Magnetic structure and ordering of multiferroic hexagonal LuFeO_{3}

We report on the magnetic structure and ordering of hexagonal LuFeO_{3} films of variable thickness grown by molecular-beam epitaxy on YSZ (111) and Al_{2}O_{3} (0001) substrates. These crystalline films exhibit long-range structural uniformity dominated by the polar P6_{3}cm phase, which is responsible for the paraelectric to ferroelectric transition that occurs above 1000 K. Using bulk magnetometry and neutron diffraction, we find that the system orders into a ferromagnetically canted antiferromagnetic state via a single transition below 155 K regardless of film thickness, which is substantially lower than that previously reported in hexagonal LuFeO_{3} films. The symmetry of the magnetic structure in the ferroelectric state implies that this material is a strong candidate for linear magnetoelectric coupling and control of the ferromagnetic moment directly by an electric field.