Thermal switching rate of a ferromagnetic material with uniaxial anisotropy

TL;DR

This paper derives an analytical expression for the thermal switching rate of a uniaxial ferromagnetic material, demonstrating the applicability of Brown's formula in low barrier conditions through the mean first-passage time approach.

Contribution

It provides a new analytical formula for the thermal switching rate that extends Brown's formula to low barrier regimes using the Fokker-Planck equation.

Findings

Brown's formula remains valid in low barrier limits with modifications

Derived an explicit expression for the switching rate

Validated the approach using the mean first-passage time method

Abstract

The field dependence of the thermal switching rate of a ferromagnetic material with uniaxial anisotropy was studied by solving the Fokker-Planck equation. We derived the analytical expression of the thermal switching rate using the mean first-passage time approach, and found that Brown's formula [Phys. Rev. 130, 1677 (1963)] is applicable even in the low barrier limit by replacing the attempt frequency with the proper factor which is expressed by the error function.