  Magnetic nanoarray with special geometries exhibits nontrivial collective
behaviors similar to those observed in the spin ice materials. Here we present
a novel circuit model to describe the complex magnetotransport phenomena in
artificial kagome spin ice. In this picture, the system can be viewed as a
resistor network driven by voltage sources that are located at vertices of the
honeycomb array. The differential voltages across different terminals of these
sources are related to the ice-rules that govern the local magnetization
ordering. The circuit model relates the transverse Hall voltage of kagome ice
to the underlying spin correlations. Treating the magnetic nanoarray as
metamaterials, we present a mesoscopic constitutive equation relating the Hall
resistance to magnetization components of the system. We further show that the
Hall signal is significantly enhanced when the kagome ice undergoes a
magnetic-charge ordering transition. Our analysis can be readily generalized to
other lattice geometry, providing a quantitative method for the design of
magnetoresistance devices based on artificial spin ices.
