Spin torque in a nanomagnet coupled to noncollinear ferromagnetic electrodes

Abstract

We present a detailed theory of the spin torque phenomena in an ultrasmall nanomagnet coupled to noncollinear ferromagnetic electrodes through tunneling junctions. This model system can be described by a simple microscopic model which captures many physical effects characteristic of spintronics: tunneling magnetoresistance, intrinsic and transport-induced magnetic relaxation, current-induced magnetization reversal, and spin accumulation. Treating on the same footing the magnetic and transport degrees of freedom, we arrive at a closed equation for the time evolution of the magnetization. This equation is very close to the Landau-Lifshitz-Gilbert equation used in spin valve structures. We discuss how the presence of the Coulomb blockade phenomena and the discretization of the one-body spectrum gives some additional features to the current-induced spin torque. The dynamic induced by the coupling to the electrodes can be viewed either as a spin torque or as a relaxation process. In addition to the possibility of stabilizing uniform spin precession states, we find that the system is highly hysteretic: up to three different magnetic states can be simultaneously stable in one region of the parameter space (magnetic field and bias voltage). We also discuss how the magnetoresistance can be used to provide additional information on the nonequilibrium peaks present in the nanomagnet spectroscopy experiments. This paper expands the results presented in a previous Letter [Phys. Rev. Lett. 94, 247206 (2005)].