Breaking Onsager's Rule: Theoretical Model Resolves Hall Effect Anomaly

Our understanding of how magnets and electricity interact took an unexpected turn with a new observation. Scientists have discovered an anomalous Hall effect that breaks a fundamental principle - Onsager's reciprocal theorem - for the first time.

The Hall effect describes how a magnetic field deflects electrons flowing through a material, creating a voltage perpendicular to both fields. Onsager's theorem states that this deflection direction remains constant, regardless of the current's direction within the plane perpendicular to the magnetic field.

However, researchers studying a thin film of the material NiCo2O4 observed a twist. This film exhibits a conical magnetic anisotropy, meaning its magnetic moments spiral in a cone-like fashion. In this material, the Hall effect's deflection direction depends on the current's direction, defying the established rule.

Unlocking the Mystery:

To understand this anomaly, the researchers analyzed the symmetry of the observed effect. They concluded that a specific magnetic structure - a clustered magnetic toroidal quadrupole - played a crucial role. 

This structure generates a distinct type of magnetic torque that alters the electron deflection based on the current's direction.

Furthermore, they proposed a theoretical model that explains this behavior without violating Onsager's theorem. This model highlights the interplay between the conical magnetic anisotropy, which allows for the toroidal quadrupole structure, and the inherent ferromagnetism of the material.

This discovery unveils a previously unknown behavior in the interaction between magnetism and electricity. It opens up new avenues for exploring unconventional magnetic phenomena and designing novel spintronic devices with unique properties. 

Additionally, it challenges established principles and encourages further investigation into the complex interplay between spin and charge in materials.


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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