  We study the origin of the strong spin Hall effect (SHE) in a recently
discovered family of Weyl semimetals, LaAl$X$ ($X$=Si, Ge) via a
first-principles approach with maximally localized Wannier functions. We show
that the strong intrinsic SHE in LaAl$X$ originates from the multiple slight
anticrossings of nodal lines and points near $E_F$ due to their high mirror
symmetry and large spin-orbit interaction. It is further found that both
electrical 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 independent
tuning of $\sigma_{SH}$ and $\sigma_{c}$ by thermal means can enhance the spin
Hall angle (proportional to $\frac{\sigma_{SH}}{\sigma_{c}}$), 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 conductivity by thermal means is revealed through the band-resolved
and $k$-resolved spin Berry curvature. Our finding offers a new way in the
search of high SHA materials for room-temperature spin-orbitronics
applications.
