Self-consistent description of spin-phonon dynamics in ferromagnets

Several recently reported exciting phenomena such as spin caloritronics or ultrafast laser-induced spin dynamics involve the action of temperature on spin dynamics. However, the inverse effect of magnetization dynamics on temperature change is very frequently ignored. Based on the density matrix approach, in this work we derive a self-consistent model for describing the magnetization and phonon temperature dynamics in ferromagnets in the framework of the quantum Landau-Lifshitz-Bloch equation. We explore potential applicability of our approach for two cases, inspired by magnetocaloric effect and magnetic fluid hyperthermia. In the first case, the spin-phonon dynamics is governed by the longitudinal relaxation in bulk systems close to the Curie temperature; while in the second case it is described by the transverse relaxation during the hysteresis cycle of individual nanoparticles well below the Curie temperature