Electronic Supplementary Information: Experimental Method and Supplementary Figures from Emergent magnetic order and correlated disorder in formate metal-organic frameworks

Magnetic materials with strong local interactions but lacking long-range order have long been a curiosity of physicists. Probing their magnetic interactions is crucial for understanding the unique properties they can exhibit. Metal-organic frameworks have recently gathered more attention as they can produce more exotic structures, allowing for controlled design of magnetic properties not found in conventional metal-oxide materials. Historically, magnetic diffuse scattering in such materials have been overlooked but has attracted greater attention recently, with advances in techniques. In this study, we investigate the magnetic structure of metal-organic formate frameworks, using heat capacity, magnetic susceptibility and neutron diffraction. In Tb(DCO₂)₃, we observe emergent magnetic order at temperatures below 1.2 K, consisting of two k-vectors. Ho(DCO₂)₃ shows diffuse scattering above 1.6 K, consistent with ferromagnetic chains packed in a frustrated antiferromagnetic triangular lattice, also observed in Tb(DCO₂)₃ above 1.2 K. The other lanthanides show no short- or long-range order down to 1.6 K. The results suggest an Ising-like one-dimensional magnetic order associated with frustration is responsible for the magnetocaloric properties, of some members in this family, improving at higher temperatures.This article is part of the theme issue ‘Mineralomimesis: natural and synthetic frameworks in science and technology’.