Orbital angular momentum driven anomalous Hall effect

Abstract

Orbital angular momentum (OAM) plays a central role in regulating the magnetic state of electrons in nonperiodic systems such as atoms and molecules. In solids, on the other hand, OAM is usually quenched by the crystal field, and thus has a negligible effect on magnetization. Accordingly, it is generally neglected in discussions around band topology such as Berry curvature and intrinsic anomalous Hall effect (AHE). Here, we present a theoretical framework demonstrating that crystalline OAM can be directionally unquenched in transition metal oxides via energetic proximity of the conducting $d$ electrons to the local magnetic moments. We show that this leads to ``composite'' Fermi pockets with topologically nontrivial OAM textures. This enables a giant Berry curvature and a resultant intrinsic nonmonotonic AHE, even in collinearly ordered spin states. We use this model to explain the origin of the giant AHE observed in the forced ferromagnetic state of ${\mathrm{EuTiO}}_{3}$ and propose it as a general scheme for OAM driven AHE.