Ultrafast laser-induced magnetization dynamics is analyzed in terms of the Landau-Lifshitz-Bloch (LLB) equation for different values of spin $S$. Within the LLB model the ultrafast demagnetization time (${\tau }_M$) and the transverse damping (${\alpha }_{\perp }$) are parametrized by the intrinsic coupling-to-the-bath parameter $\lambda$, defined by the microscopic spin-flip rate. We show that the LLB model is equivalent to a recently introduced M3TM model [B. Koopmans et al., Nature Mat. 9, 259 (2010)] with $S=1/2$ within the assumption that the intrinsic scattering mechanism is the phonon-mediated Elliott-Yafet scattering. As a result, for this process $\lambda$ is proportional to the ratio between the nonequilibrium phonon and electron temperatures, in contrast to previous models with $\lambda =\text{const}$. We investigate the influence of the finite spin number and the scattering rate parameter $\lambda$ on the ultrafast magnetization dynamics. The differences in the demagnetization time scale in transition metals and Gd are attributed to the fact that this parameter is almost two orders of magnitude smaller in the latter case. The relation between the femtosecond demagnetization rate and the perpendicular picosecond–nanosecond damping, provided by the LLB theory, is checked based on the available experimental data. A good agreement is obtained for Ni, Co, and Gd, providing validation of the LLB model.

• Received 19 November 2010

DOI:https://doi.org/10.1103/PhysRevB.84.144414