Thoeretical Study on Anomalous Spin-Hall and Magnetic Spin-Hall Effect Induced by Anisotropic Spin-flip Scattering on Ferromagnets

Abstract

Efficient spin generation methods like spin Hall effect (SHE) are being explored for the realization of next-generation spintronics devices[1]. SHE has been studied mainly in non-magnetic materials. However, because of the recent discoveries of various novel and promising effects in magnetic materials, such as anomalous spin-Hall effect (ASHE)[2,3], magnetic spin-Hall effect (MSHE)[4,5], and the spin-current driven by anisotropic magnetoresistance (AMR)[2,6], the spin-currents in magnetic materials have attracted much attention both from fundamental and applied viewpoints. Although the ASHE was initially thought to be a spin current driven by the anomalous Hall effect (AHE), some experimental results show an unaccountable spin current contribution that cannot be explained by AHE alone, and this is still an open question[7]. The theoretical studies of MSHE have so far assumed spin-independent scattering and focused largely on antiferromagnets. In ferromagnetic materials, the spin-dependent scattering can play an important role, however. In this study, we investigate the spin-dependent scattering mechanisms of ASHE and MSHE by using a microscopic model that assumes s-d scattering in 3d ferromagnetic metal (FM). The electrons in FM are described within the framework of the impurity Anderson model with spin splitting and spin-orbit coupling for 3d orbitals[8]. The spin-conductivities are calculated by using Kubo formula. We obtained both contributions of ASHE and MSHE (Fig.1) and showed that these phenomena are caused by anisotropic spin-flip scattering (Fig. 2). In particular, we found this mechanism of ASHE is different from that of conventional extrinsic SHE such as skew-scattering and side-jump. In the conference, we will present a complete expression of the magnetization direction dependence of these phenomena. In addition, we will discuss the effect of the crystal-field splitting.