Canonical magnetic insulators with isotropic magnetoelectric coupling

We have performed a systematic representation-theory-based search for the simplest structures allowing isotropic magnetoelectric coupling. We find 30 such structures, all sharing a common pattern of atomic displacements in the direction of atomic magnetic moments. We focus on one of these 30 canonical structures and find that it is generically realized in a class of fractionally substituted pyrochlore compounds with an all-in-all-out magnetic order. Furthermore, we find that these substituted pyrochlore compounds have a substantial Chern-Simons orbital magnetoelectric component (θ=0.1-0.2). While this component is also formally present in strong Z₂ topological insulators (θ=π), its effects are observable there only if time-reversal symmetry is broken at the surface.