Quantum Anomalous Hall State in Ferromagnetic SrRuO${}_3$ (111) Bilayers

Abstract

SrRuO${}_3$ heterostructures grown in the (111) direction are a rare example of thin film ferromagnets. By means of density functional theory plus dynamical mean field theory we show that the half-metallic ferromagnetic state with an ordered magnetic moment of 2${\mu }_B$/Ru survives the ultimate dimensional confinement down to a bilayer, even at elevated temperatures of 500K. In the minority channel, the spin-orbit coupling opens a gap at the linear band crossing corresponding to $\frac{3}{4}$ filling of the $t_{2g}$ shell. We demonstrate that the respective state is Haldane's quantum anomalous Hall state with Chern number $C$=1, without an external magnetic field or magnetic impurities.

5 pages, 3 figures

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