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A detailed analysis of damping and noise due to a {\it sd}-interaction in athin ferromagnetic film sandwiched between two large normal metal layers iscarried out. The magnetization is shown to obey in general a non-local equationof motion which differs from the the Gilbert equation and is extended to thenon-adiabatic regime. To lowest order in the exchange interaction and in thelimit where the Gilbert equation applies, we show that the damping term isenhanced due to interfacial effects but it also shows oscillations as afunction of the film thickness. The noise calculation is however carried out toall orders in the exchange coupling constant. The ellipticity of the precessionof the magnetization is taken into account. The damping is shown to have aGilbert form only in the adiabatic limit while the relaxation time becomesstrongly dependent on the geometry of the thin film. It is also shown that theinduced noise characteristic of sd-exchange is inherently colored in characterand depends on the symmetry of the Hamiltonian of the magnetization in thefilm. We show that the sd-noise can be represented in terms of an externalstochastic field which is white only in the adiabatic regime. The temperatureis also renormalized by the spin accumulation in the system. For largeintra-atomic exchange interactions, the Gilbert-Brown equation is no longervalid

Fluctuations of the magnetization in thin films due to conduction electrons