  Recent experimental results have pushed the limits of magnetization dynamics
to pico- and femtosecond timescales. This ultra-fast spin dynamics occurs in
extreme conditions of strong and rapidly varying fields and high temperatures.
This situation requires new description of magnetization dynamics, even on a
phenomenological level of the atomistic Landau-Lifshitz-Gilbert equation,
taking into account that the correlation time for electron system could be of
the order of the inverse characteristic spin frequency. For this case we
introduce the thermodynamically correct phenomenological approach for spin
dynamics based on the Landau-Lifshitz-Miyasaki-Seki equation. The influence of
the noise correlation time on longitudinal and transverse magnetization
relaxation is investigated. We also demonstrate the effect of the noise
correlation time on demagnetisation rate of different materials during
laser-induced dynamics.
