Critical magnetic fluctuations in the layered ruthenates Ca_{2}RuO_{4} and Ca_{3}Ru_{2}O_{7}

Abstract

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 Ca_{2}RuO_{4} and Ca_{3}Ru_{2}O_{7}. 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 Néel temperature T_{N} to determine the critical behavior of the magnetic order parameter M, correlation length ξ, susceptibility χ, and the characteristic energy Γ with the corresponding critical exponents β, ν, γ, and z, respectively. We find that the critical behaviors of the single-layer compound Ca_{2}RuO_{4} follow universal scaling laws that are compatible with predictions of the two-dimensional (2D) XY model. The bilayer compound Ca_{3}Ru_{2}O_{7} 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.