Cluster multipole theory for anomalous Hall effect in antiferromagnets

Abstract

We introduce a cluster extension of multipole moments to discuss the anomalous Hall effect (AHE) in both ferromagnetic (FM) and antiferromagnetic (AFM) states in a unified framework. We first derive general symmetry requirements for the AHE in the presence or absence of the spin-orbit coupling, by considering the symmetry of the Berry curvature in k space. The cluster multipole (CMP) moments are then defined to quantify the macroscopic magnetization in non-collinear AFM states, as a natural generalization of the magnetization in FM states. We identify the macroscopic CMP order which induces the AHE. The theoretical framework is applied to the non-collinear AFM states of Mn3Ir, for which an AHE was predicted in a first-principles calculation, and Mn3Z (Z=Sn, Ge), for which a large AHE was recently discovered experimentally. We further compare the AHE in Mn3Z and bcc Fe in terms of the CMP. We show that the AHE in Mn3Z is characterized with the magnetization of a cluster octupole moment in the same manner as that in bcc Fe characterized with the magnetization of the dipole moment.

Large magneto-optical Kerr effect and imaging of magnetic octupole domains in an antiferromagnetic metal

“…In particular, we find that despite a vanishingly small magnetization of M ~0.002 µ B /Mn, the non-collinear AF metal Mn 3 Sn 15 exhibits a large zero-field MOKE with a polar Kerr rotation angle of 20 milli-degrees, comparable to ferromagnetic metals. Our first-principles calculations have clarified that ferroic ordering of magnetic octupoles in the non-collinear Néel state 16 may cause a large MOKE even in its fully compensated AF state without spin magnetization. This large MOKE further allows imaging of the magnetic octupole domains and their reversal induced by magnetic field.…”

Room-temperature terahertz anomalous Hall effect in Weyl antiferromagnet Mn3Sn thin films

“…Below the Néel temperature 420 K, the spins on Mn atoms order in an inverse triangular spin structure, where the spins form a 120-degree order with negative vector chirality in the ab plane. Such a noncollinear antiferromagnetic spin in the Kagome bilayer is characterized by cluster magnetic octupole moments 18 , which macroscopically breaks time-reversal symmetry and is expected to result in the appearance of Weyl nodes [14][15][16][17][18] . The small net magnetization occurs in the ab plane by slight canting of the 120-degree order.…”

Anomalous Nernst and Righi-Leduc Effects in Mn3Sn : Berry Curvature and Entropy Flow

“…Recently, following a proposition by Chen, Niu and Macdonald[9], Nakasutji et al and Nayak et al found a large AHE in Mn 3 Sn [10] and Mn 3 Ge [11,12], which are noncollinear antiferromagnets at room temperature. Several recent theoretical studies were devoted to this issue [13][14][15].In this letter, we present a study of Anomalous Righi-Leduc and Nernst effects (ANE) in Mn 3 Sn in order to quantify the amplitude of these coefficients compared to their Hall counterpart.We detect a large Anomalous Righi-Leduc conductivity and find that its magnitude corresponds to what is expected according to the Wiedemann-Franz (WF) Law over an extended temperature window. The result confirms a theoretical prediction by Haldane[16] with important consequences for the debate regarding the two alternative formulations of anomalous Hall effect [16][17][18].…”

“…Recently, following a proposition by Chen, Niu and Macdonald [9], Nakasutji et al and Nayak et al found a large AHE in Mn 3 Sn [10] and Mn 3 Ge [11,12], which are noncollinear antiferromagnets at room temperature. Several recent theoretical studies were devoted to this issue [13][14][15].…”