Uncovering anisotropic magnetic phases via fast dimensionality analysis

A quantitative geometric predictor for the dimensionality of magnetic interactions is presented. This predictor is based on networks of superexchange interactions and can be quickly calculated for crystalline compounds of arbitrary chemistry, occupancy, or symmetry. The resulting data is useful for classifying structural families of magnetic compounds. Starting with 42,520 compounds, we have classified and quantified compounds with $3d$ transition metal cations. The predictor reveals trends in magnetic interactions that are often not apparent from the space group of the compounds, such as triclinic or monoclinic compounds that are strongly 2D. We present specific cases where the predictor identifies compounds that should exhibit competition between 1D and 2D interactions, and how the predictor can be used to identify sparsely-populated regions of chemical space with as-yet-unexplored topologies of specific $3d$ magnetic cations. The predictor can be accessed for the full list of compounds using a searchable web form, and further information on the connectivity, symmetry, and valence of cation-anion and cation-cation coordination can be freely exported.