Cluster multipole theory for anomalous Hall effect in antiferromagnets*

Recently, it has been theoretically and experimentally shown that antiferromagnets such as Mn₃Ir, Mn₃Sn and Mn₃Ge exhibit extremely large anomalous Hall effect (AHE) [1,2,3,4,5], anomalous Nernst effect (ANE) [6,7], and magneto-optical Kerr effect (MOKE) [8]. While AHE/ANE/MOKE in ferromagnets usually scale with the magnetization of the system, it is a non-trivial problem which macroscopic order parameter determines these effects in antiferromagnets. In this talk, we introduce a new order parameter, which we call cluster multipole (CMP) moment, and show that CMP is useful to classify the magnetic structure and discuss the physical properties of antiferromagnets. In particular, we demonstrate that AHE in Mn₃Sn and that in elemental Fe can be described in the unified scheme using CMP [9]. We also discuss how CMP is useful for constructing database for magnets and designing functional antiferromagnets.

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