Non-equilibrium formulation of helicity-dependent thermal field for ultrafast magnetization dynamics

Abstract

Far-from-equilibrium magnetization dynamics can be accessed when a magnetic material is subject to a femtosecond excitation, such as an optical laser or an electric current. Numerically, the demagnetization of magnetic materials is typically modeled by atomistic spin dynamics. Micromagnetic models generally fail to reproduce ultrafast demagnetization in a grid independent manner. Here, we propose a non-equilibrium thermal field whose features depend on atomic spin flip probabilities. Under the assumption that each spin flip is equivalent to a quantum of angular momentum, equivalent temperatures on the order of thousands of Kelvin are achieved. Demagnetization is quantitatively reproduced for several cell sizes. The presented approach can be further refined and extended towards a grid-independent and multiscale modeling of ultrafast magnetization dynamics.

Figures (2)

• Figure 1: (a) Mean and (b) standard deviation of the non-equilibrium thermal field calculated from Eq. \ref{['eq:meanstd']} subject to an ultrafast pulse and assuming $N=125$. The mean tends towards negative values at the peak of the pulse at $2$ ps while it follows the value of the initial magnetization $m_z^i$ otherwise. The field's standard deviation also increases close to the optical pulse peak.
• Figure 2: Average $m_z$ magnetization component upon optical excitation for several cases. The laser pulse is shown in (a) and (b) as a guide to the eye. (a) Demagnetization as a function of cell size. The non-equilibrium field correction is zero in the atomic case, $a=0.4$ nm shown by black symbols. In that case, the demagnetization is purely driven by the uncorrelated noise. For the other cases, the demagnetization rates closely agree. (b) Demagnetization as a function of the maximum laser temperature. The equivalent maximum probabilities are shown in the legend. The increase in demagnetization is in qualitative agreement with experimental results. (c) Demagnetization as a function of the laser pulse standard deviation $t_\sigma$ and $T_0=700$ K. As the standard deviation increases, the magnetic system has more time to react to the non-equilibrium field and full demagnetization can be achieved.