Momentum-space theory for topological magnons in 2D ferromagnetic skyrmion lattices

TL;DR

This paper develops a multi-momentum operator theory for magnons in large 2D skyrmions, revealing complex topological behaviors and deviations from simpler single-momentum models, with implications for topological magnonics.

Contribution

It introduces a comprehensive momentum-space theory for magnons in large skyrmions, capturing off-diagonal effects and topological phase transitions.

Findings

Flat bands are not universal in skyrmionic magnon spectra.

External magnetic fields induce multiple topological phase transitions.

High magnetic fields lead to a densely packed, topological magnon spectrum.

Abstract

Magnon dynamics in skyrmion lattices have garnered significant interest due to their potential applications in topological magnonics. Existing theories often follow a single-momentum approach, assuming significant Dzyaloshinskii-Moriya Interaction (DMI) to minimize the skyrmion's dimensions, which can lead to oversimplification in describing magnon behavior. This study introduces a multi-momentum operator theory for magnons in large 2D skyrmions, where each skyrmion encompasses several thousand spins. The proposed theory fully transforms the magnon Hamiltonian into momentum space, incorporating off-diagonal terms to capture umklapp scattering caused by the skyrmion wave vectors. Our results reveal deviations from single-momentum theories, demonstrating that flat bands are not universal features of the skyrmionic magnon spectrum. Additionally, we find that manipulating the skyrmion size with an external magnetic field induces multiple topological phase transitions. At high magnetic fields, the low-energy magnon spectrum becomes densely packed and entirely topological, resembling a topological band continuum.