Experiments demonstrating the controlled growth of oxide heterostructures have raised the prospect of realizing topologically nontrivial states of correlated electrons in low dimensions. Here, we study heterostructures consisting of $\{111\}$ bilayers of double perovskites separated by inert band insulators. In bulk, these double perovskites have well-defined local moments interacting with itinerant electrons leading to high temperature ferromagnetism. Incorporating spin-orbit coupling in the two-dimensional honeycomb geometry of a $\{111\}$ bilayer, we find a rich phase diagram with tunable ferromagnetic order, topological Chern bands, and a $C=\pm 2$ Chern insulator regime. Our results are of broad relevance to oxide materials such as ${\mathrm{Sr}}_2{\mathrm{FeMoO}}_6$, ${\mathrm{Ba}}_2{\mathrm{FeReO}}_6$, and ${\mathrm{Sr}}_2{\mathrm{CrWO}}_6$.

• Received 1 March 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.077203