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.

The elastic properties and the coupling of ferroelasticity with ferromagnetism and ferroelectricy are crucial for the development of multiferroic metal-organic frameworks (MOFs) with strong magnetoelectric coupling. Elastic properties and energy dissipation related to the disorder-order ferroelectric transition in [(CH3)2NH2][Fe(HCOO)3] were studied by differential scanning calorimetry (DSC), low temperature X-ray diffraction (XRD) and dynamic mechanical analysis (DMA). DSC result indicated the transition near 164 K. XRD showed the first-order structural transition from rhombohedral R3−c to monoclinic Cc at ~145 K, accompanied by the disorder-order transition of proton ordering in the N–H…O hydrogen bonds in [(CH3)2NH2]+ as well as the distortion of the framework. For single crystals, the storage modulus was ~1.1 GPa and the loss modulus was ~0.02 GPa at 298 K. DMA of single crystals showed quick drop of storage modulus and peaks of loss modulus and loss factor near the ferroelectric transition temperature ~164 K. DMA of pellets showed the minimum of the normalized storage modulus and the peaks of loss factor at ~164 K with weak frequency dependences. The normalized loss modulus reached the maximum near 145 K, with higher peak temperature at higher frequency. The elastic anomalies and energy dissipation near the ferroelectric transition temperature are caused by the coupling of the movements of dimethylammonium cations and twin walls.

Fragile topological insulator are an exotic phase with unstable edge states. Its nontrivial band topology can be removed by coupling to additional topologically trivial bands. Here we reveal that the fragile band topology can be realized in the inversion symmetric odd parity superconducting nodal line semimetal (SC-NLSM) materials with and without the spin orbital coupling. Without the spin orbital coupling, both the $s$-wave SC-NLSM and the $p$-wave SC-NLSM host a pair of Majorana zero modes on the system surface. For the spinful case, it has fourfold inverted bands and generates fourfold degenerate Majorana surface/edge states. However, we verify that for all of the systems we considered, they belong to the fragile topological superconducting system based on the Wilson loop method. The vortex bound states are studied numerically. Whether the stable Majorana zero modes exist depend strongly on the systems.

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