  Spin nutation resonance has been well-explored in one-sublattice
ferromagnets. Here, we investigate the spin nutation in two-sublattice
antiferromagnets as well as, for comparison, ferrimagnets with inter-and
intra-sublattice nutation coupling. In particular, we derive the susceptibility
of the two-sublattice magnetic system in response to an applied external
magnetic field. To this end, the antiferromagnetic and ferrimagnetic (sub-THz)
precession and THz nutation resonance frequencies are calculated. Our results
show that the precession resonance frequencies and effective damping decrease
with intra-sublattice nutation coupling, while they increase with inter
-sublattice nutation in an antiferromagnet. However, we find that the THz
nutation resonance frequencies decrease with both the intra-and
inter-sublattice nutation couplings. For ferrimagnets, conversely, we calculate
two nutation modes with distinct frequencies, unlike antiferromagnets. The
exchange-like precession resonance frequency of ferrimagnets decreases with
intra-sublattice nutation coupling and increases with inter-sublattice nutation
coupling, like antiferromagnets, but the ferromagnetic-like precession
frequency of ferrimagnets is practically invariant to the intra and
inter-sublattice nutation couplings.
