  The magnetization dynamics of ferromagnets are often formulated in terms of
the Landau-Lifshitz-Gilbert (LLG) equation. The reactive part of this equation
describes the response of the magnetization in terms of effective fields,
whereas the dissipative part is parameterized by the Gilbert damping tensor. We
formulate a scattering theory for the magnetization dynamics and map this
description on the linearized LLG equation by attaching electric contacts to
the ferromagnet. The reactive part can then be expressed in terms of the static
scattering matrix. The dissipative contribution to the low-frequency
magnetization dynamics can be described as an adiabatic energy pumping process
to the electronic subsystem by the time-dependent magnetization. The Gilbert
damping tensor depends on the time derivative of the scattering matrix as a
function of the magnetization direction. By the fluctuation-dissipation
theorem, the fluctuations of the effective fields can also be formulated in
terms of the quasistatic scattering matrix. The theory is formulated for
general magnetization textures and worked out for monodomain precessions and
domain wall motions. We prove that the Gilbert damping from scattering theory
is identical to the result obtained by the Kubo formalism.
