Orbital magnetization in interacting moire systems

Experimentally, determining the magnetization direction is critical for accurately characterizing transition metal dichalcogenide (TMD) moiré superlattices. Orbital magnetization is often overlooked in these systems because strong interaction effects frequently lead to spontaneous valley polarization, which induces spin polarization through spin-momentum locking, a key feature of TMD materials. As a result, the role of orbital magnetization is typically obscured by spin magnetization. However, previous studies have shown that under specific conditions, such as when spin polarization is quenched at a filling factor $\nu = -2$, orbital magnetization can become significant. In this work, we investigate the competition between spin and orbital magnetization, with a particular focus on how interaction effects can modify the orbital contribution in TMD moiré superlattices. We develop a framework to incorporate these interaction effects into the calculation of orbital magnetization and apply it to several moiré systems. Our numerical results reveal conditions under which orbital magnetization plays a critical role, even in the presence of strong spin magnetization.