The Curie-Weiss law is widely used to estimate the strength of frustration in spin liquid materials. However, the Curie-Weiss law was originally derived as an estimate of magnetic correlations close to a mean-field phase transition, which – by definition – is absent in spin liquids. Consequently, certain materials were reported to exhibit deviations from the Curie-Weiss law, making a conclusive determination of their Curie-Weiss temperature challenging, especially when the high-temperature regime becomes inaccessible in experiments.
In this work, we show that the concept of a ”Curie-law crossover” (see Fig.1) provides an accurate description of the thermodynamic properties in spin liquids. We study the generic aspect of the Curie-law crossover by comparing a variety of frustrated spin models in two and three dimensions, using both classical Monte Carlo simulations and analytical Husimi tree calculations. While the Husimi tree approximation is quantitatively accurate for all temperatures, we find that the crossover is influenced by the structure of the frustrated unit cell, rather than its lattice dimension. As a complement to traditional methods, we propose an “easy-to-use” fitting Ansatz of the reduced susceptibility, χT, which can be used to estimate the Curie-Weiss temperature, even when the high-temperature regime is not accessible in experiment. Applications to spin liquid candidate materials such as the S=1 pyrochlore magnet NaCaNi2F7, the square-kagome material KCu6AlBiO4(SO4)5Cl, and the spiral-spin liquid FeCl3 are discussed.

This work was published as “Curie-law crossover in spin liquids“, Rico Pohle and Ludovic D. C. Jaubert,
Phys. Rev. B 108, 024411 (2023).