Nontrivial temperature dependence of ferromagnetic resonance frequency for spin reorientation transitions

We find unusual temperature dependence of the ferromagnetic resonance (FMR) frequency $f_{\rm R}$ for the spin-reorientation (SR) transition, in which the easy axis changes depending on temperature, observed in the Nd permanent magnet, Nd$_2$Fe$_{14}$B: $f_{\rm R} \sim 0$ below the SR transition temperature ($T_{\rm R}$), drastic increase of $f_{\rm R}$ around $T_{\rm R}$, and decrease from a peak at higher temperatures. It is nontrivial that the SR transition causes the unusual behavior of the FMR frequency in a wide temperature region. We show the mechanism of the temperature dependence by theoretical and computational analyses. We derive a general relation between $f_{\rm R}$ and magnetizations to help the understanding of the mechanism, and clarify that the fluctuation of the transverse magnetization is a key ingredient for the resonance in all temperature regions.