θ=π axion angle, half-quantized Hall conductance, and magnetoelectric polarizability
A topological insulator with magnetic coating has an axion angle θ=π, producing a topological magnetoelectric effect: applying B induces P = (αe²/2πh)·B and applying E induces M = (αe²/2πh)·E, where α=e²/ħc. The surface Hall conductance is quantized at σ_xy = (n+½)·e²/h — half an integer due to θ=π. When top and bottom surfaces have opposite magnetic gaps, the system becomes an axion insulator with purely bulk magnetoelectric polarizability.