We have theoretically investigated the spin Hall magnetoresistance (SMR) and Rashba-Edelstein magnetoresistance (REMR), mediated by spin currents, in a ferrimagnetic insulator/nonmagnetic metal/heavy metal system in the diffusive regime. The magnitude of both SMR and REMR decreases with increasing thickness of the interlayer because of the current shunting effect and the reduction in spin accumulation across the interlayer. The latter contribution is due to driving a spin current and persists even in the absence of spin relaxation, which is essential for understanding the magnetoresistance ratio in trilayer structures. © 2017 The Japan Society of Applied Physics M agnetoresistance effects are important for applications in sensor and memory devices and for investigation of spin-dependent transport. [1][2][3] Recently, a new type of magnetoresistance has been demonstrated, in which a spin current generated via spin-orbit coupling from an applied charge current plays a central role. [4][5][6][7][8][9][10][11][12] The generated spin current interacts with magnetization and magnetic field and changes its magnitude. 6,8,11,13) When the spin current is converted back to a charge current by spin-orbit coupling, 14,15) the spin-current transport modulates the conductivity of the system, and then gives rise to magnetoresistance. This spin-current-induced magnetoresistance is now recognized as an indispensable tool for investigating the spin transport in ferromagnetic material=metal heterostructures. [16][17][18][19] The spin Hall magnetoresistance (SMR) refers to the resistance change due to the spin current generated by the spin Hall effect (SHE), which interacts with a ferromagnetic material. 4,6) Typically in materials consisting of heavy metals such as Pt and W, 4,9) a spin current is induced by an applied charge current, j c , due to the SHE. This spin current propagates in the material and forms spin accumulation, s , around the system edges. 20) When s acts on a ferromagnetic material, it exerts spin transfer torque on the magnetization m, which is given by 13)Here, the spin current is defined to be positive when it flows out of the F layer, and e > 0, G r , m, and s j interface respectively denote the elementary charge, the real part of the mixing conductance per unit area, and the magnetization unit vector, the spin accumulation at the interface. Since j STT s is absorbed by the magnetization, the resultant spin accumulation s decreases, which results in the reduction in backflow spin current and thus the additional charge current due to the SHE (Fig. 1). As j STT s depends on the magnetization direction, the spin-current absorption finally appears as a magnetoresistance effect, under which the total conductivity σ shows a different dependence on m from the conventional anisotropic magnetoresistance, 6) i.e.,where n, σ 0 , and Δσ SMR respectively denote the unit vector normal to the junction interface and the conductivities insensitive and sensitive to the magnetization. In the context of SMR research, an interla...