Manifestation of axion electrodynamics through magnetic ordering on edges of topological insulator

Based on a first-principles approach, we show that in a single crystal of a prototypical topological insulator such as Bi$_2$Se$_3$ the difference in the work function between adjacent surfaces with different crystal-face orientations generates a built-in electric field around facet edges. Owing to the topological magnetoelectric coupling for a given broken time-reversal symmetry in the crystal, the electric field, in turn, forces effective magnetic dipoles to accumulate along the edges, realizing the facet-edge magnetic ordering. We demonstrate that the predicted magnetic ordering which depends only on the work function difference between facets, is in fact a manifestation of the axion electrodynamics in real solids.