Skyrmion glass in a 2D Heisenberg ferromagnet with quenched disorder

A 2D Heisenberg ferromagnet with exchange J and random magnetic anisotropy of strength $D_R\ll J$ has been studied. Analytical theory for the dependence of the average size of a pinned skyrmion on the magnetic field H, and for stability of such skyrmions on a lattice, has been developed. It has been complemented by numerical studies of 2D lattices containing up to 40 million spins. At low fields the average size of the skyrmion, λ, is determined by the average size of Imry–Ma domains. On increasing the field the skyrmions first shrink, with $\lambda \propto D_R/H$, and then collapse at fields distributed around $H_c\propto D_R^{4/3}$. The concentration of the skyrmions goes down with the field as $\exp [-\frac{1}{2}{\left(H/H_c\right)}^{3/2}]$. (paper)