Proper Theory of Magnon Orbital Angular Momentum at Equilibrium

The orbital motion of chargeless bosons, unlike that of electrons, does not generate a magnetic moment and thus cannot directly interact with magnetic fields. To formulate the orbital angular momentum (OAM) of magnons, we first identify its proper conjugate variable by considering the Aharonov-Casher effect, which gives rise to a virtual perturbation to the equilibrium state, allowing us to calculate the magnon OAM as a virtual response to an infinitesimal electric field divergence. At finite temperatures, both self-rotation and topological contributions to the magnon OAM are explicitly derived, analogous to their electronic counterpart but with the correct bosonic statistics. In a two-dimensional honeycomb lattice, we show that the Dzyaloshinskii-Moriya interaction induces a large magnon OAM in both the ferromagnetic and antiferromagnetic phases. Our formalism can be generalized to other chargeless bosons with intrinsic spin.