Spin-mixing conductances of metallic and half-metallic magnetic layers

The spin-mixing conductance of a thin ferromagnetic layer attached epitaxially to two semi-infinite non-magnetic metallic leads is formulated in terms of non-equilibrium Green's functions. The spin-mixing conductance is obtained as a response of the spin torque acting on the ferromagnet with respect to the spin accumulation in one of the leads, while the spin torque is defined as a time derivative of the spin magnetic moment. The equivalence of the derived formula with a previous expression of the Landauer-Buttiker scattering theory is sketched and an implementation within the ab initio tight-binding linear muffin-tin orbital method is briefly described. Applications are made for metallic Co- and Ni-based slabs embedded between Cu(111) leads and for half-metallic Co2MnSi films sandwiched by Cr(001) leads. The calculated results throw serious doubts on the general validity of two features: fast convergence of the spin-mixing conductance with increasing thickness of the magnetic layer and negligible values of the imaginary part of the spin-mixing conductance as compared to the real part.