Emergent surface multiferroicity

We show that the surface of a centrosymmetric, collinear, compensated antiferromagnet, which hosts bulk ferroically ordered magnetic octupoles, exhibits a linear magnetoelectric effect, a net magnetization, and a net electric dipole moment. Thus, the surface satisfies all the conditions of a multiferroic, in striking contrast to the bulk, which is neither polar nor exhibits any net magnetization or linear magnetoelectric response. Of particular interest is the case of non-relativistic $d$-wave spin split antiferromagnets, in which the bulk magnetic octupoles and consequently the surface multiferroicity exist even without spin-orbit interaction. We illustrate our findings using first-principles calculations, taking FeF$_2$ as an example material. Our work underscores the bulk-boundary correspondence in these unconventional antiferromagnets.