Atomic order of rare earth ions in a complex oxide: a path to magnetotaxial anisotropy.

Complex oxides offer rich magnetic and electronic behavior intimately tied to the composition and arrangement of cations within the structure. Rare earth iron garnet films exhibit an anisotropy along the growth direction which has long been theorized to originate from the ordering of different cations on the same crystallographic site. Here, we directly demonstrate the three-dimensional ordering of rare earth ions in pulsed laser deposited (EuxTm1-x)3Fe5O12 garnet thin films using both atomically-resolved elemental mapping to visualize cation ordering and X-ray diffraction to detect the resulting order superlattice reflection. We quantify the resulting ordering-induced 'magnetotaxial' anisotropy as a function of Eu:Tm ratio using transport measurements, showing an overwhelmingly dominant contribution from magnetotaxial anisotropy that reaches 30 kJ m-3 for garnets with x = 0.5. Control of cation ordering on inequivalent sites provides a strategy to control matter on the atomic level and to engineer the magnetic properties of complex oxides.