  We have studied the charge to spin conversion in Bi$_{1-x}$Sb$_x$/CoFeB
heterostructures. The spin Hall conductivity (SHC) of the sputter deposited
heterostructures exhibits a high plateau at Bi-rich compositions, corresponding
to the topological insulator phase, followed by a decrease of SHC for Sb-richer
alloys, in agreement with the calculated intrinsic spin Hall effect of
Bi$_{1-x}$Sb$_x$ alloy. The SHC increases with increasing thickness of the
Bi$_{1-x}$Sb$_x$ alloy before it saturates, indicating that it is the bulk of
the alloy that predominantly contributes to the generation of spin current; the
topological surface states, if present in the films, play little role.
Surprisingly, the SHC is found to increase with increasing temperature,
following the trend of carrier density. These results suggest that the large
SHC at room temperature, with a spin Hall efficiency exceeding 1 and an
extremely large spin current mobility, is due to increased number of
Dirac-like, thermally-excited electrons in the $L$ valley of the narrow gap
Bi$_{1-x}$Sb$_x$ alloy.
