A scientific breakthrough challenges established laws of physics! Scientists observed a bizarre twist in the Hall effect, potentially leading to novel spintronic devices and a deeper understanding of magnetism.

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.

## Phenomenological Perspective and Theoretical Model

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.

*Sources: *

*Published 8 December 2023, Nature Communications; “Quadrupole anomalous Hall effect in magnetically induced electron nematic state” *

*DOI: 10.1038/s41467-023-43543-1*

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# Solid State Physics

This comprehensive textbook covers a wide range of topics in solid state physics, including magnetism and the Hall effect.