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Concepts from the linear magnetoelectric effect that might be useful for antiferromagnetic spintronics

We discuss the correspondence between the current-induced spin polarization in non-centrosymmetric magnetic metals and the linear magnetoelectric effect in non-centrosymmetric magnetic insulators using a linear-response theory and the concept of magnetoelectric multipoles. We show that the magnetoelectric toroidal moment is a particularly useful quantity since it determines the ground-state antiferromagnetic domain of a non-centrosymmetric antiferromagnet in the presence of a steady-state electric current. We analyze two prototypical antiferromagnetic spintronic materials— Mn 2 Au and CuMnAs—and show that the experimentally reported domain reorientations are consistent with the alignment of their toroidal moments parallel to the applied electric current. Finally, we determine whether similar behavior should be expected in the prototypical insulating magnetoelectric materials, Cr 2 O 3 and Li M PO 4, if they could be doped into a semiconducting or metallic regime.