Charge–Spin Coupling at a Ferromagnet–Nonmagnet Interface

The topic of electrical spin injection from a ferromagnetic to a nonmagnetic material is presently attracting great interest and attention. A thermodynamic study of “spin injection” across a ferromagnetic–nonmagnetic material interface is presented. Using an entropy production calculation, the linear dynamic equations for interfacial transport of charge, heat, and spin magnetic moment are derived. A general equation for the fractional polarization of injected current is developed by matching boundary conditions at the interface. Polarization efficiency is sensitive to the intrinsic interface resistance, and to the resisivities and spin diffusion lengths of both materials. The physics of nonequilibrium spin diffusion across the interface is discussed, and the limiting case where “resistance mismatch” is important is identified. Example systems of interest are spin injection from a ferromagnetic metal to a nonmagnetic metal and from a ferromagnetic metal to a semiconductor. Charge–spin coupling and spin diffusion in one dimension, compared with higher dimension, are also discussed.