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In metal-organic-framework (MOF) perovskites, both magnetic and ferroelectricorderings can be readily realized by compounding spin and charge degrees offreedom. The hydrogen bonds that bridge the magnetic framework and organicmolecules have long been thought of as a key in generating multiferroicproperties. However, the underlying physical mechanisms remain unclear. Here,we combine neutron diffraction, quasielastic and inelastic neutron scattering,and THz spectroscopy techniques to thoroughly investigate the dynamicalproperties of the multiferroic MOF candidate [CH$_3$NH$_3$][Co(HCOO)$_3$]through its multiple phase transitions. The wide range of energy resolutionsreachable by these techniques enables us to scrutinize the coupling between themolecules and the framework throughout the phase transitions and interrogate apossible magnetoelectric coupling. Our results also reveal a structural changearound 220 K which may be associated with the activation of a nodding donkeymode of the methylammonium molecule due to the ordering of the CH$_3$ groups.Upon the occurrence of the modulated phase transition around 130 K, themethylammonium molecules undergo a freezing of its reorientational motionswhich is concomitant with a change of the lattice parameters and anomalies ofcollective lattice vibrations. No significant change has been however observedin the lattice dynamics around the magnetic ordering, which therefore indicatesthe absence of a substantial magneto-electric coupling in zero-field.

Lattice dynamics and spin excitations in the metal-organic framework [CH$_3$NH$_3$][Co(HCOO)$_3$]