Theory of Spin Torque in a nanomagnet

TL;DR

This paper develops a comprehensive microscopic theory of spin torque in ultrasmall nanomagnets coupled to ferromagnetic electrodes, capturing key effects like tunneling magnetoresistance, magnetic relaxation, and current-induced magnetization dynamics.

Contribution

It introduces a unified model describing spin torque phenomena in nanomagnets, incorporating Coulomb blockade effects and spectral discretization, with a close analogy to the Landau-Lifshitz-Gilbert equation.

Findings

Multiple stable magnetic states can coexist under certain conditions.

Hysteresis effects lead to complex magnetic state dynamics.

Magnetoresistance measurements reveal non-equilibrium features.

Abstract

We present a complete theory of the spin torque phenomena in a ultrasmall nanomagnet coupled to non-collinear ferromagnetic electrodes through tunnelling junctions. This model system can be described by a simple microscopic model which captures many physical effects characteristic of spintronics: tunneling magneto resistance, 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 valves 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. Depending on the regime, the dynamic induced by the coupling to electrode 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 magneto-resistance can be used to provide additional information on the non-equilibrium peaks present in the nanomagnet spectroscopy experiments.