Quantitative analysis of spin wave dynamics in ferrimagnets across compensation points

Rare-earth transition-metal ferrimagnets have two strongly coupled sublattices of distinct chemical nature, which give rise to complex and fast dynamics of great interest to spintronics. However, the dynamics of ferrimagnets remains less understood than ferromagnets. We measure the spin wave (SW) spectra of a GdFeCo film by Brillouin light scattering spectroscopy (BLS) across its compensation temperatures-temperatures at which either the sublattices' magnetizations or their angular moments cancel out, mimicking an antiferromagnet. We find two SW modes per wave vector with complex thermal dependencies, which cross at a field-dependent temperature. We develop an analytical model based on two sublattices corresponding to the rare earth and the transition metal, which reproduces quantitatively the SW spectra and their evolution with temperature and field. This validates the proposed energy and dynamical model of the ferrimagnet, and demonstrates the usefulness of BLS in the study of this promising class of materials.