Hidden orders and (anti-)magnetoelectric effects in Cr_{2}O_{3} and α-Fe_{2}O_{3}

We present ab initio calculations of hidden magnetoelectric multipolar order in Cr_{2}O_{3} and its iron-based analog, α-Fe_{2}O_{3}. 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 Cr_{2}O_{3} and centrosymmetric α-Fe_{2}O_{3}, which has the same crystal structure as Cr_{2}O_{3} 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.