The Orbital Magnetic Moment (OMM) of Bloch electrons has come under renewed scrutiny recently as part of a general effort to understand angular momentum dynamics in systems in which spin-orbit interactions are absent or negligible. I will present two recent results from our group. The first is related to the orbital Hall effect. We have determined the full OHE in the presence of short-range disorder using 2D massive Dirac fermions as a prototype. We find that, in doped systems, extrinsic effects (skew scattering and side jump) provide ≈95% of the OHE. This suggests that, at experimentally relevant transport densities, the OHE is primarily extrinsic. In the second part I will show that the OMM is in general not conserved in an electric field. The force moment produces a torque on the OMM, which is determined by the quantum geometric tensor and the group velocities of Bloch bands. The torque vanishes in two-band systems with particle-hole symmetry but is nonzero otherwise. For tilted massive Dirac fermions the torque is determined by the magnitude and direction of the tilt.
The role of topological insulator (TI) bulk states in the the enormous spin torques recorded at TI/ferromagnet (FM) interfaces is poorly understood. Here we study spin torques due to TI bulk states focusing on magnetized TIs. We find that there is a novel spin transfer torque on an inhomogeneous magnetization, it is small in our idealized
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