Spin accumulation in a 2D electron gas with Rashba spin-orbit interaction subject to an electric field can take place without bulk spin currents (edge spin Hall effect). This is demonstrated for the collisional regime using the non-equilibrium distribution function determined from the standard Boltzmann equation. Spin accumulation originates from interference of incident and reflected electron waves at the sample boundary.
Spin accumulation generated by the anomalous Hall effects (AHE) in mesoscopic ferromagnetic Ni81Fe19 (permalloy or Py) films is detected electrically by a nonlocal method. The reciprocal phenomenon, inverse spin Hall effects (ISHE), can also be generated and detected all-electrically in the same structure. For accurate quantitative analysis, a series of nonlocal AHE/ISHE structures and supplementary structures are fabricated on each sample substrate to account for statistical variations and to accurately determine all essential physical parameters in-situ. By exploring Py thicknesses of 4 nm, …
The Kirchhoff-Helmholtz principle of least heat dissipation is applied in order to derive the stationary state of the spin-Hall effect. Spin-accumulation due to spin-orbit interaction, spin-flip relaxation, and electrostatic interaction due to charge accumulation are treated on an equal footing. A nonlinear differential equation is derived, that describes both surface and bulk currents and spin-dependent chemical potentials. It is shown that if the ratio of the spin-flip relaxation length over the Debye-Fermi length is small, the stationary state is defined by a linear spin-accumulation potent…
A variational approach is used in order to study the stationary states of Hall devices. Charge accumulation, electric potentials and electric currents are investigated on the basis of the Kirchhoff-Helmholtz principle of least heat dissipation. A simple expression for the state of minimum power dissipated -- that corresponds to zero transverse current and harmonic chemical potential -- is derived. It is shown that a longitudinal surface current proportional to the charge accumulation is flowing near the edges of the device. Charge accumulation and surface currents define a boundary layer over …
Intrinsic spin-Hall accumulation in honeycomb lattices: Band structure effects
用Landauer-Keldysh方法计算了二维蜂窝晶格上的局域自旋和电荷密度。通过经验紧束缚方法，我们展示了如何现实的能带结构可以带入LKF。取Bi（111）表面，其上存在强表面态和Rashba自旋轨道耦合[Phys. Rev. Lett. 93，046403（2004）]，作为数值示例，我们在其上示出了典型的本征自旋霍尔累积（ISHA）图案。随后分析了双端纳米结构样品中自旋和电荷输运的费米能量依赖性。通过改变E_{F}，我们表明，ISHA模式是近各向同性（自由电子类），只有当E_{F}是接近带底，是敏感/不敏感的E_{F}的低/高的偏压制度与这样的E_{F}。当E_{F}远离能带底部时，能带结构效应因此进入ISHA图案并且输运方向变得显著。
We study the low temperature conductivity of the electron accumulation layer induced by the very strong electric field at the surface of $\text{SrTiO}_3$ sample. Due to the strongly nonlinear lattice dielectric response, the three-dimensional density of electrons $n(x)$ in such a layer decays with the distance from the surface $x$ very slowly as $n(x) \propto 1/x^{12/7}$. We show that when the mobility is limited by the surface scattering the contribution of such a tail to the conductivity diverges at large $x$ because of growing time electrons need to reach the surface. We explore truncation …
The characterization of the stationary states in the spin-Hall effect is discussed within the framework of the phenomenological two spin-channel model. It is shown that two different definitions of the stationary states can be applied in the spin-Hall effect, leading to two different types of state in the bulk: zero transverse spin-current or non-zero pure spin-current. This difference is due to the treatment of the region near the edges, in which electric charge accumulation occurs. The screening equations that describe the accumulation of electric charges due to spin-orbit coupling are deriv…
We report a novel mechanism for the electrical injection and detection of out-of-plane spin accumulation via the anomalous spin Hall effect (ASHE), where the direction of the spin accumulation can be controlled by manipulating the magnetization of the ferromagnet. This mechanism is distinct from the spin Hall effect (SHE), where the spin accumulation is created along a fixed direction parallel to an interface. We demonstrate this unique property of the ASHE in nanowires made of permalloy (Py), to inject and detect out-of-plane spin accumulation in a magnetic insulator, yttrium iron garnet (YIG…
Charge-to-spin conversion in inhomogeneous systems is studied theoretically. We consider free electrons subject to impurities with spin-orbit interaction and with spatially modulated distribution, and calculate spin accumulation and spin current induced by an external electric field. It is found that the spin accumulation is induced by the vorticity of electron flow through the side-jump and skew-scattering processes, and the differences of the two processes are discussed. The results can be put in a form of generalized spin diffusion equation with a spin source term given by the divergence of…
In this work, we study the spin Hall effect and Rashba-Edelstein effect of a 2D Weyl fermion system in the clean limit using the Kubo formalism. Spin transport is solely due to the spin-torque current in this strongly spin-orbit coupled (SOC) system, and chiral spin-flip scattering off non-SOC scalar impurities, with potential strength $V$ and size $a$, gives rise to a skew-scattering mechanism for the spin Hall effect. The key result is that the resultant spin-Hall angle has a fixed sign, with $θ^{SH} \sim O \left(\tfrac{V^2}{v_F^2/a^2} (k_F a)^4 \right)$ being a strongly-dependent function o…
The stationary state of the spin-Hall bar is studied in the framework of a variational approach that includes non-equilibrium screening effects. The minimization of the power dissipated in the system is performed with taking into account the spin-flip relaxation and the global constrains due to the electric generator and global charge conservation. The calculation is performed in both approximations of negligible spin-flip scattering and strong spin-flip scattering. In both cases, the expressions of the spin-accumulation and the longitudinal and transverse pure spin-currents are derived analyt…
We present a formalism that simultaneously incorporates the effect of quantum tunneling and spin diffusion on spin Hall magnetoresistance observed in normal metal/ferromagnetic insulator bilayers (such as Pt/YIG) and normal metal/ferromagnetic metal bilayers (such as Pt/Co), in which the angle of magnetization influences the magnetoresistance of the normal metal. In the normal metal side the spin diffusion is known to affect the landscape of the spin accumulation caused by spin Hall effect and subsequently the magnetoresistance, while on the ferromagnet side the quantum tunneling effect is det…
Spin accumulation induced by spin-orbit coupling is experimentally quantified in stack with in-plane magnetic anisotropy via the contribution of spin accumulation to Hall resistances. Using a biasing direct current the spin accumulation within the structure can be tuned, enabling quantification. Quantification shows the spin accumulation can be more than ten percentage of local magnetization, when the electric current is 1E11 A/m*m. The spin accumulation is dependent of the thickness of Ta layer, the trend agrees with that of spin Hall angle indicating the capability of Ta and Pt in generating…
We study the topological Hall effect in a diffusive ferromagnetic metal thin film by solving a Boltzmann transport equation in the presence of spin-flip scattering. A generalized spin diffusion equation is derived, which contains an additional source term associated with the gradient of the emergent magnetic field that arises, and its solution shows that spin accumulation may build up in the vicinity of the magnetic skyrmions. We show that the spin accumulation gives rise to a spin polarized diffusion current that in general suppresses that bulk topological Hall current. Only when the spin dif…
We report simultaneous transport and scanning microwave impedance microscopy to examine the correlation between transport quantization and filling of the bulk Landau levels in the quantum Hall regime in gated graphene devices. Surprisingly, a comparison of these measurements reveals that quantized transport typically occurs below the complete filling of bulk Landau levels, when the bulk is still conductive. This result points to a revised understanding of transport quantization when carriers are accumulated by gating. We discuss the implications on transport study of the quantum Hall effect in…
