Thermal magnetization noise, damping fundamentals, and mode analysis: application to a thin film GMR sensor

Magnetization dynamic equations with thermal fluctuations are derived fundamentally for small amplitude oscillations. A tensor form of phenomenological damping occurs whose components reflect a general elliptical magnetization motion. This analysis implies that thermal energy and associated damping must be applied to independent normal modes of the system. As an example, this formalism is applied to a thin film magnetoresistance sensor to rind the eigenmodes for general nonuniform magnetization variations. Examples are given of both the various modes and the noise power spectra.