Fluctuation theorem for spin transport at insulating ferromagnetic junctions

General relations for nonequilibrium spin transport at a magnetic junction between a normal metal and a ferromagnetic insulator are derived from the quantum fluctuation theorem. They include the extended Onsager relations between the spin conductance and the spin-current noise that hold for nonequilibrium states driven by an external current. These relations are valid for a general setup of spin Hall magnetoresistance (SMR) when the main contribution is due to the interfacial spin conductance. Unidirectional spin Hall magnetoresistance (UMR) in insulating ferromagnetic junctions can be understood in a similar way. Therefore, our work can provide a comprehensive viewpoint for understanding of SMR and UMR in insulating ferromagnetic junctions. Our result also predicts relations for higher-order coefficients with respect to the external current in terms of higher-order cumulants in a unified framework.