Spin Fluctuations and Correlations of XY Macrospins*

Uniformly magnetized nano islands resembling macrospins have become prototypical systems for studying spin frustration and fluctuations at the microscale. The capability to mimic magnetic exchange via dipole-dipole interaction has been used to study artificial spin ice, and recently extended to colloidal spin glass. In view of spin liquids, we have investigated XY macrospins utilizing nanodisk systems with absent energy barriers, various thickness and spacing. We have used XPEEM to study fluctuations and correlations in planar square and honeycomb XY macrospin arrays with various geometries at remanence and at temperatures from 120-390K. The lack of an energy barrier in individual disks leads to a high sensitivity of the magnetization configuration on the lattice parameters and temperature, with fluctuation rates orders of magnitude larger than those of biaxial spin systems. We find experimental evidence of a Berezinskii-Thouless-Kosterlitz-like phase transition solely mediated by magnetostatics that favors a trigonal vortex lattice similar to Skyrmion lattices stabilized by the Dzyaloshinskii-Moriya interaction. Our results open a new avenue for artificial spin ices, spin liquids, Kitaev honeycomb lattices, magnonics.