Generation of Phonons with Angular Momentum During Ultrafast Demagnetization

Abstract

A major question in the field of femtosecond laser-induced demagnetization is whereto the angular momentum lost by the electrons is transferred. Recent ultrafast electron diffraction measurements [Tauchert \textit{et al.}, Nature {\bf 602}, 73 (2022)] suggest that this angular momentum is transferred to the rotational motion of atoms on a sub-picosecond timescale, but a theory confirmation of this proposition has yet to be given. Here we investigate the coupled electron-nuclear dynamics during ultrafast demagnetization of L1$_0$ FePt, using Ehrenfest nuclear dynamics simulations combined with the time-dependent density functional theory (TDDFT) framework. We demonstrate that atomic rotations appear, i.e., the generation of phonons carrying finite angular momentum following ultrafast demagnetization. We further show that both ultrafast demagnetization and the generation of phonons with angular momentum arise from symmetry constraints imposed by the spin-orbit coupling, thus providing insight in spin-phonon interaction at ultrafast timescales.

Figures (4)

• Figure 1: Graphical illustration of the generation of phonons with angular momentum following ultrafast demagnetization. The blue and red spheres represent Fe and Pt atoms, respectively. Transparent (solid) arrows represent their magnetic moments before (after) the laser pulse (purple curve). The calculated rotational motions in nuclear coordinates (green arrows) are exaggerated for better visualization.
• Figure 2: Laser-driven dynamics of spin-angular momentum in L1$_0$ FePt, simulated with (orange) and without (green) spin-orbit coupling. The right ordinate is normalized to the equilibrium value ($S_0=S_z(0)$). The gray curve represents the temporal profile of the laser electric field. The inset illustrates the simulation setup, where the spin is aligned along the $z$ axis and the laser electric field is $x$ polarized.
• Figure 3: (a) Ab initio computed phonon dispersion of L1$_0$ FePt with zone-center ($\mathbf{q} = \mathbf{0}$) optical phonon modes marked by yellow circles. (b) Illustration of zone-center optical phonon mode with frequency of 6.16THz, and (c) of 4.42THz (degenerate mode). The blue (red) spheres represent Fe (Pt) atoms.
• Figure 4: Laser-driven nuclear dynamics following ultrafast demagnetization of L1$_0$ FePt. Shown are the relative displacements, $\Delta\textbf{R}_i(t)=\textbf{R}_i(t)-\textbf{R}_i(0)$. (a) The nuclear dynamics calculated without SOC, and (b) with SOC. The primed coordinate of Pt is scaled as $\Delta \mathbf{R}_{\text{Pt}}^\prime = \frac{\text{M}_{\rm Pt}}{\text{M}_{\rm Fe}} \times \Delta \mathbf{R}_{\text{Pt}}$, where $\text{M}_{\rm Fe}$ ($\text{M}_{\rm Pt}$) is the atomic mass of Fe (Pt). The gray curves in the top panels represent the temporal profile of the laser electric field. Panels (c) and (d) show the atomic trajectories of the Fe and Pt atom in the $x-y$ plane, computed without and with SOC, respectively.