The field dependence of the thermal switching rate of a ferromagneticmaterial with uniaxial anisotropy was studied by solving the Fokker-Planckequation. We derived the analytical expression of the thermal switching rateusing 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 byreplacing the attempt frequency with the proper factor which is expressed bythe error function.
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