  We report a combined study of imaging the antiferromagnetic (AFM) spin
structure and measuring the spin Hall magnetoresistance (SMR) in epitaxial thin
films of the insulating non-collinear antiferromagnet SmFeO$_3$. X-ray magnetic
linear dichroism photoemission electron microscopy measurements reveal that the
AFM spins of the SmFeO$_3$(110) align in the plane of the film. Angularly
dependent magnetoresistance measurements show that SmFeO$_3$/Ta bilayers
exhibit a positive SMR, in contrast to the negative SMR expected in previously
studied collinear AFMs. The SMR amplitude increases linearly with increasing
external magnetic field at higher magnetic field, suggesting that field-induced
canting of the AFM spins plays an important role. In contrast, around the
coercive field, no detectable SMR signal is observed, indicating that SMR of
AFM and canting magnetization components cancel out. Below 50~K, the SMR
amplitude increases sizably by a factor of two as compared to room temperature,
which likely correlates with the long-range ordering of the Sm ions. Our
results show that the SMR is a sensitive technique for non-equilibrium spin
system of non-collinear AFM systems.
