Inverse Design of2D Altermagnetic Metal–OrganicFramework Monolayers from Huckel Theory of Nonbonding MolecularOrbitals

Altermagnets, characterized by spontaneous spin-splitting without net magnetization, are challenging to realize due to their unique spin group symmetries. Two-dimensional (2D) magnetic metal–organic frameworks (MOFs), with tunable topologies and spins, offer promising platforms for achieving altermagnetism. In this study, we propose a general strategy to create 2D altermagnetic monolayers by bridging Cr with organic ligands exhibiting nonbonding molecular orbitals (NBMOs) based on the Hückel molecular orbital theory and first-principles calculations. Three 2D MOFs, namely, Cr(diz)₂, Cr(<i>c</i>-pyr)₂, and Cr(<i>f</i>-pid)₂ (diz = 1,3-diazete, <i>c</i>-pyr = pyrrolo[3,4-<i>c</i>]pyrrole, <i>f</i>-pid = pyrrolo[3,4-<i>f</i>]isoindole), are constructed using this strategy and exhibit the altermagntic ground state. These MOFs possess the spin point group ²4̅¹<i>m</i>²2 and exhibit critical temperatures reaching up to 183 K. Analyses of orbital symmetry and energy levels rationalize the presence of altermagnetism. Our findings highlight the critical role of NBMOs in realizing 2D-MOF-based altermagnets with enhanced critical temperatures.