Interplay of Anisotropy, Dzyaloshinskii Moriya Interaction and Symmetry breaking Fields in a 2D XY Ferromagnet

A two dimensional classical ferromagnetic XY model with its bound vortex-antivortex dominated quasi long range ordered phase at low temperatures is a long standing as well as well studied problem of interest in the field of condensed matter. We conduct a detailed Monte Carlo study of such model in a square lattice with rather unexplored extensions where additional anisotropic exchange coupling and Dzyaloshinskii-Moriya interactions (DMI) together affect the Kosterlitz-Thouless (KT) transition in presence/ absence of symmetry breaking fields. Without DMI, the exchange term promotes collinear (ferromagnetic) order, whereas the DMI term induces spin cantings. By tuning anisotropy upto Ising limit, we document energy, specific-heat, magnetizations as well as helicity modulus and vortex densities for different temperatures and DMI strength. We also compute the 2nd moment of correlation lengths in order to probe the spatial correlation of the spins. Furthermore, the effect of U(1) symmetry breaking 4-fold and 8-fold symmetric h4 and h8 fields are explored which shows how the double-peaked specific heat profiles changes in presence of DMI. Overall, our findings append many important updates in the low temperature phases of a topological XY ferromagnet when additional DMI and isotropy-breaking exchange and/or field terms are considered thereby providing a few practical blueprints for suitably engineering topological spin systems.