  We investigate non-adiabatic effects on the magnon frequency in an
interacting system of localized spins and itinerant electrons. Including the
lowest order corrections to the adiabatic dynamics in an analytically solvable
model, applicable to simple ferromagnets like Fe, Co and Ni, we find that the
magnon frequency is renormalized by a geometrical torque arising from the
electronic spin Berry curvature. Comparison to exact numerical simulations
reveals that our analytical solution captures essential low-energy features,
and provides a mechanism for the magnon frequency hardening observed in recent
first principles calculations for Fe, provided the geometrical torque is taken
into account.
