The “Hall effect” or “anomalous Hall effect” occurs when an electric current flows through a conductor or magnet in a magnetic field, creating a voltage perpendicular to the directions of the electric and magnetic fields. Onsager’s reciprocal theorem, a fundamental theorem in materials science, states that the direction of electron deflection remains constant regardless of the direction of the current in a plane perpendicular to the magnetic field or magnetization.

A phenomenon that contradicts this theorem has not yet been discovered. In this study, researchers observed for the first time the anisotropic anomalous Hall effect in NiCo spinel oxide thin film.₂HE₄ with conical magnetic anisotropy; This property depends on the direction of the current.

Phenomenological perspective and theoretical model

To understand this phenomenon, researchers evaluated the symmetry of the experimentally observed anisotropic anomalous Hall effect from a phenomenological perspective. The results showed the involvement of a magnetic structure called a cluster magnetic toroidal quadrupole.

As a result, they proposed a physical model that explains the anisotropic anomalous Hall effect without violating Onsager’s reciprocal theorem. This model successfully explains the coexistence of magnetic toroidal quadrupoles and ferromagnetism due to conical magnetic anisotropy.