Edge states in a two-dimensional honeycomb lattice of massive magnetic skyrmions

TL;DR

This paper investigates the collective edge modes in a 2D honeycomb lattice of magnetic skyrmions, revealing topologically protected chiral states and non-chiral Tamm-Shockley states, supported by advanced modeling and simulations.

Contribution

It introduces a generalized Thiele's equation including higher-order inertial and gyroscopic terms to model multiband skyrmion edge states, validated by simulations.

Findings

Identification of multiple chiral and non-chiral edge modes

Topological protection of chiral edge states against defects

Modeling of multiband edge states with extended Thiele's equation

Abstract

We study the collective dynamics of a two-dimensional honeycomb lattice of magnetic skyrmions. By performing large-scale micromagnetic simulations, we find multiple chiral and non-chiral edge modes of skyrmion oscillations in the lattice. The non-chiral edge states are due to the Tamm-Shockley mechanism, while the chiral ones are topologically protected against structure defects and hold different handednesses depending on the mode frequency. To interpret the emerging multiband nature of the chiral edge states, we generalize the massless Thiele's equation by including a second-order inertial term of skyrmion mass as well as a third-order non-Newtonian gyroscopic term, which allows us to model the band structure of skrymion oscillations. Theoretical results compare well with numerical simulations. Our findings uncover the importance of high order effects in strongly coupled skyrmions and are helpful for designing novel topological devices.