A Theory of Skyrmion Size in Skyrmion Crystals

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 class 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, κ=π2D2⁄(16AK)=1 separates isolated skyrmions from condensed skyrmion states. In contrast to isolated skyrmions whose size increases with D⁄K and is insensitive to κ<<1 and stripe skyrmions whose width increases with A⁄D and is insensitive to κ>>1, 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 searching for stable smaller skyrmions at the room temperature.