Size and profile of skyrmions in skyrmion crystals

Size is a fundamental quantity of magnetic skyrmions. A magnetic skyrmion can be a local circular object and in an isolated form. A skyrmion can also coexist with a group of its siblings in a condensed phase. Each skyrmion in a condensed phase takes a stripe shape at low skyrmion density and a circular shape at high skyrmion density. Skyrmions at high density form a skyrmion crystal (SkX). So far, skyrmion size in an SkX has not been seriously studied. Here, by using a generic chiral magnetic film, it is found that skyrmion size in an SkX has a different parameter dependence as those for isolated skyrmions and stripes. A size formula and a good spin profile for skyrmions in SkXs are proposed. These findings have important implications in searching for stable smaller skyrmions at the room temperature. Understanding the parameters which govern the size of a skyrmion are important to gain greater control over their stability and dynamics but the underlying mechanisms differ from individual skyrmions to skyrmion crystals. To this end, using micromagnetic simulations, the authors theoretically investigate the relationship between the underlying material parameters and skyrmion radius within a skyrmion crystal