Spin-torque switching: Fokker-Planck rate calculation

TL;DR

This paper introduces a novel Fokker-Planck approach to accurately calculate spin-torque induced magnetization switching rates, revealing that current increases effective temperature rather than lowering energy barriers, aligning well with experimental data.

Contribution

It extends Kramers' reaction rate theory to include spin-torque effects via a Fokker-Planck equation, enabling efficient calculation of switching rates and noise in spin-torque phenomena.

Findings

Spin-torque increases the effective spin temperature, not the energy barrier.

The method accurately predicts switching rates consistent with experiments.

It enables calculation of magnetic noise in spin valve read heads.

Abstract

We describe a new approach to understanding and calculating magnetization switching rates and noise in the recently observed phenomenon of "spin-torque switching". In this phenomenon, which has possible applications to information storage, a large current passing from a pinned ferromagnetic (FM) layer to a free FM layer switches the free layer. Our main result is that the spin-torque effect increases the Arrhenius factor $\exp(-E/kT)$ in the switching rate, not by lowering the barrier $E$, but by raising the effective spin temperature $T$. To calculate this effect quantitatively, we extend Kramers' 1940 treatment of reaction rates, deriving and solving a Fokker-Planck equation for the energy distribution including a current-induced spin torque of the Slonczewski type. This method can be used to calculate slow switching rates without long-time simulations; in this Letter we calculate rates for telegraph noise that are in good qualitative agreement with recent experiments. The method also allows the calculation of current-induced magnetic noise in CPP (current perpendicular to plane) spin valve read heads.