Nutational resonance modes in antiferromagnetic materials

The Landau-Lifshitz-Gilbert (LLG) equation is well-established to describe the spin dynamics of magnetic materials. This first-order differential equation is based on the assumption that the spin angular momenta and corresponding magnetic moments are always parallel. While this assumption is largely unproblematic, both theoretical considerations and experimental results have indicated that the two may become separated on ultrafast timescales, giving rise to inertial dynamics along with a modified spin wave dispersion. Here, we apply linear spin wave theory to the inertial LLG equation to compute the eigenmodes of the altermagnetic materials SmErFeO₃ and α-Fe₂O₃. We find the largest influence of nutation on the magnetic resonances in the case of hematite, which exhibits both a sizeable shift of the resonance frequencies as compared to the inertia-free case and additional nutational resonances that are in a similar order of magnitude to the materials' higher-frequency precessional exchange modes. While the realistic magnitude of the inertial parameter remains an open question, we hope that our quantitative analysis provides the starting point for further experimental investigations.