  Damping of magnetization dynamics in a ferromagnetic metal is usually
characterized by the Gilbert parameter alpha. Recent calculations of this
quantity, using a formula due to Kambersky, find that it is infinite for a
perfect crystal owing to an intraband scattering term which is of third order
in the spin-orbit parameter xi This surprising result conflicts with recent
work by Costa and Muniz who study damping numerically by direct calculation of
the dynamical transverse spin susceptibility in the presence of spin-orbit
coupling. We resolve this inconsistency by following the Costa-Muniz approach
for a slightly simplified model where it is possible to calculate alpha
analytically. We show that to second order in the spin-orbit parameter xi one
retrieves the Kambersky result for alpha, but to higher order one does not
obtain any divergent intraband terms. The present work goes beyond that of
Costa and Muniz by pointing out the necessity of including the effect of
long-range Coulomb interaction in calculating damping for large xi. A direct
derivation of the Kambersky formula is given which shows clearly the
restriction of its validity to second order in xi so that no intraband
scattering terms appear. This restriction has an important effect on the
damping over a substantial range of impurity content and temperature. The
experimental situation is discussed.
