Inverse Lieb materials: altermagnetism and more

The Lieb lattice, originally proposed for cuprate superconductors, has gained new attention in the emerging field of altermagnetism as a minimal analytical model for the latter. While the inverse Lieb lattice (ILL) was once considered purely theoretical, several materials with this motif have recently been discovered. Its unique geometry supports complex magnetic orders driven by geometric frustration, offering high tunability. In this work, we provide comprehensive insights into ILL magnetic phases and establish guidelines for identifying altermagnets. Using a Heisenberg model, we first construct phase diagrams to elucidate the mechanisms underlying experimental magnetic phases. We then bridge theory and experiment via density functional theory (DFT) calculations on existing ILL compounds, finding results consistent with experimental data. Notably, we identified a trend linking d-shell filling to magnetic order, where dx (x≤5) configurations show a propensity for altermagnetism. We also highlight Sr2CrO2Cr2OAs2 as a promising metallic altermagnet with highly anisotropic J2 exchange and a high Néel temperature (~600 K). Finally, our magnon spectra calculations confirm that chiral splittings correlate directly with anisotropies between inequivalent J2 interactions.