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SrMnO$_{3}$ (SMO) is a magnetic insulator and predicted to exhibit amultiferroic phase upon straining. Strained films of SMO display a wide rangeof magnetic orders, ranging from G-type to C-and A-type, indicative ofcompeting 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 designingand positioning electrodes of different sizes on the film. The findingsdemonstrate antiferromagnetic domains with different magnetocrystallineanisotropies along with a ferromagnetic order, where the magnetization arisesfrom double exchange mediated ferromagnetic order and canted antiferromagneticmoments. Further, from a complete analysis of the SMR, a predominance ofantiferromagnetic domain sizes of 3.5 $\mu$m$^2$ is extracted. This workenhances the applicability of SMR in unraveling the richness of correlationeffects in complex oxides, as manifested by the detection of coexisting andcompeting ground states and lays the foundation for the study of magnontransport for different magnetoelectric based computing applications.

Probing spatial variation of magnetic order in strained SrMnO$_3$ thin films using Spin Hall Magnetoresistance