Sub-terahertz/terahertz electron resonances in hard ferrimagnets

Intensive development of ultrafast electronics requires materials with high-frequency spin dynamics. In this light, the insulators that possess the magnetization precession phenomenon due to magnetic anisotropy are dark horses. On the one hand, modern hard magnetic materials reveal relatively moderate resonance frequencies of the ferromagnetic mode (generally, dozens of GHz), which are lower than the frequencies of the antiferromagnetic resonances; on the other hand, the research in this area is quite scanty, which implies a room for a breakthrough. Here, an example of a hard ferrimagnetic insulator (cobalt ferrite CoFe2O4) was obtained in the form of nanoparticles and bulk ceramics via high-temperature methods. Due to high magnetic anisotropy fields, the samples in a single domain state show broad hysteresis loops. The materials also possess intensive resonance absorption at frequencies higher than 0.20 THz in zero external magnetic fields. For the first time, natural ferromagnetic resonance (NFMR) frequencies higher than 0.30 THz were registered. The ceramic sample demonstrates the highest-known NFMR frequency of 0.35 THz. The model based on the Landau-Lifshitz equation was developed to explain the demonstrated magnetodynamic properties and shed light on those of hard ferrimagnets in general. The practical application of the electron resonances in hard magnetic insulators, including cobalt ferrite, Al-doped M-type hexaferrite, and epsilon iron oxide, is discussed. Our findings reveal that these materials should provide several orders of magnitude more powerful spin pumping at sub-terahertz/terahertz frequencies compared to insulating antiferromagnets, even under unpolarized irradiation and even in the absence of external magnetic fields. This opens new horizons for the development of practical ultrafast electronics.