Hidden Order in Cr₂O₃ and α-Fe₂O₃ as a Predictor for (anti-)Magnetoelectricity

With first-principles calculations of Cr₂O₃ and its iron-based analog, α-Fe₂O₃, we show that the different magnetoelectric effects in these materials result from the ordering of hidden magnetic multipoles [1]. Starting from the established connection between ferroically-ordered magnetic quadrupoles and the linear magnetoelectric effect in Cr₂O₃, we explore the presence of additional multipoles. We reveal for the first time anti-ferroically ordered magnetic multipoles in both Cr₂O₃, and isostructural α-Fe₂O₃, in which the global inversion symmetry is preserved by the different magnetic dipolar ordering. Using symmetry considerations, we can relate each of these multipoles and their ordering to linear, quadratic, and cubic (anti-) magnetoelectric effects, where in an anti-magnetoelectric effect the induced moments are ordered antiferromagnetically in the unit cell. We confirm the predicted induced moments using first-principles calculations, showing the lowest response in α-Fe₂O₃, a centrosymmetric magnetic material, to be a linear anti-magnetoelectric effect, revealing the presence of the magnetoelectric coupling despite the preserved global inversion symmetry. Our results demonstrate the existence of hidden magnetic multipoles leading to local linear magnetoelectric responses, even in centrosymmetric magnetic materials, and broaden the definition of magnetoelectric materials by including those showing such local magnetoelectric responses.<br/><br/>References:<br/>[1] X. H. Verbeek, et al., arXiv:2303.00513<br/>&lt;!--[if !supportLineBreakNewLine]--&gt;<br/>&lt;!--[endif]--&gt;