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Discovery of a New Hall Effect: Does It Violate Onsager's reciprocal theorem?

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Researchers at the University of Tsukuba and NIMS have observed a novel Hall effect wherein the deflection direction of current varies according to the current flow direction. Onsager's reciprocal theorem, a fundamental theorem in materials science, asserts the impossibility of such a phenomenon. However, the researchers found that the observed phenomenon could be explained without contradicting the reciprocal theorem by assuming an unconventional magnetic arrangement.

Tsukuba, Japan—The "Hall effect" or "anomalous Hall effect" occurs when electric current flows through a conductor or magnet in a magnetic field, generating voltage perpendicular to the electric and magnetic field directions. Onsager's reciprocal theorem, a fundamental theorem in materials science, states that the deflection direction of electrons remains constant, irrespective of the current's direction in the plane perpendicular to the magnetic field or magnetization. A phenomenon contradicting this theorem has not been discovered until now. In this study, for the first time, researchers have observed an anisotropic anomalous Hall effect in a spinel oxide NiCo2O4 thin film with conical magnetic anisotropy; this characteristic depends on the current's direction.

To understand this phenomenon, researchers considered the symmetry of the experimentally observed anisotropic anomalous Hall effect from a phenomenological perspective. The findings indicated the involvement of a magnetic structure termed a clustered magnetic toroidal quadrupole. Consequently, they proposed a physical model that explained the anisotropic anomalous Hall effect without violating Onsager's reciprocal theorem. This model successfully accounts for the coexistence of the magnetic toroidal quadrupole and ferromagnetism owing to conical magnetic anisotropy.

This work was performed under the approval of the "Photon Factory Program Advisory Committee" (proposals No.2017G602 and No.2016S2-005). This project is partly supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI (23H01842:H.Y., 22H04966:H.Y., 21H01750:H.Y. and 19H04399:Y.Y.) and TIA-Kakehashi (TK22-023:H.Y. and TK23-017:H.Y.). This work is also partially supported by PRESTO (JPMJPR177A:Y.Y.) and CREST(JPMJCR1861:Y.Y.), Japan Science and Technology Agency (JST). H.K. acknowledges partly supports of Grant-in-Aid for JSPS Fellows (20J10749:H.K. and 22J00871:H.K.).

Original Paper

Title of original paper:
Quadrupole anomalous Hall effect in magnetically induced electron nematic state
Nature Communications


Professor YANAGIHARA Hideto
Institute of Pure and Applied Sciences, University of Tsukuba

Research and Services Division of Materials Data and Integrated System (MaDIS), National Institute for Materials Science (NIMS)

Assistant Professor KOIZUMI Hiroki
Center for Science and Innovation in Spintronics (CSIS), Tohoku University (Affiliation at the time of research: Degree Programs in Pure and Applied Sciences, Graduate School of Science and Technology, University of Tsukuba)

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