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 ($\theta =0.1$–$0.2$). 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.

Figure 1

Sketch of one out of 30 canonical structures in which isotropic ME coupling ${\alpha }^{\mathrm{iso}}$ is allowed by symmetry. Atoms (gray spheres) are displaced in the direction of their magnetic moments (arrows). These displacements change the network of corner sharing tetrahedra by shrinking half of the tetrahedra (red) and enlarging the other half (blue).

Figure 2

First-principles fully relativistic computed band structure of Zn${}_2$Os${}_2$O${}_7$ with partial Te substitution (Zn${}_2$Os${}_2$O${}_{6.5}$Te${}_{0.5}$).