Strain Coupling and Dynamic Relaxation in a Molecular Perovskite-Like Multiferroic Metal–Organic Framework

Magnetic metal–organic frameworks (MOFs) with a perovskite structure AMX₃ are emerging single-phased multiferroics with different sources of magnetic and electric ordering. However, the atomic mechanism underlying the multiple ferroic coupling is convincingly clarified. In this work, large single crystals of [(CH₃)₂NH₂][Ni(HCOO)₃] are synthesized and shown to exhibit a first-order ferroelectric phase transition at ≈178 K during heating and at ≈151 K during cooling, as confirmed by temperature-dependent differential scanning calorimetry, Raman scattering, and X-ray diffraction studies. Resonant ultrasound spectroscopy (RUS) is used to investigate the elastic and anelastic properties between 5 and 300 K. The RUS results show an abrupt disappearance of resonance peaks above the ferroelectric transition point of ≈178 K. This is probably due to the unfreezing of dimethylammonium cation motion which couples with local strain. Small changes in elastic properties associated with two known magnetic transition at ≈35 and ≈15 K, respectively, are indicative of weak magnetoelastic coupling. An apparent peak in acoustic loss accompanying the canted antiferromagnetic ordering (≈35 K) and spin reorientation transition (≈15 K) is attributed to dynamical magnetoelastic coupling on the RUS time scale of ≈10⁻⁶ s. In comparison with the same MOF structures containing Mn²⁺ and Co²⁺, the smaller Ni²⁺ ions effectively generate an internal chemical pressure and induce a compressed ion force on the anion frameworks. This study opens up a new landscape to explore possibilities for ferroic-order coupling in molecular MOFs.