  Nutation has been recognized as of great significance for spintronics; but
justifying its presence has proven to be a hard problem, since overdamping has
long been assumed to wash out its effects. In this paper we show that nutation
can be understood as emerging from a systematic expansion of a kernel that
describes the history of the interaction of a magnetic moment with a bath of
colored noise. The parameter of the expansion is the ratio of the colored noise
timescale to the precession period. In the process we obtain the Gilbert
damping from the same expansion. We recover the known results, when the
coefficients of the two terms are proportional to one another, in the white
noise limit; and show how colored noise leads to situations where this simple
relation breaks down, but what replaces it can be understood by the appropriate
generalization of the fluctuation--dissipation theorem. Numerical simulations
of the stochastic equations support the analytic approach. In particular we
find that the equilibration time is about an order of magnitude longer than the
timescale set by the colored noise for a wide range of values of the latter and
we can identify the presence of nutation in the non-uniform way the
magnetization approaches equilibrium.
