Multiferroicity in the Two-Dimensional Limit in Hexagonal LuFeO_{3} Films

Multiferroic oxides, which host coexisting ferroelectric and magnetic orders, are central to understanding correlated quantum phenomena. Yet, as thickness approaches the two-dimensional (2D) limit, both ferroelectricity and magnetism are generally expected to be strongly suppressed by depolarization fields and finite-size effects, respectively. Here, we show that hexagonal LuFeO_{3} (h-LuFeO_{3}) retains multiferroic behavior down to a thickness of only one and a half unit cells. The polar structural distortion remains robust at room temperature and is comparable to that of the bulk, while robust magnetic order persists at low temperatures. We further find that the magnetic response can be reproducibly modulated through ferroelectric domain-state control. Structural analysis indicates that the K_{3} distortion remains stable down to the two-dimensional limit, providing the basis for the survival of improper ferroelectricity in this regime. These results establish h-LuFeO_{3} as an oxide platform in which ferroelectricity and magnetic order coexist at the atomic-scale limit, and provide insight into how coupled ferroic behavior can persist in ultrathin complex oxides.