Stability of Skyrmions in discrete arrays of spins with Heisenberg and truncated RKKY-interaction and single-spin anisotropy

In two-dimensional discrete classical spin arrays subject to ferromagnetic nearest-neighbour isotropic Heisenberg exchange interaction and single-spin anisotropy D localised single excitations of Skyrmion-type are studied. Following Abanov and Pokrovsky (AP) [Ar. Abanov, V.L. Pokrovsky, Phys. Rev. 58 (1998) R8889], also RKKY interaction is simulated by including antiferromagnetic next-nearest-neighbour interaction. Their stability is tested numerically by letting their energy relax. For the isotropic case (D=0), the narrowing of single Skyrmions with larger radius is very slow. Excitations with easy axis anisotropy shrink in size much faster than in the isotropic case, whereas excitations with easy plane anisotropy are stable. Already RKKY interaction truncated to AF next-nearest-neighbour interaction stabilises Skyrmions to distinct radius in agreement with (AP), including also D=0 beyond their treatment.