Proper Theory of Magnon Orbital Angular Momentum

TL;DR

The work develops a gauge-invariant, finite-temperature theory for the orbital angular momentum (OAM) of magnons by coupling magnons to a spatially varying electric field via the Aharonov-Casher effect. It separates the OAM into a self-rotation term and a Berry-curvature (topological) term, and provides both multi-band and single-band formulas that apply to chargeless bosons with intrinsic spin, including finite-temperature effects. Applying the framework to a honeycomb lattice with Dzyaloshinskii–Moriya interaction, the authors show that magnons can acquire large OAM in both ferromagnetic and antiferromagnetic ground states, and they connect the topological contribution to the magnon spin Nernst effect. The theory clarifies prior ambiguities, enables edge-polarization-based detection, and offers a foundation for orbital dynamics of chargeless bosons in spintronics and orbitronics contexts.

Abstract

The orbital motion of chargeless bosons, unlike that of electrons, does not generate a magnetic moment and thus cannot directly interact with magnetic fields. Utilizing the Aharonov-Casher effect and perturbation theory, we formulate a proper theory for the magnon orbital angular momentum (OAM) at finite temperatures, explicitly identifying both self-rotation and topological contributions, analogous to the electronic counterpart but with correct bosonic statistics. Comparing with previous studies on magnon OAM, the magnon spin Nernst effect can only be correctly reproduced using the proper theory for magnon OAM. In a two-dimensional honeycomb lattice, we show that the Dzyaloshinskii-Moriya interaction induces a large magnon OAM in both ferromagnetic and antiferromagnetic ground states. Our formulation provides a foundation for studying orbital dynamics of chargeless bosons with intrinsic spin.

Figures (4)

• Figure 1: Schematics of the magnon OAM (green arrow) with a radius of classical trajectory $r_m$ (orange arrow) on a 2D honeycomb lattice, which generates a relativistic electric polarization $\bm{P}\propto \bm{v}\times\hat{\bm{z}}$ (brown arrow). The A and B sublattices are colored in red and blue, respectively. The purple arrows mark three nearest-neighbor bonds with the exchange interaction $J$, and the black dashed arrows are three clockwise next-nearest neighbor bonds $\bm{\delta}_i$ with the DMI vector along $+\hat{z}$ (cyan arrow).
• Figure 2: (a) FM magnon band structure (weighted by magnon OAM). Integers represent the Chern numbers of the corresponding bands. (b) the $k$-space distribution of total FM magnon OAM. The dashed lines mark the first Brillouin zone with $b_0$ the length of reciprocal lattice. (c) FM Magnon OAM $L$ per unit cell as a function a temperature and (d) exchange interaction for different DMI. In all figures, magnon OAM are plotted in the unit of $\rm m^2/s$.
• Figure 3: (a) AFM magnon band structure (weighted by magnon OAM). Both bands have zero Chern number. (b) the $k$-space distribution of total AFM magnon OAM. (c) AFM Magnon OAM $L$ per unit cell as a function a temperature and (d) magnetic field for different DMI. In all figures, magnon OAM are plotted in the unit of $\rm m^2/s$.
• Figure S1: The upper-band Berry curvature of (a) FM magnon and (b) AFM magnon. The dashed lines mark the first Brillouin zone with $b_0$ the length of reciprocal lattice.