Realization of the Ruby Lattice Antiferromagnet in Layered Transition-Metal Fluorides

The antiferromagnet on the ruby lattice is expected to host a range of exotic emergent phenomena, yet its material realization has remained elusive. Here we show that the layered transition metal fluorides CsBaFe$_3$F$_{12}$ and CsBaCr$_3$F$_{12}$ with Fe$^{3+}$ and Cr$^{3+}$ ions realize only slightly distorted ruby lattice geometries with spin moments $S=5/2$ and $S=3/2$, respectively. Their microscopic Hamiltonians, calculated with DFT energy mapping, are dominated by short-ranged antiferromagnetic interactions within the ruby layers. Classical Monte Carlo simulations reveal strong frustration in both compounds, with local N\'eel correlations on the hexagonal plaquettes and distinct long-range ordering tendencies governed by weaker triangular links. For CsBaFe$_3$F$_{12}$, the calculated thermodynamic behaviour is consistent with the experimentally reported magnetic ordering scale. For CsBaCr$_3$F$_{12}$, classical Monte Carlo and Luttinger-Tisza analysis reveal competing low-energy ordering wave vectors, strong finite-size sensitivity, and a tendency toward incommensurate order. Overall, our results establish these fluorides as experimentally accessible ruby-lattice antiferromagnets and provide quantitative predictions for future neutron-scattering studies.