Gauge-Invariant Measure of the Magnon Orbital Angular Momentum

Abstract

Unlike the Berry phase, the orbital angular momentum (OAM) of magnons with two-dimensional wavevector k in band n is not gauge invariant for arbitrary phase lambda_n(k). However, by integrating the OAM over the orientation $\varphi$ of wavevector k, we construct a gauge-invariant function F_n(k). Like F_n(k), the average OAM for magnon band n in a circle of radius k is also gauge invariant. We demonstrate these results for a ferromagnet on a honeycomb lattice with Dzyalloshinskii-Moriya interactions between next-nearest neighbor spins. With wavevectors k restricted to the first Brillouin zone, the angular averaged OAM F_n(k) then has opposite signs for lower and upper bands n=1 and 2 for all k.

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Cited by in corpus (5)

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• Electric polarization induced by magnons and magnon Nernst effects
• Chiral magnon in ferromagnetic chiral crystals
• Proper Theory of Magnon Orbital Angular Momentum at Equilibrium