Hidden orders and (anti-)magnetoelectric effects in Cr₂O₃ and -Fe₂O₃

We present ab initio calculations of hidden magnetoelectric multipolar order in Cr2O3 and its iron-based analog, alpha-Fe2O3. First, we discuss the connection between the order of such hidden multipoles and the linear magnetoelectric effect. Next we show the presence of hidden antiferroically ordered magnetoelectric multipoles in both the prototypical magnetoelectric material Cr2O3 and centrosymmetric alpha-Fe2O3, which has the same crystal structure as Cr2O3 but a different magnetic dipolar ordering. In turn, we predict antimagnetoelectric effects, in which local magnetic dipole moments are induced in opposite directions under the application of an uniform external electric field to create an additional antiferromagnetic ordering. We confirm the predicted induced moments using first-principles calculations. Our results demonstrate the existence of hidden magnetoelectric multipoles leading to local linear magnetoelectric responses even in centrosymmetric magnetic materials, where a net bulk linear magnetoelectric effect is forbidden by symmetry, and broaden the definition of magnetoelectric materials by including those showing such local magnetoelectric responses.