  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.
