Topological spin multipolization and linear magnetoelectric coupling in two-dimensional antiferromagnets

In this paper we predict that the magnetoelectric response of two-dimensional (2D) antiferromagnets is determined by the topology of the ground state. This topological magnetoelectric response, encoded in the spin magnetoelectric polarizability and its closely related spin multipolization, occurs when the electronic structure of the antiferromagnetic insulator is described by massive 2D Dirac fermions, and is therefore native to 2D, unlike the topological magnetoelectric effect of three-dimensional topological insulators. To demonstrate the topological contribution to the (spin) magnetoelectric polarizability, we compute the magnetoelectric polarizability microscopically for two distinct minimal lattice models: a spin-orbit coupled N\'eel antiferromagnet and a spin-orbit-free noncollinear antiferromagnet with double-$Q$ spin order. We show that the topological origin of the revealed magnetoelectric effect can be traced back to the electromagnetic response of topological semimetals in two dimensions, and hence is ultimately governed by a strong topological invariant in one dimension. Given this dimensional hierarchy, we further consider two minimal lattice models in one dimension, both one-dimensional variants of the 2D lattice models, and show that the magnetoelectric polarizability exhibits a clear signature of nontrivial crystalline topology. Possible material realizations are discussed.