Magnetic Resonance Frequency of Two-Sublattice Ferrimagnet with Magnetic Compensation Temperature

Ferrimagnetic materials with a compensation temperature have recently attracted interest because of their unique combination of ferromagnetic and antiferromagnetic properties. However, their magnetization dynamics near the compensation temperature are complex and cannot be fully explained by conventional ferromagnetic resonance (FMR) or exchange resonance modes. Therefore, practical models are necessary to capture these dynamics accurately. In this study, we derived the analytical solutions for the magnetic resonance frequencies of compensated ferrimagnets over all temperature ranges, considering both the in-plane and out-of-plane orientations of the magnetization. Our solutions successfully reproduce the experimental data obtained from time-resolved magneto-optical Faraday rotation and Brillouin light scattering measurements for the in-plane and out-of-plane cases, respectively. This reproduction is achieved by incorporating the exchange stiffness and temperature dependence of the magnetic anisotropy into the free energy density. Additionally, at temperatures sufficiently far from the compensation temperature, our analytical solutions converge with the conventional FMR and exchange resonance models.