In this paper, we predict that the magnetoelectric response of two-dimensional (2D) antiferromagnets contains a contribution determined by the topological properties of the ground state. The quasitopological magnetoelectric response, encoded in the spin magnetoelectric polarizability and the 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 topology-induced contribution to the (spin) magnetoelectric polarizability, we compute the magnetoelectric polarizability microscopically for two distinct minimal lattice models: a spin-orbit-coupled Néel 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.

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• Magnetoelectric effect
• Antiferromagnets
• Topological materials
• Tight-binding model