Normal metal (N) interfaces is the so-called spin mixing conductance that governs the absorbance of a transverse spin current and generation of spin transfer torque. The spin-mixing conductance is a purely non-relativistic concept, while there is mounting evidence that spin-orbit interaction at interfaces is important (such as spin-flip at interface, interface spin-orbit torques). Here we address the effective spin mixing conductance for the metal–ferromagnetic insulator interfaces and magnetic tunnel junctions by first principles calculations. We predict an effective spin mixing conductance for metal–ferromagnetic insulator interfaces that are anisotropic in the presence of spin-orbit coupling, which indicates that the spin pumping and its relate spin transfer torques can be turned with spin orbit interaction.