Classical spin model of the relaxation dynamics of rare-earth doped permalloy

In this paper, the ultrafast dynamic behavior of rare-earth doped permalloy is investigated using an atomistic spin model with Langevin dynamics. In line with experimental work, the effective Gilbert damping is calculated from transverse relaxation simulations, which shows that rare-earth doping causes an increase in the damping. Analytic theory suggests that this increase in damping would lead to a decrease in the demagnetization time. However, longitudinal relaxation calculations show an increase with doping concentration instead. The simulations are in a good agreement with previous experimental work of Radu et al. [Radu et al., Phys. Rev. Lett. 102, 117201 (2009)]. The longitudinal relaxation time of the magnetization is shown to be driven by the interaction between the transition metal and the laser-excited conduction electrons, whereas the effective damping is predominantly determined by the slower interaction between the rare-earth elements and the phonon heat bath. We conclude that for complex materials, it is evidently important not to expect a single damping parameter but to consider the energy transfer channel relevant to the technique and time scale of the measurement.