  Using tight-binding models and first-principles calculations, we demonstrate
the possibility to achieve a quantum anomalous Hall (QAH) phase on a
two-dimensional square lattice, which can be realized in monolayers of double
perovskites. We show that effective intersite spin-orbit coupling between eg
orbitals can be induced perturbatively, giving rise to a QAH state. Moreover,
the effective spin-orbit coupling can be enhanced by octahedral rotations.
Based on first-principles calculations, we propose that this type of QAH state
could be realized in La2MnIrO6 monolayers, with the size of the gap as large as
26 meV in the ideal case. We observe that the electronic structure is sensitive
to structural distortions, and that an enhanced Hubbard U tends to stabilize
the nontrivial gap.
