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.

中文翻译：

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XY宏自旋的时空相关性

我们使用具有方形和蜂窝对称性的纳米磁盘阵列来研究XY的磁相和自旋相关性微尺度的偶极系统。利用磁化敏感的X射线光发射电子显微镜，我们探究了磁性基态和30年前预测的“按序失序”现象。我们在正方形晶格中观察到反铁磁条纹基态，并在蜂窝晶格中观察到六重对称结构，包括三角涡旋晶格和无序浮动涡旋。蜂窝晶格中的自旋受挫会导致从长程有序锁相到具有准长程序的浮相的相变，并显示出类似Berezinskii-Thouless-Kosterlitz的特征，并转变为热激发的顺磁态。在准远程有序相中，孤立的涡旋缺乏空间相关性和准周期性切换，暗示了涡旋环流的退化。