Spin-torque effects in thermally assisted magnetization reversal: Method of statistical moments

TL;DR

This paper develops a statistical moments method to analyze thermal fluctuation effects on magnetization reversal in spin-torque devices, revealing new effects and dependencies on external conditions.

Contribution

It introduces a hierarchy of differential-recurrence relations for statistical moments to study thermally assisted spin-torque magnetization dynamics.

Findings

Thermal fluctuations significantly influence switching times and magnetization states.

Switching characteristics depend strongly on external magnetic field and spin polarization directions.

New spin-torque effects are identified across various temperature and current regimes.

Abstract

Thermal fluctuations of nanomagnets driven by spin-polarized currents are treated via the Landau-Lifshitz-Gilbert equation generalized to include both the random thermal noise field and the Slonczewski spin-transfer torque term. By averaging this stochastic (Langevin) equation over its realizations, the explicit infinite hierarchy of differential-recurrence relations for statistical moments (averaged spherical harmonics) is derived for arbitrary demagnetizing factors and magnetocrystalline anisotropy for the generic nanopillar model of a spin-torque device comprising two ferromagnetic strata representing the free and fixed layers and a nonmagnetic conducting spacer all sandwiched between two ohmic contacts. The influence of thermal fluctuations and spin-transfer torques on relevant switching characteristics, such as the stationary magnetization, the magnetization reversal time, etc., is calculated by solving the hierarchy for wide ranges of temperature, damping, external magnetic field, and spin-polarized current indicating new spin-torque effects in the thermally assisted magnetization reversal comprising several orders of magnitude. In particular, a pronounced dependence of the switching characteristics on the directions of the external magnetic field and the spin polarization exists.