  Metallic ferromagnets subjected to a temperature gradient exhibit a magnonic
drag of the electric current. We address this problem by solving a stochastic
Landau-Lifshitz equation to calculate the magnon-drag thermopower. The
long-wavelength magnetic dynamics result in two contributions to the
electromotive force acting on electrons: (1) An adiabatic Berry-phase force
related to the solid angle subtended by the magnetic precession and (2) a
dissipative correction thereof, which is rooted microscopically in the
spin-dephasing scattering. The first contribution results in a net force
pushing the electrons towards the hot side, while the second contribution drags
electrons towards the cold side, i.e., in the direction of the magnonic drift.
The ratio between the two forces is proportional to the ratio between the
Gilbert damping coefficient $\alpha$ and the coefficient $\beta$ parametrizing
the dissipative contribution to the electromotive force.
