Phase competition in quantum critical multiferroics Rb₂Cu₂Mo₃O₁₂ and Cs₂Cu₂Mo₃O₁₂

Rb₂Cu₂Mo₃O₁₂ and Cs₂Cu₂Mo₃O₁₂ are quasi-1D magnets recently demonstrated to host unconventional multiferroic phenomena [1,2]. Despite the close similarity of crystal structure and magnetic phase diagram shapes, only Cs₂Cu₂Mo₃O₁₂ demonstrates dielectric relaxation by magnons [1]. Here, we explore the phase space of the spin ladder model associated with this family of materials using Density Matrix Renormalization Group. We find the model to be in the vicinity of a triple point in the phase space, with three closely competing phases. Comparing the computed spin correlations in different phases with experimental data, we conclude that the ordered phases realized in Rb₂Cu₂Mo₃O₁₂ and Cs₂Cu₂Mo₃O₁₂ are actually different and discuss the consequences for explaining the observed dielectric behavior.

[1] Flavian et al. Phys. Rev. Lett. 130, 216501 (2023)

[2] Hayashida et al., Phys. Rev. Research 3, 033053 (2021)