$\mathbb{C}P^2$ Skyrmion Crystals in an SU(3) Magnet with a Generalized Dzyaloshinskii-Moriya Interaction

TL;DR

This paper investigates complex $P^2$ Skyrmion crystals in an SU(3) magnetic model, revealing two types of Skyrmion configurations with potential for advanced applications due to their additional degrees of freedom.

Contribution

It introduces $P^2$ Skyrmion crystals in an SU(3) model with generalized interactions, expanding the understanding of Skyrmion structures beyond the conventional $P^1$ case.

Findings

Identified two distinct $P^2$ Skyrmion crystal types.

Skyrmions interpreted as bound states of half- and quarter-Skyrmions.

Potential for future applications due to increased degrees of freedom.

Abstract

We study $\mathbb{C}P^2$ Skyrmion crystals in the ferromagnetic SU(3) Heisenberg model with a generalization of the Dzyaloshinskii-Moriya interaction and the Zeeman term. The model possesses two different types of Skyrmion crystals with unit-Skyrmions that can be interpreted as bound states of two half-Skyrmions or four quarter-Skyrmions. Our study on $\mathbb{C}P^2$ Skyrmion crystals opens up the possibility for useful future applications since $\mathbb{C}P^2$ Skyrmions have more degrees of freedom than the usual $\mathbb{C}P^1$ (magnetic) Skyrmions.