  Transition metal monosilicides CoSi, CoGe, RhSi and RhGe in the chiral cubic
B20 structure have recently been found to host unconventional chiral fermions
beyond spin-1/2 WFs, and also exhibit exotic physical phenomena such as long
Fermi arc surface states, GME and quantized CPGE. Thus, exploring novel
spin-related transports in these unconventional chiral fermion semimetals may
open a new door for spintronics and spin caloritronics. In this paper, we study
the intrinsic SHE and SNE in the CoSi family based on ab initio relativistic
band structure calculations. First, we find that unlike nonchiral cubic metals,
the CoSi family have two independent nonzero SHC (SNC) tensor elements, namely,
$\sigma_{xy}^z$ and $\sigma_{xz}^y$ ($\alpha_{xy}^z$ and $\alpha_{xz}^y$)
instead of one element. Furthermore, the SHC ($\sigma_{xy}^z$ and
$\sigma_{xz}^y$) and helicity of the chiral structure are found to be
correlated, thus enabling SHE detection of structural helicity and also chiral
fermion chirality. Second, the intrinsic SHE and SNE in some of the CoSi family
are large. In particular, the calculated SHC of RhGe is as large as -140
($\hbar$/e)(S/cm). The calculated SNC of CoGe is also large, being -1.3
($\hbar$/e)(A/m K) at room temperature. Due to their semimetallic nature with
low electrical conductivity, these topological semimetals may have large spin
Hall and spin Nernst angles, being comparable to that of Pt metal. The SHC and
SNC of these compounds can also be increased by raising or lowering $\mu$ to,
e.g., the topological nodes, via either chemical doping or electrical gating.
Our findings thus indicate that the CoSi family not only would provide a
material platform for exploring novel spin-transports and exotic phenomena in
unconventional chiral fermion semimetals but also could be promising materials
for developing better spintronic and spin caloritronic devices.
