Inertial spin waves in ferromagnets and antiferromagnets

Inertial effects in spin dynamics are theoretically predicted to emerge at ultrashort time scales, but their experimental signatures are often ambiguous. Here, we calculate the spin-wave spectrum in ferromagnets and two-sublattice antiferromagnets in the presence of inertial effects. It is shown how precession and nutation spin waves hybridize with each other, leading to the renormalization of the frequencies, the group velocities, the effective gyromagnetic ratios and the effective damping parameters. Possible ways of distinguishing between the signatures of inertial dynamics and similar effects explainable within conventional models are discussed.