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Register a new userThe spin Hall effect of Bi-Sb alloys driven by thermally excited Dirac-like electrons
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We have studied the charge to spin conversion in Bi$_{1-x}$Sb$_x$/CoFeB heterostructures. The spin Hall conductivity (SHC) of the sputter deposited heterostructures exhibits a high plateau at Bi-rich compositions, corresponding to the topological insulator phase, followed by a decrease of SHC for Sb-richer alloys, in agreement with the calculated intrinsic spin Hall effect of Bi$_{1-x}$Sb$_x$ alloy. The SHC increases with increasing thickness of the Bi$_{1-x}$Sb$_x$ alloy before it saturates, indicating that it is the bulk of the alloy that predominantly contributes to the generation of spin current; the topological surface states, if present in the films, play little role. Surprisingly, the SHC is found to increase with increasing temperature, following the trend of carrier density. These results suggest that the large SHC at room temperature, with a spin Hall efficiency exceeding 1 and an extremely large spin current mobility, is due to increased number of Dirac-like, thermally-excited electrons in the $L$ valley of the narrow gap Bi$_{1-x}$Sb$_x$ alloy.
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Spin-Hall conductivity (SHC) of fully relativistic (4x4 matrix) Dirac electrons is studied based on the Kubo formula aiming at possible application to bismuth and bismuth-antimony alloys. It is found that there are two distinct contributions to SHC, one only from the states near the Fermi energy and the other from all the occupied states. The latter remains even in the insulating state, i.e., when the chemical potential lies in the band-gap, and turns to have the same dependences on the chemical potential as the orbital susceptibility (diamagnetism), a surprising fact. These results are applied to bismuth-antimony alloys and the doping dependence of the SHC is proposed.
Spin-Hall conductivity $sigma_{{rm s}xy}$ and orbital susceptibility $chi$ are investigated for the anisotropic Wolff Hamiltonian, which is an effective Hamiltonian common to Dirac electrons in solids. It is found that, both for $sigma_{{rm s}xy}$ and $chi$, the effect of anisotropy appears only in the prefactors, which is given as the Gaussian curvature of the energy dispersion, and their functional forms are equivalent to those of the isotropic Wolff Hamiltonian. As a result, it is revealed that the relationship between the spin Hall conductivity and the orbital susceptibility in the insulating state, $sigma_{{rm s}xy}=(3mc^2/hbar e)chi$, which was firstly derived for the isotropic Wolff Hamiltonian, is also valid for the anisotropic Wolff Hamiltonian. Based on this theoretical finding, the magnitude of spin-Hall conductivity is estimated for bismuth and its alloys with antimony by that of orbital susceptibility, which has good correspondence between theory and experiments. The magnitude of spin-Hall conductivity turns out to be as large as $esigma_{{rm s}xy} sim 10^4 {Omega}^{-1}{rm cm}^{-1}$, which is about 100 times larger than that of Pt.
A strategy to drive skyrmion motion by a combination of an anisotropy gradient and spin Hall effect has recently been demonstrated. Here, we study the fundamental properties of this type of motion by combining micromagnetic simulations and a generalized Thiele equation. We find that the anisotropy gradient drives the skyrmion mainly along the direction perpendicular to the gradient, due to the conservative part of the torque. There is some slower motion along the direction parallel to the anisotropy gradient due to damping torque. When an appropriate spin Hall torque is added, the skyrmion velocity in the direction of the anisotropy gradient can be enhanced. This motion gives rise to acceleration of the skyrmion as this moves to regions of varying anisotropy. This phenomenon should be taken into account in experiments for the correct evaluation of the skyrmion velocity. We employ a Thiele like formalism and derive expressions for the velocity and the acceleration of the skyrmion that match very well with micromagnetic simulation results.
The experimental realization of the quantum anomalous Hall (QAH) effect in magnetically-doped (Bi, Sb)2Te3 films stands out as a landmark of modern condensed matter physics. However, ultra-low temperatures down to few tens of mK are needed to reach the quantization of Hall resistance, which is two orders of magnitude lower than the ferromagnetic phase transition temperature of the films. Here, we systematically study the band structure of V-doped (Bi, Sb)2Te3 thin films by angle-resolved photoemission spectroscopy (ARPES) and show unambiguously that the bulk valence band (BVB) maximum lies higher in energy than the surface state Dirac point. Our results demonstrate clear evidence that localization of BVB carriers plays an active role and can account for the temperature discrepancy.
Using circularly polarized light is an alternative to electronic ways for spin injection into materials. Spins are injected at a point of the light illumination, and then diffuse and spread radially due to the in-plane gradient of the spin density. This diffusion is converted into a circular charge current by the inverse spin Hall effect (ISHE). With shining the circularly polarized light at asymmetric parts of the sample, such as near edges, we detected this current as a helicity-dependent component in the photocurrent. We present a model for this ISHE based on the experimental results and the finite-element-method (FEM) simulation of the potential distribution induced by spin injection. Our model shows that the ISHE photocurrent generates an electric dipole at the edge of the sample, causing the measured charge current. The asymmetric light-illumination shown here is a simple way to inject and manipulate spins, opening up a door for novel spintronic devices.
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