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The sawtooth chain compound CsCo 2 (MoO 4 ) 2 (OH) is a complex magnetic system and here, we present a comprehensive series of magnetic and neutron scattering measurements to determine its magnetic phase diagram. The magnetic properties of CsCo 2 (MoO 4 ) 2 (OH) exhibit a strong coupling to the crystal lattice and its magnetic ground state can be easily manipulated by applied magnetic fields. There are two unique Co 2+ ions, base and vertex, with J bb and J bv magnetic exchange. The magnetism is highly anisotropic with the b -axis (chain) along the easy axis and the material orders antiferromagnetically at T N = 5 K. There are two successive metamagnetic transitions, the first at H c 1 = 0.2 kOe into a ferrimagnetic structure, and the other at H c 2 = 20 kOe to a ferromagnetic phase. Heat capacity measurements in various fields support the metamagnetic phase transformations, and the magnetic entropy value is intermediate between S = 3/2 and 1/2 states. The zero field antiferromagnetic phase contains vertex magnetic vectors (Co(1)) aligned parallel to the b -axis, while the base vectors (Co(2)) are canted by 34° and aligned in an opposite direction to the vertex vectors. The spins in parallel adjacent chains align in opposite directions, creating an overall antiferromagnetic structure. At a 3 kOe applied magnetic field, adjacent chains flip by 180° to generate a ferrimagnetic phase. An increase in field gradually induces the Co(1) moment to rotate along the b -axis and align in the same direction with Co(2) generating a ferromagnetic structure. The antiferromagnetic exchange parameters are calculated to be J bb = 0.028 meV and J bv = 0.13 meV, while the interchain exchange parameter is considerably weaker at J ch = (0.0047/ N ch ) meV. Our results demonstrate that the CsCo 2 (MoO 4 ) 2 (OH) is a promising candidate to study new physics associated with sawtooth chain magnetism and it encourages further theoretical studies as well as the synthesis of other sawtooth chain structures with different magnetic ions. 

Owing to their overall low energy scales, flexible molecular architectures, and ease of chemical substitution, molecule-based multiferroics are extraordinarily responsive to external stimuli and exhibit remarkably rich phase diagrams. Even so, the stability and microscopic properties of various magnetic states in close proximity to quantum critical points are highly under-explored in these materials. Inspired by these opportunities, we combined pulsed-field magnetization, first-principles calculations, and numerical simulations to reveal the magnetic field–temperature (B–T) phase diagram of multiferroic (NH₄)₂FeCl₅⋅H₂O. In this system, a network of intermolecular hydrogen and halogen bonds creates a competing set of exchange interactions that generates additional structure in the phase diagram—both in the vicinity of the spin flop and near the 30 T transition to the fully saturated state. Consequently, the phase diagrams of (NH₄)₂FeCl₅⋅H₂O and its deuterated analog are much more complex than those of other molecule-based multiferroics. The entire series of coupled electric and magnetic transitions can be accessed with a powered magnet, opening the door to exploration and control of properties in this and related materials.