  Spin-dependent transport phenomena due to relativistic spin-orbit coupling
and broken space-inversion symmetry are often difficult to interpret
microscopically, in particular when occurring at surfaces or interfaces. Here
we present a theoretical and experimental study of spin-orbit torque and
unidirectional magnetoresistance in a model room-temperature ferromagnet NiMnSb
with inversion asymmetry in the bulk of this half-heusler crystal. Besides the
angular dependence on magnetization, the competition of Rashba and
Dresselhaus-like spin-orbit couplings results in the dependence of these
effects on the crystal direction of the applied electric field. The
phenomenology that we observe highlights potential inapplicability of commonly
considered approaches for interpreting experiments. We point out that, in
general, there is no direct link between the current-induced non-equilibrium
spin polarization inferred from the measured spin-orbit torque and the
unidirectional magnetiresistance. We also emphasize that the unidirectional
magnetoresistance has not only longitudinal but also transverse components in
the electric field -- current indices which complicates its separation from the
thermoelectric contributions to the detected signals in common experimental
techniques. We use the theoretical results to analyze our measurements of the
on-resonance and off-resonance mixing signals in microbar devices fabricated
from an epitaxial NiMnSb film along different crystal directions. Based on the
analysis we extract an experimental estimate of the unidirectional
magnetoresistance in NiMnSb.
