Here, we study diffusive spin transport in two dimensions and demonstrate that an intrinsic analog to a previously predicted extrinsic spin swapping effect, where the spin polarization and the direction of flow are interchanged due to spin-orbit coupling at extrinsic impurities, can be induced by intrinsic (Rashba) spin-orbit coupling. The resulting accumulation of intrinsically spin-swapped polarizations is shown to be much larger than for the extrinsic effect. Intrinsic spin swapping is particularly strong when the system dimensions exceed the spin-orbit precession length and the generated transverse spin currents are of the order of the injected primary spin currents. In contrast, spin accumulations and spin currents caused by extrinsic spin swapping are proportional to the spin-orbit coupling. We present numerical and analytical results for the secondary spin currents and accumulations generated by intrinsic spin swapping, and we derive analytic expressions for the induced spin accumulation at the edges of a narrow strip, where a long-range propagation of spin polarizations takes place.
We theoretically study the crossover between spin Hall effect and spin swapping, a recently predicted phenomenon that consists in the interchange between the current flow and its spin polarization directions [Lifshits and Dyakonov, Phys. Rev. Lett. 103, 186601 (2009)]. Using a tight-binding model with spin-orbit coupled disorder, spin Hall effect, spin relaxation and spin swapping are treated on equal footing. We demonstrate that spin Hall effect and spin swapping present very different dependences as a function of the spin-orbit coupling and disorder strengths. As a consequence, we show that …
Planar spin transport in disordered ultrathin magnetic bilayers comprising a ferromagnet and a normal metal (typically used for spin pumping, spin Seebeck and spin-orbit torque experiments) is investigated theoretically. Using a tight-binding model that treats extrinsic spin Hall effect, spin swapping and spin relaxation on equal footing, we show that the nature of spin-orbit coupled transport dramatically depends on ratio between the layers thickness $d$ and the mean free path $λ$. While spin Hall effect dominates in the diffusive limit ($d\ggλ$), spin swapping dominates in Knudsen regime ($d…
A complete set of the generalized drift-diffusion equations for a coupled charge and spin dynamics in ferromagnets in the presence of extrinsic spin-orbit coupling is derived from the quantum kinetic approach, covering major transport phenomena, such as the spin and anomalous Hall effects, spin swapping, spin precession and relaxation processes. We argue that the spin swapping effect in ferromagnets is enhanced due to spin polarization, while the overall spin texture induced by the interplay of spin-orbital and spin precessional effects displays a complex spatial dependence that can be exploit…
The concept of swapping the two most important spin interactions -- exchange and spin-orbit coupling -- is proposed based on two-dimensional multilayer van der Waals heterostructures. Specifically, we show by performing realistic ab initio simulations, that a single device consisting of a bilayer graphene sandwiched by a 2D ferromagnet Cr$_2$Ge$_2$Te$_6$ (CGT) and a monolayer WS$_2$, is able not only to generate, but also to swap the two interactions. The highly efficient swapping is enabled by the interplay of gate-dependent layer polarization in bilayer graphene and short-range spin-orbit an…
Evidence for spin swapping from modulation of transverse resistance in magnetic heterostructures with Rashba interface
Institute for Solid State Physics, University of Tokyo（东京大学固体物理研究所）；Universidad del Pais Vasco UPV/EHU（巴斯克地区大学）；Center for Emergent Matter Science, RIKEN（理化学研究所新兴物质科学中心）
We consider the spin-orbit-induced spin Hall effect and spin swapping in diffusive superconductors. By employing the non-equilibrium Keldysh Green's function technique in the quasiclassical approximation, we derive coupled transport equations for the spectral spin and particle distributions and for the energy density in the elastic scattering regime. We compute four contributions to the spin Hall conductivity, namely, skew scattering, side-jump, anomalous velocity, and the Yafet contribution. The reduced density of states in the superconductor causes a renormalization of the spin Hall angle. W…
We analyze the effect known as "spin current swapping" (SCS) due to electron-impurity scattering in a uniform spin-polarized two-dimensional electron gas. In this effect a primary spin current $J_i^a$ (lower index for spatial direction, upper index for spin direction) generates a secondary spin current $J_a^i$ if $i \neq a$, or $J_j^j$, with $j\ne i$, if $i= a$. Contrary to naive expectation, the homogeneous spin current associated with the uniform drift of the spin polarization in the electron gas does not generate a swapped spin current by the SCS mechanism. Nevertheless, a swapped spin curr…
The interfaces in hybridized structures could give rise to rich phenomena, which open the way to novel devices with extraordinary performance. Here, we investigate the interface-related spin transport properties in Fe|Au bilayer based on first-principle calculation. We find that the spin Hall current in the Au side near the interface flows in the opposite direction to the bulk spin Hall current with the magnitude sensitive to the magnetization direction of Fe. This negative interfacial contribution is attributed to the spin dependent transmission within a few atomic layers, where a strong inte…
We develop the Keldysh formalism for the polarization dynamics of an open spin system. We apply it to the swapping between two qubit states in a model describing an NMR cross-polarization experiment. The environment is a set of interacting spins. For fast fluctuations in the environment, the analytical solution shows effects missed by the secular approximation of the Quantum Master Equation for the density matrix: a frequency decrease depending on the system-environment escape rate and the quantum quadratic short time behavior. Considering full memory of the bath correlations yields a progress…
We present a scheme for efficient state teleportation and entanglement swapping using a single quantum-dot spin in an optical microcavity based on giant circular birefringence. State teleportation or entanglement swapping is heralded by the sequential detection of two photons, and is finished after the spin measurement. The spin-cavity unit works as a complete Bell-state analyzer with a built-in spin memory allowing loss-resistant repeater operation. This device can work in both the weak coupling and the strong coupling regime, but high efficiencies and high fidelities are only achievable when…
We numerically study the hyperfine induced nuclear spin dynamics in a system of two coupled quantum dots in zero magnetic field. Each of the electron spins is considered to interact with an individual bath of nuclear spins via homogeneous coupling constants (all coupling coefficients being equal). In order to lower the dimension of the problem, the two baths are approximated by two single long spins. We demonstrate that the hyperfine interaction enables to utilize the nuclear baths for quantum information purposes. In particular, we show that it is possible to swap the nuclear ensembles on tim…
Quantum Information Processing relies on coherent quantum dynamics for a precise control of its basic operations. A swapping gate in a two-spin system exchanges the degenerate states |+,-> and |-,+>. In NMR, this is achieved turning on and off the spin-spin interaction b=ΔE that splits the energy levels and induces an oscillation with a natural frequency ΔE/\hbar. Interaction of strength \hbar/τ_{SE}, with an environment of neighboring spins, degrades this oscillation within a decoherence time scale τ_ϕ. While the experimental frequency ωand decoherence time τ_ϕ were expected to be roughly pro…
Strong electron and spin correlations are studied in parallel-coupled double quantum dots with interdot spin superexchange $J$. In the Kondo regime with {\it}{degenerate} dot energy levels, a coherent transport occurs at zero temperature, where two entangled (bonding and antibonding) resonances are formed near the Fermi energy. When increasing $J$ or the dot-lead parallel-coupling \QTR{it}{asymmetry} ratio $Γ_{2}/Γ_{1}$, a swap between two entangled resonances occurs and the line shapes of the linear conductance are interchanged. The zero-bias differential conductance shows a peak at the criti…
The inversion symmetry breaking at the interface between different materials generates a strong interfacial spin-orbit coupling (ISOC) that may influence the spin and charge transport in hybrid structures. Here we use a simple analytically solvable model to study in the ballistic approximation various spin transport phenomena induced by ISOC in a bilayer metallic system. In this model a non-equilibrium steady state carrying a spin current is created by applying a spin dependent bias across the metallic junction. Physical observables are then calculated using the scattering matrix approach. In …
We have observed an environmentally induced quantum dynamical phase transition in the dynamics of a two spin experimental swapping gate [J. Chem. Phys. 124, 194507 (2006)]. There, the exchange of the coupled states |+,-> and ,+> gives an oscillation with a Rabi frecuency b/$\hbar$ (the spins coupling). The interaction, $\hbar$/tSE with a spin-bath degrades the oscillation with a characteristic decoherence time. We showed that the swapping regime is restricted only to b\tSE>$hbar$. However, beyond a critical interaction with the environment the swapping freezes and the system enters to a Quantu…
In a two dimensional electron gas with Rashba spin-orbit coupling, the external electric field may cause a spin Hall current in the direction perpendicular to the electric field. This effect was called the intrinsic spin Hall effect. In this paper, we investigate the influences of spin accumulation on this intrinsic spin Hall effect. We show that due to the existence of boundaries in a real sample, the spin Hall current generated by the intrinsic spin Hall effect will cause spin accumulation near the edges of the sample, and in the presence of spin accumulation, the spin Hall conductivity will…
In these lecture notes we study the disordered two-dimensional electron gas in the presence of Rashba spin-orbit coupling, by using the Keldysh non-equilibrium Green function technique. We describe the effects of the spin-orbit coupling in terms of a SU(2) gauge field and derive a generalized Boltzmann equation for the charge and spin distribution functions. We then apply the formalism to discuss the spin Hall and the inverse spin galvanic (Edelstein) effects. Successively we show how to include, within the generalized Boltzmann equation, the side jump, the skew scattering and the spin current…
Layered 2D van der Waals materials, such as transition metal dichalcogenides, are promising for nanoscale spintronic and optoelectronic applications. Harnessing their full potential requires understanding both intrinsic transport and the dynamics of optically excited spin and charge carriers -- particularly the transition between excited spin polarization and the conduction band's intrinsic spin texture. Here, we investigate the spin polarization of the conduction bands of bulk WSe$_2$ using static and time-resolved spin-resolved photoemission spectroscopy, complemented by photocurrent calcula…
We derive the spin continuity equation by using the Noether's theorem. A new type of spin-tensor Hall current is found in the continuity equation. The spin-tensor Hall current is originating from the coupling of the spin-tensor and the momentum. The intrinsic spin Hall effect in the two-dimensional fermion model with the spin-orbit coupling and spin-tensor-momentum coupling is studied. The total spin Hall conductivity with the presence of the spin-tensor Hall current is calculated. The numerical results indicate that the total spin Hall conductivity is enhanced by the contribution of the spin-…
Similar to the Landauer electric dipole created around an impurity by the electric current, a spin polarized cloud of electrons can be induced by the intrinsic spin-Hall effect near a spin independent elastic scatterer. It is shown that in the ballistic range around the impurity, such a cloud appears in the case of Rashba spin-orbit interaction, even though the bulk spin-Hall current is absent.
We study intrinsic spin Hall effect in p-type GaAs quantum well structure described by Luttinger Hamiltonian and a Rashba spin-orbit coupling arising from the structural inversion symmetry breaking. The Rashba term induces an energy level crossing in the lowest heavy hole subband, which gives rise to a resonant spin Hall conductance. The resonance may be used to identify the intrinsic spin Hall effect in experiments.
We derive an intrinsic contribution to the non-adiabatic spin torque for non-uniform magnetic textures. It differs from previously considered contributions in several ways and can be the dominant contribution in some models. It does not depend on the change in occupation of the electron states due to the current flow but rather is due to the perturbation of the electronic states when an electric field is applied. Therefore it should be viewed as electric-field-induced rather than current-induced. Unlike previously reported non-adiabatic spin torques, it does not originate from extrinsic relaxa…
We report the observation of the crossover between the extrinsic and intrinsic spin Hall effect induced by alloying. We found that the spin Hall angle, the ratio of the spin Hall conductivity to the electric conductivity, changes drastically by tuning the composition of Au-Cu alloy. The spin Hall angle changes the sign only in a limited range of the Cu concentration due to the extrinsic skew scattering, while the intrinsic contribution becomes dominant with increasing the Cu concentration. This observation provides essential information for fundamental understanding of spin-orbit physics.
The spin-orbit coupling may generate spin transverse force on moving electron spin, which gives a heuristic picture for the quantum transverse transport of electron. A relation between the spin and anomalous Hall conductance and spin force was established, and applied to several systems. It was predicted that the sign change of anomalous Hall conductance can occur in diluted magnetic semiconductors of narrow band and can be applied to identify intrinsic mechanism experimentally.
We investigate the spin Hall effect (SHE) in a wide class of spin-orbit coupling systems by using spin force picture. We derive the general relation equation between spin force and spin current and show that the longitudinal force component can induce a spin Hall current, from which we reproduce the spin Hall conductivity obtained previously using Kubo's formula. This simple spin force picture gives a clear and intuitive explanation for SHE.
A brief review is given on the spin Hall effect, where an external electric field induces a transverse spin current. It has been recognized over 30 years that such effect occurs due to impurities in the presence of spin-orbit coupling. Meanwhile, it was proposed recently that there is also an intrinsic contribution for this effect. We explain the mechanism for this intrinsic spin Hall effect. We also discuss recent experimental observations of the spin Hall effect.
In order to describe correctly the interplay of extrinsic and intrinsic spin-orbit mechanisms to the spin Hall effect, it is necessary to consider different sources of spin relaxation. We take into account the spin relaxation time $τ_{DP}$ due to the Dyakonov-Perel mechanism as well as the Elliot-Yafet spin-relaxation time $τ_s$ due to the spin-orbit scattering from impurities. The total spin Hall conductivity depends crucially on the ratio $τ_s /τ_{DP}$.
First-principles calculations of the essential spin-orbit and spin relaxation properties of phosphorene are performed. Intrinsic spin-orbit coupling induces spin mixing with the probability of $b^2 \approx 10^{-4}$, exhibiting a large anisotropy, following the anisotropic crystalline structure of phosphorene. For realistic values of the momentum relaxation times, the intrinsic (Elliott--Yafet) spin relaxation times are hundreds of picoseconds to nanoseconds. Applying a transverse electric field (simulating gating and substrates) generates extrinsic $C_{2v}$ symmetric spin-orbit fields in phosp…
First principles calculations show that electric fields applied to ferromagnets generate spin currents flowing perpendicularly to the electric field. Reduced symmetry in these ferromagnets enables a wide variety of such spin currents. However, the total spin current is approximately the sum of a magnetization-independent spin Hall current and an anisotropic spin anomalous Hall current. Intrinsic spin currents are not subject to dephasing, enabling their spin polarizations to be misaligned with the magnetization, which enables the magnetization-independent spin Hall effect. The spin Hall conduc…
A semi-classical description of the intrinsic spin-Hall effect (SHE) is presented which is relevant for a wide class of systems. A heuristic model for the SHE is developed, starting with a fully quantum mechanical treatment, from which we construct an intuitive expression for the spin-Hall current and conductivity. Our method makes transparent the physical mechanism which drives the effect, and unifies the SHE across several spintronic and optical systems. Finally, we propose an analogous effect in bilayer graphene.
Intrinsic contribution to the spin Hall effect in a two-dimensional silicene is considered theoretically within the linear response theory and Green function formalism. When an external voltage normal to the silicene plane is applied, the spin Hall conductivity is shown to reveal a transition from the spin Hall insulator phase at low voltages to the conventional insulator phase at higher voltages. This transition resembles recently reported phase transition in a bilayer graphene. The spin-orbit interaction responsible for this transition in silicene is much stronger than in graphene, which sho…
We have investigated spin Hall effects in 4$d$ and 5$d$ transition metals, Nb, Ta, Mo, Pd and Pt, by incorporating the spin absorption method in the lateral spin valve structure; where large spin current preferably relaxes into the transition metals, exhibiting strong spin-orbit interactions. Thereby nonlocal spin valve measurements enable us to evaluate their spin Hall conductivities. The sign of the spin Hall conductivity changes systematically depending on the number of $d$ electrons. This tendency is in good agreement with the recent theoretical calculation based on the intrinsic spin Hall…
We investigate the characteristic spin dynamics corresponding to semiconductor quantum dots within the multiband envelope function approximation (EFA). By numerically solving an $8\times8$ $k\cdot p$ Hamiltonian we treat systems based on different III-V semiconductor materials.It is shown that, even in the absence of an applied magnetic field, these systems show intrinsic spin dynamics governed by intraband and interband transitions leading to characteristic spin frequencies ranging from the THz to optical frequencies.
We present a unified theory of charge and spin transport using quaternionic formalism. It is shown that both charge current and spin currents can be combined together to form a quaternionic current. The scalar and vector part of quaternionic currents correspond to charge and spin current respectively. We formulate a unitarity condition on the scattering matrix for quaternionic current conservation. It is shown that in presence of spin flip interactions a weaker quaternionic unitarity condition implying charge flux conservation but spin flux non conservation is valid. Using this unified theory …
The intrinsic spin Hall conductance shows rich sign changes by applying a perpendicular magnetic field in a two-dimensional hole gas. Especially, a notable sign changes can be achieved by adjusting the characteristic length of the Rashba coupling and hole density at moderate magnetic fields. This sign issue may be easily realized in experiments. The oscillations of the intrinsic spin Hall conductance as a function of 1/$B$ is nothing else but Shubnikov-de Haas oscillations, and the additional beatings can be quantitatively related to the value of the spin-orbit coupling parameter. The Zeeman s…
Intrinsic and extrinsic spin Hall effects are considered together on an equal theoretical footing for the Rashba spin-orbit coupling in two-dimensional (2D) electron and hole systems, using the diagrammatic method for calculating the spin Hall conductivity. Our analytic theory for the 2D holes shows the expected lowest-order additive result for the spin Hall conductivity. But, the 2D electrons manifest a very surprising result, exhibiting a non-analyticity in the Rashba coupling strength $α$ where the strictly extrinsic spin Hall conductivity (for $α= 0$) cannot be recovered from the $α\to 0$ …
The prediction of intrinsic spin Hall currents by Murakami \textit{et al.} and Sinova \textit{et al.} raised many questions about methods of detection and the effect of disorder. We focus on a contact between a Rashba type spin orbit coupled region with a normal two-dimensional electron gas and show that the spin Hall currents, though vanishing in the bulk of the sample, can be recovered from the edges. We also show that the current induced spin accumulation in the spin orbit coupled system diffuses into the normal region and contributes to the spin current in the leads.
Spin-polarized transport through quantum dots is analyzed theoretically in the cotunneling regime. It is shown that the zero-bias anomaly, found recently in the antiparallel configuration, can also exist in the case when one electrode is magnetic while the other one is nonmagnetic. Physical mechanism of the anomaly is also discussed. It is demonstrated that intrinsic spin relaxation in the dot has a significant influence on the zero-bias maximum in the differential conductance -- the anomaly becomes enhanced by weak spin-flip scattering in the dot and then disappears in the limit of fast spin …
We study intrinsic DC spin and valley Hall conductivity in doped ferromagnetic silicene in the presence of an electric filed applied perpendicular to silicene sheet. By calculating its energy spectrum and wavefunction and by making use of Kubo formalism, we obtain a general relation for the transverse Hall conductivity which can be used to obtain spin- and valley-Hall conductivity. Our results, in the zero limit of the exchange field, reduces to the previous results. Furthermore we discuss electrically tunable spin and valley polarized transport in ferromagnetic silicene and obtain the necessa…
In this article, the modified Kane-Mele Hamiltonian is derived for graphene with wedge disclination and spin orbit couplings (intrinsic and Rashba). The wedge disclination changes the flat lattice into the conical lattice and hence modifies the spin orbit couplings. The Hamiltonian is exactly solved for the intrinsic spin orbit interaction and perturbatively for the Rashba spin orbit interaction. It is shown that there exists the Kramer's degenerate midgap localized spin separated fluxon states around the defect. These zero energy spin separated states occur at the external magnetic flux value…
The Rashba spin-orbit coupling arising from structure inversion asymmetry couples spin and momentum degrees of freedom providing a suitable (and very intensively investigated) environment for spintronic effects and devices. Here we show that in the presence of strong disorder, non-homogeneity in the spin-orbit coupling gives rise to a finite spin Hall conductivity in contrast with the corresponding case of a homogeneous linear spin-orbit coupling. In particular, we examine the inhomogeneity arising from a striped structure for a two-dimensional electron gas, affecting both density and Rashba s…
The emergent induction of spiral magnets that was proposed [Jpn. J. Appl. Phys. 58, 120909 (2019)] and recently demonstrated [Nature 586, 232 (2020)] is shown to be further extended by a comprehensive treatment of the Rashba spin-orbit coupling and the electron spin relaxation that affect the underlying processes of spin-transfer torque and spinmotive force. Within adiabatic approximation, we show that the output voltages are widely altered intrinsically via the Rashba effect whereas extrinsically via the nonadiabatic correction due to the spin relaxation and sample disorder. The findings resp…
In 2005 Kane & Mele[C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005)], predicted that at sufficiently low energy, graphene exhibits a topological state of matter with an energy gap generated by the atomic spin-orbit interaction. However, this intrinsic gap has not been measured to this date. In this letter, we exploit the chirality of the low energy states to resolve this gap. We probe the spin states experimentally, by employing low temperature microwave excitation in a resistively detected electron spin resonance on graphene. The structure of the topological bands is reflected i…
Starting from a microscopic tight-binding model and using second order perturbation theory, we derive explicit expressions for the intrinsic and Rashba spin-orbit interaction induced gaps in the Dirac-like low-energy band structure of an isolated graphene sheet. The Rashba interaction parameter is first order in the atomic carbon spin-orbit coupling strength $ξ$ and first order in the external electric field $E$ perpendicular to the graphene plane, whereas the intrinsic spin-orbit interaction which survives at E=0 is second order in $ξ$. The spin-orbit terms in the low-energy effective Hamilto…
Current-induced magnetic switching of a single magnetic molecule attached to two ferromagnetic contacts is considered theoretically, with the main emphasis put on the role of intrinsic spin relaxation processes. It is shown that spin-polarized current can switch magnetic moment of the molecule, despite of the intrinsic spin relaxation in the molecule. The latter processes increase the threshold voltage (current) above which the switching takes place.
Spin Hall effect can be induced both by the extrinsic impurity scattering and by the intrinsic spin-orbit coupling in the electronic structure. The HgTe/CdTe quantum well has a quantum phase transition where the electronic structure changes from normal to inverted. We show that the intrinsic spin Hall effect of the conduction band vanishes on the normal side, while it is finite on the inverted side. This difference gives a direct mechanism to experimentally distinguish the intrinsic spin Hall effect from the extrinsic one.
The spin Hall angle in Pt is evaluated in Pt/NiFe bilayers by spin torque ferromagnetic resonance (ST-FMR) measurements, and is found to increase with increasing the NiFe thickness. To extract the intrinsic spin Hall angle in Pt by estimating the total spin current injected into NiFe from Pt, the NiFe thickness dependent measurements are performed and the spin diffusion in the NiFe layer is taken into account. The intrinsic spin Hall angle of Pt is determined to be 0.068 at room temperature, and is found to be almost constant in the temperature range 13 - 300 K.
We describe a new effect in semiconductor spintronics that leads to dissipationless spin-currents in paramagnetic spin-orbit coupled systems. We argue that in a high mobility two-dimensional electron system with substantial Rashba spin-orbit coupling, a spin-current that flows perpendicular to the charge current is intrinsic. In the usual case where both spin-orbit split bands are occupied, the spin-Hall conductivity has a universal value.
We obtain the exact one-spin intrinsic localized excitation in an anisotropic Heisenberg ferromagnetic spin chain in a constant/variable external magnetic field with Gilbert damping included. We also point out how an appropriate magnitude spin current term in a spin transfer nano-oscillator (STNO) can stabilize the tendency towards damping. Further, we show how this excitation can be sustained in a recently suggested PT-symmetric magnetic nanostructure. We also briefly consider more general spin excitations.
We consider spin Hall effect in a system of massless Dirac fermions in a graphene lattice. Two types of spin-orbit interaction, pertinent to the graphene lattice, are taken into account - the intrinsic and Rashba terms. Assuming perfect crystal lattice, we calculate the topological contribution to spin Hall conductivity. When both interactions are present, their interplay is shown to lead to some peculiarities in the dependence of spin Hall conductivity on the Fermi level.
