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

Abstract

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 Néel 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.

11+8 pages, 7+5 figures