Thermal switching rate of a ferromagnetic material with uniaxial anisotropy

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.