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

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 nonchiral edge modes of skyrmion oscillations in the lattice. The nonchiral edge states are due to the Tamm-Shockley mechanism, while the chiral ones are topologically protected against structure defects and hold different handedness 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 skyrmion 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 skyrmionic topological devices.