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Materials that exhibit simultaneous order in their electric and magnetic ground states hold promise for use in next-generation memory devices in which electric fields control magnetism^,. Such materials are exceedingly rare, however, owing to competing requirements for displacive ferroelectricity and magnetism. Despite the recent identification of several new multiferroic materials and magnetoelectric coupling mechanisms^,,,,,,,,,,,, known single-phase multiferroics remain limited by antiferromagnetic or weak ferromagnetic alignments, by a lack of coupling between the order parameters, or by having properties that emerge only well below room temperature, precluding device applications. Here we present a methodology for constructing single-phase multiferroic materials in which ferroelectricity and strong magnetic ordering are coupled near room temperature. Starting with hexagonal LuFeO₃—the geometric …