@Tatara2006; @Kajiwara2006; @Kimura2007; @Nakayama2013; @Chen2013]: an electric current (${\bf j}_e$) induces a spin current ${\bf j}_s = \theta_\textup{SH} {\bf j}_e \times \boldsymbol{\sigma}$, where $\theta_\textup{SH}$ is the spin Hall angle and $\boldsymbol{\sigma}$ is the spin of the conduction electron. Such induced spin current in turn generates an electric current whose direction is opposite to the original ${\bf j}_e$, and thus the spin Hall and inverse spin Hall effects increase the resistivity by a factor of $1+\theta_\textup{SH}^2$. However, in the case of a thin film in contact with a magnetic insulator, the spin current may be either reflected back, which would reduce the spin current in the film, or absorbed via spin transfer torques, which would preserve the spin current in the film [@Nakayama2013; @Chen2013]. The reflection is strongest when the magnetization direction of the insulator is parallel to the spin current, therefore the spin current is least when $\hat{\bf m}$ is parallel to $\hat{\bf z}\times \hat{\bf j}$, leading to the minimum resistivity as described in Eq. (1). Another model is based on the spin-dependent scattering and Rashba spin-orbit coupling (SOC) [@Zhang2014-2; @Grigoryan2014]. When the electron scatters off the magnetic interface, the resistivity for spin up and down relative to the direction 