(M = Cr, Cu) by first-principles calculations*

Multiferroic metal-organic framework (MOF) [C(NH₂)₃]M(HCOO)₃ (M = Cr, Cu) adopts a hybrid perovskite ABX₃ structure. Jahn-Teller distortion is responsible for both the weak-ferromagnetism and ferroelectricity in these materials. Unlike the M = Cu analogue which has been well studied, the [C(NH₂)₃]Cr(HCOO)₃ has been synthesized very recently [1] overcoming the rapid oxidation of Cr²⁺. The measurements of its magnetic properties following the successful synthesis exhibit quantitative deviation from the previous theoretical estimations [2]. In order to resolve this discrepancy, we performed the density functional theory calculations and the Monte Carlo simulations to improve the previous estimations. In addition, we suggest two unusual aspects of the electronic and magnetic properties of these materials. In terms of the Landau free energy theory, the polar distortion mode in these materials appears by the trilinear coupling to two non-polar modes (hybrid improper ferroelectricity) [2]. Interestingly, the combination of the two non-polar modes, i.e., the hybrid mode, is the main origin of polarization in these materials [3]. In the M = Cu case, we found that the orbital magnetic moment is a main contribution to the weak-ferromagnetism [1].

[1] K. Yananose et al., Inorg. Chem. 2023, 62, 42, 17299–17309

[2] A. Stroppa et al., Adv. Mater. 2013, 25, 2284–2290.

[3] K. Yananose et al., arXiv.2202.06537, in preparation.