Insights into the orbital magnetism of noncollinear magnetic systems

TL;DR

This paper introduces a minimal theoretical model to understand how noncollinear magnetic structures influence orbital magnetism, highlighting the roles of spin-orbit coupling, magnetic noncollinearity, and symmetry breaking.

Contribution

It provides a step-by-step hierarchy of models that elucidate the effects of noncollinearity on orbital magnetic moments, connecting to atomic and circulating current contributions.

Findings

Orbital magnetism can be driven by magnetic noncollinearity independently of spin-orbit interaction.

The model identifies couplings between spin-orbit and orbit-orbit interactions arising from noncollinearity.

The connection between orbital magnetism and scalar spin chirality is explored.

Abstract

The orbital magnetic moment is usually associated with the relativistic spin-orbit interaction, but recently it has been shown that noncollinear magnetic structures can also be its driving force. This is important not only for magnetic skyrmions, but also for other noncollinear structures, either bulk-like or at the nanoscale, with consequences regarding their experimental detection. In this work we present a minimal model that contains the effects of both the relativistic spin-orbit interaction and of magnetic noncollinearity on the orbital magnetism. A hierarchy of models is discussed in a step-by-step fashion, highlighting the role of time-reversal symmetry breaking for translational and spin and orbital angular motions. Couplings of spin-orbit and orbit-orbit type are identified as arising from the magnetic noncollinearity. We recover the atomic contribution to the orbital magnetic moment, and a nonlocal one due to the presence of circulating bound currents, exploring different balances between the kinetic energy, the spin exchange interaction, and the relativistic spin-orbit interaction. The connection to the scalar spin chirality is examined. The orbital magnetism driven by magnetic noncollinearity is mostly unexplored, and the presented model contributes to laying its groundwork.