Critical magnetic fluctuations in the layered ruthenates Ca$_2$RuO$_4$ and Ca$_3$Ru$_2$O$_7$

TL;DR

This study investigates magnetic fluctuations in layered ruthenates Ca$_2$RuO$_4$ and Ca$_3$Ru$_2$O$_7$ using neutron spectroscopy, revealing 2D-XY critical behavior in the single-layer and 3D-Ising behavior in the bilayer compound.

Contribution

It provides experimental evidence of 2D-XY critical behavior in Ca$_2$RuO$_4$ and highlights the influence of interlayer interactions and anisotropy in Ca$_3$Ru$_2$O$_7$, advancing understanding of magnetic models in layered materials.

Findings

Ca$_2$RuO$_4$ follows 2D-XY universality class.

Ca$_3$Ru$_2$O$_7$ exhibits 3D-Ising critical behavior.

Layered ruthenates are promising for studying 2D magnetic models.

Abstract

Materials realizing the XY model in two dimensions (2D) 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 (AFM) Bragg-intensity, the $Q$-width, the amplitude, and the energy-width of the magnetic diffuse scattering in vicinity to the N\'eel 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 Ca$_{2}$RuO$_{4}$ follow universal scaling laws that are compatible with predictions of the 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 Ising (3D-I) model, which is likely a consequence of the intra-bilayer 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.