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The spin current can result in a spin-transfer torque in thenormal-metal(NM)|ferromagnetic-insulator(FMI) ornormal-metal(NM)|ferromagnetic-metal(FMM) bilayer. In the earlier study on thisissue, the spin relaxations were ignored or introduced phenomenologically. Inthis paper, considering the FMM or FMI with spin relaxations described by anon-Hermitian Hamiltonian, we derive an effective spin-transfer torque and aneffective spin mixing conductance in the non-Hermitian bilayer. The dependenceof the effective spin mixing conductance on the system parameters (such asinsulating gap, \textit{s-d} coupling, and layer thickness) as well as therelations between the real part and the imaginary part of the effective spinmixing conductance are given and discussed. We find that the effective spinmixing conductance can be enhanced in the non-Hermitian system. This providesus with the possibility to enhance the spin mixing conductance.

Effect of spin relaxations on the spin mixing conductances for a bilayer structure