Skyrmion Glass in a Disordered Magnetic Film

We show that high concentration of skyrmions can be achieved in magnetic films with quenched disorder. A 2D system of Heisenberg spins with feromagnetic exchange, $J$, and random magnetic anisotropy of strength $D_R\ll J$ has been studied. Analytical theory for the dependence of the average skyrmion size on the magnetic field $H$, and for the stability of pinned skyrmions, is complemented by numerical studies of 2D lattices containing up to 40 million spins. At low fields the average size of the skyrmion, $\lambda$, is determined by the average size of Imry-Ma domains. On increasing the field the skyrmions first shrink, with $\lambda \propto D_R\mathrm{/}H$, and then collapse at fields distributed around $H_c\propto D_R^{4\mathrm{/}3}$. Concentration of the skyrmions goes down with the field as $\exp [-(H\mathrm{/}{H}_c{)}^{3\mathrm{/}2}]$.