Quantum Anomalous Hall Effect in Kagome Ice

An anomalous Hall insulator without magnetic long-range ordering is theoretically reported in the absence of the relativistic spin-orbit coupling. It is realized in itinerant electrons coupled with the Ising spins on a <111> kagome plane of pyrochlore spin ice in applied magnetic field. We find that the kagome-ice type local spin correlation in the magnetization plateau state opens a charge gap without magnetic ordering, which results in quantization of the Hall conductivity. By Monte Carlo simulation, we identify the anomalous Hall insulating region in the magnetic phase diagram, in addition to another anomalous Hall insulator in a fully-saturated state.