Spatial and Temporal Correlations of XY Macro Spins.

We use nano disk arrays with square and honeycomb symmetry to investigate magnetic phases and spin correlations of XY dipolar systems at the micro scale. Utilizing magnetization sensitive X-ray photoemission electron microscopy, we probe magnetic ground states and the "order-by-disorder" phenomenon predicted 30 years ago. We observe the antiferromagnetic striped ground state in square lattices, and 6-fold symmetric structures, including trigonal vortex lattices and disordered floating vortices, in the honeycomb lattice. The spin frustration in the honeycomb lattice causes a phase transition from a long-range ordered locked phase over a floating phase with quasi long-range order and indications of a Berezinskii-Thouless-Kosterlitz-like character, to the thermally excited paramagnetic state. Absent spatial correlation and quasi periodic switching of isolated vortices in the quasi long-range ordered phase suggest a degeneracy of the vortex circulation.