Ultrafast Demagnetization Dynamics Due to Electron-Electron Scattering and Its Relation to Momentum Relaxation in Ferromagnets

TL;DR

This paper presents a theoretical analysis of ultrafast demagnetization in ferromagnets, linking electron-electron scattering and momentum relaxation times to demagnetization dynamics, and introduces a simplified model for practical calculations.

Contribution

It introduces a generalized relaxation-time ansatz for the spin-density matrix that accurately models demagnetization dynamics across different scattering regimes.

Findings

The ansatz reproduces the inverse proportionality of demagnetization time to momentum relaxation time.

It accurately describes demagnetization behavior in both short and long relaxation time limits.

The approach can be integrated into broader magnetization dynamics models involving transport and phonon effects.

Abstract

We analyze theoretically the demagnetization dynamics in a ferromagnetic model system due to the interplay of spin-orbit coupling and electron-electron Coulomb scattering. We compute the $k$-resolved electronic reduced spin-density matrix including precessional dynamics around internal spin-orbit and exchange fields as well as the electron-electron Coulomb scattering for densities and spin coherences. Based on a comparison with numerical solutions of the full Boltzmann scattering integrals, we establish that the $k$-resolved reduced spin-density matrix dynamics are well described using a simpler generalized relaxation-time ansatz for the reduced spin-density matrix. This ansatz allows one to relate the complicated scattering dynamics underlying the demagnetization dynamics to a physically meaningful momentum relaxation time $\tau$. Our approach reproduces the behaviors of the demagnetization time $\tau_{m} \propto 1/\tau$ and $\tau_{m} \propto \tau$ for the limits of short and long $\tau$, respectively, and is also valid for the intermediate regime. The ansatz thus provides a tool to include the correct demagnetization behavior in approaches that treat other contributions to the magnetization dynamics such as transport or magnon/phonon dynamics.