SU(4) description of bilayer skyrmion-antiskyrmion pairs

Abstract

The antiferromagnetic coupling and entanglement between skyrmion lattices are treated in magnetic bilayer systems. We first formulate the problem of large bilayer skyrmions using the-theory. We have considered bilayer skyrmions under the presence of Dzyaloshinskii-Moriya (DMI) and Zeeman interactions confined in a two-dimensional chiral magnet such as Fe0.5Co0.5Si. We parametrize bilayer skyrmions using the SU(4) representation, and represent each skyrmion and antiskyrmion using the Schmidt decomposition. The reduced density matrices for skyrmion and antiskyrmion have been calculated. The conditions for maximal, partial entanglement and separable bilayer skyrmions are presented. Our results can be used for generating entanglement in systems with a large number of spins.