Spin-orbit Interaction Region Research Articles

Charge Hall effect generated by spin-polarized current injected into Rashba spin orbit coupling media

Using the Keldysh Green’s function method, we study theoretically the electron accumulation induced by the inverse spin Hall effect in a spin valve structure in which a clean quantum wire formed from a 2D electron gas (2DEG) with Rashba/Dresselahaus spin orbit interaction (SOI) is connected to two ferromagnet electrodes. In a nonequilibrium situation when a spin current with an out-of plane (the 2DEG plane) spin polarization is driven through the SOI region by an external voltage, non-equilibrium electron accumulation or a Hall voltage forms at the two lateral sides of the quantum wire and exhibits an oscillation along the wire like the Rashba spin precession; the magnetization directions of FMs affect the Hall voltage and their parallel or antiparallel alignment along the normal direction of the 2DEG plane is most favorable to the Hall voltage. In an equilibrium situation, two planar magnetizations which are not collinear can generate an electron accumulation/a Hall voltage too. When one of the FM electrodes is replaced by a normal metal (NM), the electron accumulation is still present along the wire and its magnitude remains nearly unchanged in the biased case, whereas in the unbiased case it is reduced significantly and even vanishes.

Spin currents in a normal two-dimensional electron gas in contact with a spin–orbitinteraction region

Spin effects in a normal two-dimensional (2D) electron gas in lateral contact with a 2Dregion with spin–orbit interaction are studied. The peculiarity of this system is the presenceof spin-dependent scattering of electrons from the interface. This results in an equilibriumedge spin current and nontrivial spin responses to a particle current. We investigate thespatial distribution of the spin currents and spin density under non-equilibrium conditionscaused by a ballistic electron current flowing normal or parallel to the interface. Theparallel electron current is found to generate a spin density near the interface and tochange the edge spin current. The perpendicular electron current changes theedge spin current proportionally to the electron current and produces a bulkspin current penetrating deep into the normal region. This spin current has twocomponents, one of which is directed normal to the interface and polarized parallelto it, and the second is parallel to the interface and is polarized in the planeperpendicular to the contact line. Both spin currents have a high degree of polarization (∼40–60%).

Spin polarization of electron current through a potential barrier in two-dimensionalstructures with spin–orbit interaction

We show that an initially unpolarized electron flow acquires spin polarization afterpassing through a lateral barrier in a two-dimensional (2D) system with spin–orbitinteraction (SOI) even if the current is directed normally to the barrier. Thegenerated spin current depends on the distance from the barrier. It oscillates with thedistance in the vicinity of the barrier and asymptotically reaches a constant value.The most efficient generation of the spin current (with polarization above 50%)occurs when the Fermi energy is near the potential barrier maximum. Since thespin current in the SOI medium is not unambiguously defined, we propose topass this current from the SOI region into a contacting region without SOI andshow that the spin polarization loss under such transmission can be negligible.

Persistent spin current in nanodevices and definition of the spin current

We investigate two closely related subjects: (i) the existence of a pure persistent spin current without an accompanying charge current in a semiconducting mesoscopic device with a spin-orbit interaction (SOI) and (ii) the definition of the spin current in the presence of SOI. Through physical argument from four physical pictures in different aspects, we provide strong evidences that the equilibrium persistent spin current does exist in a device with SOI in the absence of any magnetic field or magnetic materials. This persistent spin current is an analog of the persistent charge current in a mesoscopic ring threaded by a magnetic flux, and it describes the real spin motion and can be measured experimentally. We then investigate the definition of the spin current. We point out that (i) the nonzero spin current in the equilibrium SOI device is the persistent spin current, (ii) the spin current is, in general, not conserved, and (iii) the Onsager relation is violated for the spin transport no matter what definition of the spin current is used. These issues, the nonzero spin current in the equilibrium case, the nonconserved spin current, and the violation of the Onsager relation, are intrinsic properties of spin transport. We note that the conventional definition of the spin current has very clear physical intuition and describes the spin motion very well. Therefore, we feel that the conventional definition of the spin current makes physical sense, and there is no need to modify it. (Note that this conclusion is not in contradiction with the opinions in our previous papers). In addition, the relationship between the persistent spin current and transport spin current, the persistent linear and angular spin currents in the SOI region of the hybrid ring, and the measurement of the persistent spin current are discussed. Finally, we show that if the spin-spin interaction is included into the Hamiltonian, the persistent spin current is automatically conserved using the conventional definition.

Spin transport and spin Hall effect in an electron waveguide in the presence of an in-plane magnetic field and spin-orbit interaction

We study electron spin transport and the spin Hall effect in a quantum waveguide in the presence of Rashba spin-orbit interaction (SOI) and a homogeneous in-plane magnetic field, as well as the energy dispersion relation and spin polarization properties of the electron states in the corresponding infinite system. A general expression for the spin polarization of the outgoing flux, resulting from an arbitrarily polarized injection source, is derived for the quantum waveguide without the assumption of spin-degenerate leads. We further derive constraints on the spin-resolved transmission coefficients by analyzing the symmetries of the system. These constraints will impose restrictions on the spin-dependent conductances as well as the spin polarization of the outgoing flux. For an applied in-plane magnetic field parallel to the waveguide, conductance oscillations as a function of the SOI strength are diminished when the Zeeman energy exceeds the Rashba energy, due to spin alignment with the applied magnetic field. Furthermore, the calculated spin and charge probability distributions in the SOI waveguide region show spin Hall patterns and zitterbewegung patterns, respectively. For an applied transverse in-plane magnetic field, the SOI induced effective magnetic field is parallel or antiparallel with the applied field. The conductance of the system is then dominantly determined by spin-conserved transport processes, and spin-flipped transport processes can occur only through interchannel scattering and are therefore greatly suppressed. Furthermore, no zitterbewegung pattern in the charge density distribution can be found in the SOI region when the electrons are injected from a lead with spin polarization along the applied in-plane transverse field direction. However, the spin polarization probability distribution can still show a spin Hall pattern in the SOI region and the sign of the spin polarization in the spin Hall pattern can be reversed by tuning the applied magnetic field strength. For the corresponding infinite waveguide systems with uniform SOI and in-plane magnetic field, we show that the interplay between the applied in-plane magnetic field and the SOI induced effective magnetic field, together with subband hybridizations, will create a wave-vector-dependent spin polarization of the Bloch states with rich features and that these features cannot be captured by employing a simple one-dimensional model.

Scattering matrix method for multimode electron transport through quantum wires under a local magnetic field modulation and spin-orbit interaction

A generalized scattering matrix method is presented for spin-dependent electron transport in a quantum waveguide under the modulations of local magnetic field and/or spin-orbit interaction (SOI). All the required Hamiltonian matrices are expressed in terms of a common basis spanned by the products of the transverse spatial eigenstates and the spin eigenstates of the leads. In the formulation we have included an additional SOI term caused by an in-plane electric potential modulation and have assumed a free choice of magnetic vector potential. Thus the method can easily be applied to two-dimensional electron gas systems with complex geometrical structure, SOI strength profile, distributions of electric potential and magnetic field, etc. The method is numerically stable and can be used to treat accurately spin-dependent, multisubband, electron scattering processes. As an application, the method has been implemented for a Rashba SOI wire subject to a local magnetic field generated by a single ferromagnetic metal stripe on top. In the absence of the magnetic field, the conductance of electrons passing through the SOI region shows a series of Fano-resonance type dips in the vicinity of the onsets of subbands (with the subband index n >= 2). When the local magnetic field is present, the degeneracy of SOI-induced bound states is removed, leading to splittings of these conductance dips. At two split conductance dips originated from the same degenerate dip, a remarkable difference is found in the spatial distribution of spin-projected probability and in the spatial distribution of local spin polarization. It is seen that for a Rashba wire a Hall-like spin accumulation appears at the conductance dips at zero magnetic field. However, in the presence of a local magnetic field a separation of opposite spins along the transport direction is observed in the Rashba wire. In contrast, the zitterbewegung oscillations can show up, when the conductance is at a plateau, and disappear, when the conductance is at a Fano-resonance type dip, regardless the presence of the local magnetic field. (Less)

Multimode electron transport through quantum waveguides with spin-orbit interaction modulation: Applications of the scattering matrix formalism

We present a formulation of the scattering matrix method for spin-dependent electron transport in a quantum waveguide with spin-orbit interaction (SOI). All the required Hamiltonian matrices needed in the implementation of the formulation are represented in a basis of the transverse spatial eigenstates and the spin eigenstates of the leads. Thus the method has great flexibility and can be easily applied to systems with complex geometrical structure, potential distribution, and SOI strength profile. Also, the method is numerically stable and can be used to treat spin-dependent multisubband scattering processes accurately. We have applied the method to the spin-dependent electron transport in quasi-one-dimensional (Q1D) conductors, with a region of the Rashba SOI of uniform strength and with a region containing a Rashba SOI superlattice, made from a semiconductor heterostructure. The total conductance, spin-dependent conductances, and spin polarization of the system are calculated for a fully spin-polarized electron beam injected from a lead into the SOI region. For the Q1D conductor with a single region of the Rashba SOI, it is found that when the Fermi energy is set at a value, for which the total conductance is at a plateau, the spin-dependent conductances show regular oscillations with increasing SOI strength. This is approximately true even when the total conductance is at a high plateau and thus multiple subbands in the waveguide are open for conduction. However, when the Fermi energy is set at a value close to the onset of a subband (with the subband index $n\ensuremath{\geqslant}2$), the spin-polarized conductances plotted against the SOI strength and the SOI region length show sharp resonance features or complex fluctuations. These irregular conductance characteristics arise from SOI-induced strong coupling between subbands. For the Q1D conductor modulated by an array of strong Rashba SOI stripes, the total conductance shows regular superlattice behavior, while the spin-dependent conductances show complex behavior with regions of slow oscillations and regions of rapid oscillations. As in the Q1D conductor with a single SOI region, the slow oscillations are found in the energy regions where the total conductance is at plateaus. However, the rapid oscillations appear at energies close to the onsets of subbands with the subband index $n\ensuremath{\geqslant}2$. These oscillations originate from strong spin scattering by localized states formed in the SOI-modulated superlattice region.

Effects of multi-band mixing on the spin-polarized transport in quasi-one-dimensional electron waveguides

We present numerical calculations of the energy dispersion of spin-polarized electrons in quasi-one-dimensional electronic waveguides in the presence of Rashba spin–orbit interaction (SOI), by using an efficient expanded basis method. Within this model, the general mixing between any two subbands is taken into account. We investigate the properties of spin-polarized transport in the nonuniform SOI system. It is found that the multi-band mixing brings significant effects on the properties of multiple subbands transport in the regime of high energy, especially for the cases of the wide waveguide, the strong SOI and the long extension of the SOI region.