Abstract
Two-dimensional magnetic systems with continuous spin degrees of freedom exhibit a rich spectrum of thermal behaviour due to the strong competition between fluctuations and correlations. When such systems incorporate coupling via the anisotropic dipolar interaction, a discrete symmetry emerges, which can be spontaneously broken leading to a low-temperature ordered phase. However, the experimental realisation of such two-dimensional spin systems in crystalline materials is difficult since the dipolar coupling is usually much weaker than the exchange interaction. Here we realise two-dimensional magnetostatically coupled XY spin systems with nanoscale thermally active magnetic discs placed on square lattices. Using low-energy muon-spin relaxation and soft X-ray scattering, we observe correlated dynamics at the critical temperature and the emergence of static long-range order at low temperatures, which is compatible with theoretical predictions for dipolar-coupled XY spin systems. Furthermore, by modifying the sample design, we demonstrate the possibility to tune the collective magnetic behaviour in thermally active artificial spin systems with continuous degrees of freedom.
Highlights
Two-dimensional magnetic systems with continuous spin degrees of freedom exhibit a rich spectrum of thermal behaviour due to the strong competition between fluctuations and correlations
We further demonstrate the emergence of spatial correlations, which is compatible with the long-range order theoretically predicted for dXY spin systems, with the observation of magnetic superstructure peaks by resonant elastic X-ray scattering
Most previously considered artificial spin systems consist of arrays of elongated magnetic islands with Ising-like degrees of freedom
Summary
Two-dimensional magnetic systems with continuous spin degrees of freedom exhibit a rich spectrum of thermal behaviour due to the strong competition between fluctuations and correlations When such systems incorporate coupling via the anisotropic dipolar interaction, a discrete symmetry emerges, which can be spontaneously broken leading to a lowtemperature ordered phase. We further demonstrate the emergence of spatial correlations, which is compatible with the long-range order theoretically predicted for dXY spin systems, with the observation of magnetic superstructure peaks by resonant elastic X-ray scattering This realisation of strongly coupled thermally active systems with continuous spin degrees of freedom opens the way for future investigations of dXY spin systems with a variety of arrangements that are predicted to have rich phase diagrams
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