Formation And Annihilation Of Magnetic Skyrmions On A Square Lattice Heisenberg Ferromagnet: The Role Played By The Pure And Random Anisotropy Configurations

We investigate the formation and stabilisation of magnetic skyrmions defined on a ferromagnetic square lattice Heisenberg model in the presence of single ion anisotropy. By means of Monte Carlo simulations, we show in the absence of magnetic anisotropy that for the ground state and finite temperature region, the present model exhibits spiral, skyrmion lattice and field polarised phases in the presence of Dzyaloshinskii-Moriya interaction and magnetic field. For this particular case, our simulation results suggest that in the low magnetic field region, there exists a critical value of DM interaction above which formation of skyrmions takes place. Besides, density and size of skyrmions emerging in the system depends on the competition between local energies due to DM interaction and magnetic field. We also focus on the influence of non-zero magnetic anisotropy energy on the emergence of skyrmions with a special emphasis on disordered anisotropy configurations represented by a certain probability distribution. In order to model a disordered magnetic anisotropy effect, we consider a model with a diluted single ion anisotropy distribution, as well as a disordered model mimicked by a Gaussian distribution of magnetic anisotropy constants accompanied to each lattice site. Our results show that when the antisymmetric exchange (DM) interaction and the magnetic field are kept fixed, skyrmion phase disappears with increasing magnetic anisotropy, however it can be recovered by properly tuning the relevant probability distribution parameters.