Strongly fluctuating moments in the high-temperature magnetic superconductor RbEuFe4As4

The iron-based superconductor $\mathrm{Rb}\mathrm{Eu}{\mathrm{Fe}}_{4}{\mathrm{As}}_{4}$ undergoes a magnetic phase transition deep in the superconducting state. We investigate the calorimetric response of $\mathrm{Rb}\mathrm{Eu}{\mathrm{Fe}}_{4}{\mathrm{As}}_{4}$ single crystals of the magnetic and the superconducting phase and its anisotropy to in-plane and out-of-plane magnetic fields. Whereas the unusual cusplike anomaly associated with the magnetic transition is suppressed to lower temperatures for fields along the crystallographic $c$ axis, it rapidly transforms to a broad shoulder shifting to higher temperatures for in-plane fields. We identify the cusp in the specific-heat data as a Berezinskii-Kosterlitz-Thouless transition with fine features caused by the three-dimensional effects. The high-temperature shoulder in high magnetic fields marks a crossover from a paramagnetically disordered to an ordered state. This observation is further supported by Monte Carlo simulations of an easy-plane two-dimensional Heisenberg model and a fourth-order high-temperature expansion, both of which agree qualitatively and quantitatively with the experimental findings.