Skyrmion size in skyrmion crystals

TL;DR

This paper investigates how skyrmion sizes in various phases depend on material parameters, revealing unique relationships for skyrmions in skyrmion crystals that could aid in designing smaller, stable skyrmions for room-temperature applications.

Contribution

It uncovers the distinct dependence of skyrmion sizes in skyrmion crystals on material parameters, differing from isolated and stripe skyrmions, with implications for stable skyrmion design.

Findings

Skyrmion size in SkXs is inversely proportional to the square root of skyrmion density.

Size of skyrmions in SkXs decreases with the ratio A/D.

Different skyrmion types exhibit unique size dependencies on material parameters.

Abstract

A magnetic skyrmion is a topological object that can exist as a solitary embedded in the vast ferromagnetic phase, or coexists with a group of its "siblings" in various stripy phases as well as skyrmion crystals (SkXs). Isolated skyrmions and skyrmions in an SkX are circular while a skyrmion in other phases is a stripe of various forms. Unexpectedly, the sizes of the three different types of skyrmions depend on material parameters differently. For chiral magnetic films with exchange stiffness constant $A$, the Dzyaloshinskii-Moriya interaction (DMI) strength $D$, and perpendicular magnetic anisotropy $K$, $\kappa\equiv\pi^2D^2/(16AK)=1$ separates isolated skyrmions from condensed skyrmion states. In contrast to isolated skyrmions whose size increases with $D/K$ and is insensitive to $\kappa\ll1$ and stripe skyrmions whose width increases with $A/D$ and is insensitive to $\kappa\gg1$, the size of skyrmions in SkXs is inversely proportional to the square root of skyrmion number density and decreases with $A/D$. This finding has important implications in our search for stable smaller skyrmions at the room temperature in applications.