Enhanced spin-orbit coupling and orbital moment in ferromagnets by electron correlations

TL;DR

This paper demonstrates that electron correlations can significantly enhance spin-orbit coupling and orbital magnetic moments in ferromagnets, providing a fundamental understanding relevant for spintronics applications.

Contribution

It introduces a model showing how Coulomb interactions amplify SOC and orbital moments in ferromagnets, supported by Hubbard model calculations.

Findings

Effective SOC and orbital moments can be enhanced by Coulomb interactions.

Spin polarization is more dominant than orbital polarization.

The enhancement factor depends on Coulomb parameters and density of states.

Abstract

In atomic physics, the Hund rule says that the largest spin and orbital state is realized due to the interplay of the spin-orbit coupling (SOC) and the Coulomb interactions. Here, we show that in ferromagnetic solids the effective SOC and the orbital magnetic moment can be dramatically enhanced by a factor of $1/[1-(2U^\prime-U-J_H)\rho_0]$, where $U$ and $U^\prime$ are the on-site Coulomb interaction within the same oribtals and between different orbitals, respectively, $J_H$ is the Hund coupling, and $\rho_0$ is the average density of states. This factor is obtained by using the two-orbital as well as five-orbital Hubbard models with SOC. We also find that the spin polarization is more favorable than the orbital polarization, being consistent with experimental observations. This present work provides a fundamental basis for understanding the enhancements of SOC and orbital moment by Coulomb interactions in ferromagnets, which would have wide applications in spintronics.