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The effects of competing magnetic interactions in stabilizing different spinconfigurations are drawing a renewed attention in order to both unveil emergingtopological spin textures and to highlight microscopic mechanisms leading totheir stabilization. The possible key role of the two-site exchange anisotropyin selecting specific helicity and vorticity of skyrmionic lattices has onlyrecently been proposed. In this work we explore the phase diagram of afrustrated localized magnet on a two-dimensional centrosymmetric triangularlattice, focusing on the interplay between the two-ion anisotropy (TIA) and thesingle-ion anisotropy (SIA). The effects of an external magnetic field appliedperpendicularly to the magnetic layer are also investigated. By means of MonteCarlo simulations, we find a profusion of different spin configurations, goingfrom trivial to high-order Q skyrmionic and meronic lattices. In closer detail,we find that a dominant role is played by the two-ion over the single-ionanisotropy in determining the planar spin texture, whereas the strength andsign of SIA, together with the magnitude of the magnetic field, tune theperpendicular spin components, mostly affecting the polarity (and, in turn, thetopology) of the spin-texture. Our analysis confirms the crucial role ofanisotropic symmetric exchange in systems with dominant short-rangeinteractions, at the same time predicting a rich variety of complex magnetictextures that may arise from a fine tuning of competing anisotropic mechanisms.

Tuning of magnetic structures topology via single-ion anisotropy and magnetic field in frustrated 2D semiconductors