Correlation Between Spin and Orbital Dynamics During Laser-Induced Femtosecond Demagnetization

TL;DR

This study introduces a novel spin-orbital correlation diagram to analyze ultrafast spin and orbital dynamics during laser-induced demagnetization, revealing distinct patterns for iron and cobalt and emphasizing the role of spin-orbit coupling.

Contribution

The paper presents the first use of spin-orbital correlation diagrams to visualize ultrafast spin and orbital evolution, supported by experimental data and first-principles calculations.

Findings

Iron shows an arc-shaped correlation pattern with a cusp at demagnetization end.

Cobalt exhibits a more linear correlation with kinks, differing from iron.

Spin-orbit coupling links spin and orbital dynamics, influenced by orbital occupations.

Abstract

Spin and orbital angular momenta are two intrinsic properties of an electron and are responsible for the physics of a solid. How the spin and orbital evolve with respect to each other on several hundred femtoseconds is largely unknown, but it is at the center of laser-induced ultrafast demagnetization. In this paper, we introduce a concept of the spin-orbital correlation diagram, where spin angular momentum is plotted against orbital angular momentum, much like the position-velocity phase diagram in classical mechanics. We use four sets of highly accurate time-resolved x-ray magnetic circular dichroism (TR-XMCD) data to construct four correlation diagrams for iron and cobalt. To our surprise, a pattern emerges. The trace on the correlation diagram for iron is an arc, and at the end of demagnetization, it has a pronounced cusp. The correlation diagram for cobalt is different and appears more linear, but with kinks. We carry out first-principles calculations with two different methods: time-dependent density functional theory (TDDFT) and time-dependent Liouville density functional theory (TDLDFT). These two methods agree that the experimental findings for both Fe and Co are not due t experimental errors. It is the spin-orbit coupling that correlates the spin dynamics to the orbital dynamics.Microscopically, Fe and Co have different orbital occupations, which leads to distinctive correlation diagrams. We believe that this correlation diagram presents a useful tool to better understand spin and orbital dynamics on an ultrafast time scale. A brief discussion on the magnetic anisotropy energy is also provided.