Theory of magnetic inertial dynamics in two-sublattice ferromagnets

The magnetic inertial dynamics have been investigated for one sublattice ferromagnets. Here, we develop the magnetization dynamics in two-sublattice ferromagnets including the intra- and inter-sublattice inertial dynamics. First, we derive the magnetic susceptibility of such a ferromagnet. Next, by finding the poles of the susceptibility, we calculate the precession and nutation resonance frequencies. Our results suggest that while the resonance frequencies show decreasing behavior with the increasing intra-sublattice relaxation time, the effect of inter-sublattice inertial dynamics is contrasting.