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

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

Geometric phases in a scattering process

The study of geometric phase in quantum mechanics has so far be confined to discrete (or continuous) spectra and trace preserving evolutions. Consider only the transmission channel, a scattering process with internal degrees of freedom is neither a discrete spectrum problem nor a trace preserving process. We explore the geometric phase in a scattering process taking only the transmission process into account. We find that the geometric phase can be calculated by the some method as in an unitary evolution. The interference visibility depends on the transmission amplitude. The dependence of the geometric phase on the barrier strength and the spin-spin coupling constant is also presented and discussed.Comment: 4 pages, 5 figure