  SrMnO$_{3}$ (SMO) is a magnetic insulator and predicted to exhibit a
multiferroic phase upon straining. Strained films of SMO display a wide range
of magnetic orders, ranging from G-type to C-and A-type, indicative of
competing magnetic interactions. The potential of spin Hall magnetoresistance
(SMR) is exploited as an electrical probe for detecting surface magnetic order,
to read surface magnetic moments in SMO and its spatial variation, by designing
and positioning electrodes of different sizes on the film. The findings
demonstrate antiferromagnetic domains with different magnetocrystalline
anisotropies along with a ferromagnetic order, where the magnetization arises
from double exchange mediated ferromagnetic order and canted antiferromagnetic
moments. Further, from a complete analysis of the SMR, a predominance of
antiferromagnetic domain sizes of 3.5 $\mu$m$^2$ is extracted. This work
enhances the applicability of SMR in unraveling the richness of correlation
effects in complex oxides, as manifested by the detection of coexisting and
competing ground states and lays the foundation for the study of magnon
transport for different magnetoelectric based computing applications.
