  We report the observation of the three-dimensional angular dependence of the
spin Hall magnetoresistance (SMR) in a bilayer of the epitaxial
antiferromagnetic insulator NiO(001) and the heavy metal Pt, without any
ferromagnetic element. The detected angular-dependent longitudinal and
transverse magnetoresistances are measured by rotating the sample in magnetic
fields up to 11 T, along three orthogonal planes (xy-, yz- and xz-rotation
planes, where the z-axis is orthogonal to the sample plane). The total
magnetoresistance has contributions arising from both the SMR and ordinary
magnetoresistance. The onset of the SMR signal occurs between 1 and 3 T and no
saturation is visible up to 11 T. The three-dimensional angular dependence of
the SMR can be explained by a model considering the reversible field-induced
redistribution of magnetostrictive antiferromagnetic S- and T-domains in the
NiO(001), stemming from the competition between the Zeeman energy and the
elastic clamping effect of the non-magnetic MgO substrate. From the observed
SMR ratio, we estimate the spin mixing conductance at the NiO/Pt interface to
be greater than $2\times10^{14}$ ${\Omega}^{-1}$ $m^{-2}$. Our results
demonstrate the possibility to electrically detect the N\'eel vector direction
in stable NiO(001) thin films, for rotations in the xy- and xz- planes.
Moreover, we show that a careful subtraction of the ordinary magnetoresistance
contribution is crucial to correctly estimate the amplitude of the SMR.
