  We employ first-principles techniques tailored to properly describe
semiconductors (modified Becke-Johnson potential added to the
exchange-correlation functional), to obtain the electronic band structures of
both the zinc-blende and wurtzite phases of GaAs, GaSb, InAs, and InSb. We
extract the spin-orbit fields for the relevant valence and conduction bands at
zone center, by fitting the spin-splittings resulting from the lack of space
inversion symmetry of these bulk crystal structures, to known functional
forms---third-order polynomials. We also determine the orientations of the
spin-orbit vector fields (for conduction bands) and the average spins (valence
bands) in the momentum space. We describe the dependence of the spin-orbit
parameters on the cation and anion atomic weights. These results should be
useful for spin transport, spin relaxation, and spin optical orientation
modeling of semiconductor heterostructures, as well as for realistic studies of
semiconductor-based Majorana nanowires, for which accurate values of spin-orbit
couplings are needed.
