%0 Journal Article %T Canonical magnetic insulators with isotropic magnetoelectric coupling %A Sinisa Coh %A David Vanderbilt %J Physics %D 2013 %I arXiv %R 10.1103/PhysRevB.88.121106 %X We have performed an exhaustive 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 (\theta=0.1--0.2). While this component is also formally present in strong Z_2 topological insulators (\theta=\pi), its effects are observable there only if time-reversal symmetry is broken at the surface. %U http://arxiv.org/abs/1308.2977v2