Magnetization reversal driven by spin injection: A diffusive spin-transfer effect

An out-of-equilibrium description of spin-transfer effect is proposed, based on the spin-injection mechanism occurring at the junction with a ferromagnet. The effect of spin injection is to locally modify, in the ferromagnetic configuration space, the density of magnetic moments. The corresponding gradient leads to a current-dependent diffusion process of magnetization. In order to describe this effect, the dynamics of the magnetization of a ferromagnetic single domain is reconsidered in the framework of the thermokinetic theory of mesoscopic systems. Assuming an Onsager cross coefficient that couples the currents, it is shown that spin-dependent electric transport leads to a correction of the Landau-Lifshitz-Gilbert equation of the ferromagnetic order parameter with supplementary diffusion terms. The consequence of spin injection in terms of the activation process of the ferromagnet is deduced, and the expressions of the effective energy barrier and of the critical current are derived. Magnetic fluctuations are calculated: the correction to the fluctuations is similar to that predicted for the activation. These predictions are consistent with the measurements of spin transfer obtained both in the activation regime and for ferromagnetic resonance under spin injection.