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Magnetoresistance has been one of the important phenomena in spintronics for a long time. Recently, a novel type of magnetoresistance called spin Hall magnetoresistance (SMR) has been observed in a bilayer system composed of a normal metal and a ferromagnetic insulator. While its qualitative behavior has been explained well by the semiclassical theory based on a mixing conductance [1], this theory could not describe temperature dependence of the SMR. In this talk, I present a microscopic theory [2,3] for SMR by formulating a spin conductance in terms of spin susceptibilities. We reveal that SMR is composed of static and dynamic parts; The static part originates from spin flip caused by an interfacial exchange coupling. On the other hand, the dynamic part, which is induced by the creation or annihilation of magnons, has an opposite sign from the static part. I also present the temperature dependence of SMR derived by our theory using the spin-wave approximation [2] and a quantum Monte Carlo simulation [3].

[1] Y. T. Chen, et al., Phys. Rev. B 87, 144411 (2013).
[2] T. Kato, Y. Ohnuma, and M. Matsuo, Phys. Rev. B 102, 094437 (2020).
[3] T. Ishikawa, M. Matsuo, and T. Kato, Phys. Rev. B 107, 054426 (2023).

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