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We study the origin of the strong spin Hall effect (SHE) in a recentlydiscovered family of Weyl semimetals, LaAl$X$ ($X$=Si, Ge) via afirst-principles approach with maximally localized Wannier functions. We showthat the strong intrinsic SHE in LaAl$X$ originates from the multiple slightanticrossings of nodal lines and points near $E_F$ due to their high mirrorsymmetry and large spin-orbit interaction. It is further found that bothelectrical and thermal means can enhance the spin Hall conductivity($\sigma_{SH}$). However, the former also increases the electrical conductivity($\sigma_{c}$), while the latter decreases it. As a result, the independenttuning of $\sigma_{SH}$ and $\sigma_{c}$ by thermal means can enhance the spinHall angle (proportional to $\frac{\sigma_{SH}}{\sigma_{c}}$), a figure ofmerit of charge-to-spin current interconversion of spin-orbit torque devices.The underlying physics of such independent changes of the spin Hall andelectrical conductivity by thermal means is revealed through the band-resolvedand $k$-resolved spin Berry curvature. Our finding offers a new way in thesearch of high SHA materials for room-temperature spin-orbitronicsapplications.

Origin and Large Enhancement of Large Spin Hall Angle in Weyl Semimetals LaAl$X$ ($X$=Si, Ge)