbit interaction kRL$k_{R}L$ variation, which reveals that the Fano parameter q will be extended to a complex number, although the system maintains time-reversal symmetry (TRS) under the Rashba SO interaction. Furthermore, it is shown that the modulation of the external magnetic field, which is applied not only inside the frame, but also on the QD, leads to the Fano resonance split due to Zeeman effect, which indicates that the hybrid is an ideal candidate for the spin readout device.     

Effect of non-uniform exchange field in ferromagnetic graphene

We have presented here the consequences of the non-uniform exchange field on the spin transport issues in spin chiral configuration of ferromagnetic graphene. Taking resort to the spin–orbit coupling (SOC) term and non-uniform exchange coupling term we are successful to express the expression of Hall conductivity in terms of the exchange field and SOC parameters through the Kubo formula approach. However, for a specific configuration of the exchange parameter we have evaluated the Berry curvature of the system. We also have paid attention to the study of SU(2) gauge theory of ferromagnetic graphene. The generation of anti damping spin–orbit torque in spin chiral magnetic graphene is also briefly discussed.     

Effective period potential in a hybrid mesoscopic ring with Rashba spin–orbit interaction

We investigate theoretically the persistent charge current (PCC) and pure spin current (PSC) in a hybrid mesoscopic ring with Rashba spin–orbit interaction (RSOI). The PCC and PSC surviving in the ring would experience a periodic potential formed by the band offset of the constituent materials. Similarly, an effective tunnel barrier can be introduced by a region with different RSOI strength. This provides us a convenient way to manipulate the periodic potential by changing the RSOI strength through an electric field. With the increment of the RSOI strength, the PCC is suppressed, while the PSC presents an oscillatory pattern changing from negative to positive.     

Magnetic interactions in strongly correlated systems: Spin and orbital contributions

We present a technique to map an electronic model with local interactions (a generalized multi-orbital Hubbard model) onto an effective model of interacting classical spins, by requiring that the thermodynamic potentials associated to spin rotations in the two systems are equivalent up to second order in the rotation angles, when the electronic system is in a symmetry-broken phase. This allows to determine the parameters of relativistic and non-relativistic magnetic interactions in the effective spin model in terms of equilibrium Green’s functions of the electronic model. The Hamiltonian of the electronic system includes, in addition to the non-relativistic part, relativistic single-particle terms such as the Zeeman coupling to an external magnetic field, spin–orbit coupling, and arbitrary magnetic anisotropies; the orbital degrees of freedom of the electrons are explicitly taken into account. We determine the complete relativistic exchange tensors, accounting for anisotropic exchange, Dzyaloshinskii–Moriya interactions, as well as additional non-diagonal symmetric terms (which may include dipole–dipole interaction). The expressions of all these magnetic interactions are determined in a unified framework, including previously disregarded features such as the vertices of two-particle Green’s functions and non-local self-energies. We do not assume any smallness in spin–orbit coupling, so our treatment is in this sense exact. Finally, we show how to distinguish and address separately the spin, orbital and spin–orbital contributions to magnetism, providing expressions that can be computed within a tight-binding Dynamical Mean Field Theory.     

Electrical generation of pure spin current with oscillating spin-orbit interaction

We propose an electrical scheme for the generation of a pure spin current without a charge current in a two-terminal device, which consists of a scattering region of a two-dimensional electron gas (2DEG) with Rashba (R) and/or Dresselhaus (S) spin-orbit interaction (SOI) and two normal leads. The SOI is modulated by a time-dependent gate voltage to pump a spin current. Based on a tight-binding model and the Keldysh Green’s function technique, we obtain the analytical expression of the spin current. It is shown that a pure spin current can be pumped out, and its magnitude could be modulated by device parameters such as the oscillating frequency of the SOI, as well as the SOI strength. Moreover, the spin polarisation direction of the spin current could also be tuned by the strength ratio between RSOI and DSOI. Our proposal provides not only a fully electrical means to generate a pure spin current but also a way to control the spin polarisation direction of the generated spin current.     

Odd-frequency pairings in a non-centrosymmetric system

We study possible pairing symmetries of non-centrosymmetric superconductors in the Hubbard model with the Rashba-type spin–orbit interaction (RSOI). Because of the breakdown of space inversion symmetry due to RSOI, a mixture of pairing states with different symmetries can emerge. We find that the RSOI mixes not only the spin-singlet even-parity pairing and spin-triplet odd-parity pairings with even-frequency symmetry, but it also mixes the spin-singlet odd-parity pairing and spin-triplet even-parity pairings with odd-frequency symmetry.