Thermal magnetization fluctuations in thin films and a new physical form for magnetization damping

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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.