Origin and enhancement of the spin Hall angle in the Weyl semimetals LaAlSi and LaAlGe
Truman Ng, Yong Zheng Luo, Jiaren Yuan, Yihong Wu, Hyunsoo Yang, Lei Shen
Abstract
We study the origin of the strong spin Hall effect (SHE) in a recently discovered family of Weyl semimetals, $\mathrm{LaAl}X$ ($X$ = Si, Ge) via first-principles with maximally localized Wannier functions. We show that the strong intrinsic spin Hall effect in $\mathrm{LaAl}X$ originates from the multiple slight anticrossings of nodal lines and points near to the Fermi energy due to their high-mirror symmetry and large spin-orbit interaction. It is further found that hole doping and increasing the temperature can enhance the spin Hall conductivity (${\ensuremath{\sigma}}_{\mathrm{SH}}$). However, the former also increases the electrical conductivity (${\ensuremath{\sigma}}_{c}$), while the latter decreases it. As a result, the independent tuning of ${\ensuremath{\sigma}}_{\mathrm{SH}}$ and ${\ensuremath{\sigma}}_{c}$ by increasing the temperature can enhance the spin Hall angle (proportional to $\frac{{\ensuremath{\sigma}}_{\mathrm{SH}}}{{\ensuremath{\sigma}}_{c}}$), a figure of merit of charge-to-spin current interconversion of spin-orbit torque devices. The underlying physics of such independent changes of the spin Hall and electrical conductivities by thermal means is revealed through the band-resolved and $k$-resolved spin Berry curvature. Our finding offers a way in the search of high spin Hall angle materials for room temperature spin-orbitronics applications.