Spin Transfer from the point of view of the ferromagnetic degrees of freedom

Abstract

Spintronics is the generic term that describes magnetic systems coupled to an electric generator, taking into account the spin attached to the charge carriers. For this topical review of {\it Spin Caloritronics}, we focus our attention on the study of {\it irreversible processes} occuring in spintronic devices, that involve both the spins of the conduction electrons and the ferromagnetic degrees of freedom. The aim of this report is to clarify the nature of the different kinds of power dissipated in metallic ferromagnets contacted to an electric generator, and to exploit it in the framework of the theory of mesoscopic non-equilibrium thermodynamics. The expression of the internal power (i.e. the internal entropy production multiplied by the temperature) dissipated by a generic system connected to different reservoirs, allows the corresponding kinetic equations to be derived with the introduction of the relevant phenomenological kinetic coefficients. After derivation of the kinetic equations for the ferromagnetic degrees of freedom (i.e. the Landau-Lifshitz equation) and the derivation of the kinetic equations for the spin-accumulation effects (within a two channel model), the kinetic equations describing spin-transfer are obtained. Both spin-dependent relaxation (usual spin-accumulation) and spin-precession in quasi-ballistic regime (transverse spin-accumulation) are taken into account. The generalization of the Landau-Lifshitz equation to spin-accumulation is then performed with the introduction of two potential energy terms, that are experimentally accessible.