Heiko Trepka, Trevor Keller, Maximilian Josef Krautloher, J. Xu, Klaus Habicht, Martin Böhm, Bernhard Keimer, Matthias Hepting

• Materials realizing the XY model in two dimensions are sparse. Here we use neutron triple-axis spectroscopy to investigate the critical static and dynamical magnetic fluctuations in the square-lattice antiferromagnets Ca2RuO4 and Ca3Ru2O7. We probe the temperature dependence of the antiferromagnetic Bragg intensity, the Q width, the amplitude, and the energy width of the magnetic diffuse scattering in the vicinity of the Neel temperature T-N to determine the critical behavior of the magnetic order parameter M, correlation length xi, susceptibility chi, and the characteristic energy Gamma with the corresponding critical exponents beta, nu, gamma, and z, respectively. We find that the critical behaviors of the single-layer compound Ca2RuO4 follow universal scaling laws that are compatible with predictions of the two-dimensional (2D) XY model. The bilayer compound Ca3Ru2O7 is only partly consistent with the 2D XY theory and best described by the three-dimensional (3D) Ising model, which is likely a consequence of theMaterials realizing the XY model in two dimensions are sparse. Here we use neutron triple-axis spectroscopy to investigate the critical static and dynamical magnetic fluctuations in the square-lattice antiferromagnets Ca2RuO4 and Ca3Ru2O7. We probe the temperature dependence of the antiferromagnetic Bragg intensity, the Q width, the amplitude, and the energy width of the magnetic diffuse scattering in the vicinity of the Neel temperature T-N to determine the critical behavior of the magnetic order parameter M, correlation length xi, susceptibility chi, and the characteristic energy Gamma with the corresponding critical exponents beta, nu, gamma, and z, respectively. We find that the critical behaviors of the single-layer compound Ca2RuO4 follow universal scaling laws that are compatible with predictions of the two-dimensional (2D) XY model. The bilayer compound Ca3Ru2O7 is only partly consistent with the 2D XY theory and best described by the three-dimensional (3D) Ising model, which is likely a consequence of the intrabilayer exchange interactions in combination with an orthorhombic single-ion anisotropy. Hence, our results suggest that layered ruthenates are promising solid-state platforms for research on the 2D XY model and the effects of 3D interactions and additional spin-space anisotropies on the magnetic fluctuations.…