| Summary: | 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 $\exp [-\tfrac{1}{2}{(H/{H}_{c})}^{3/2}]$ .
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