  The effect of thermal fluctuations on a thin film magnetoresistive element
has been calculated. The technique involves adding to the basic spin dynamics a
general form of interaction with a thermal bath. For a general anisotropic
magnetic system the resulting equation can be written as a Langevin equation
for a harmonic oscillator. Our approach predicts two times smaller noise power
at low frequencies than the conventional stochastic Landau-Lifshitz-Gilbert
equation. It is shown that equivalent results can be obtained by introducing a
tensor phenomenological damping term to the gyromagnetic dynamics driven by a
thermal fluctuating field.
