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Aug. 17, 2023 Research Highlight Physics / Astronomy

Quantum question about the anomalous Hall effect is answered

A unifying description for the curving path of electrons in some magnetic materials has been derived

A mysterious magnetic effect that causes the path that electrons take through a material to bend—called the anomalous Hall effect—has been elucidated in a new mathematical analysis by two RIKEN physicists1.

First discovered nearly a century and a half ago by American physicist Edwin Hall, the conventional Hall effect is a well-understood electrical and magnetic phenomenon. When just an electric field is applied to a conducting material, the electrons will move in a straight line that is parallel to that field. But when a magnetic field is added too, it causes the electrons’ path to curve.

The anomalous Hall effect is a related phenomenon that happens in some magnetic materials. In this case, no external magnetic field needs to be applied since the material supplies the magnetic field.

But the cause of the anomalous Hall effect seems to vary between materials. “The difficulty is that there are many possible mechanisms but no unifying explanation,” says Hiroki Isobe of the RIKEN Center for Emergent Matter Science, who co-authored the analysis with RIKEN colleague Naoto Nagaosa. “This makes it very complicated, even for specialists.”

image of graphene

Figure 1: The anomalous Hall effect has been demonstrated in materials such as graphene (pictured). © ELLA MARU STUDIO/SCIENCE PHOTO LIBRARY

The physicists’ goal was to simplify this by finding an underlying explanation for all materials that display the anomalous Hall effect.

Following a mathematical analysis of the description of the energy of systems in which the effect occurs, the pair found a commonality based on two quantum features.

The first important quantum idea is that electrons can behave like both particles and waves. However, the wave-like nature of electrons can easily be disturbed as they move through the material, especially when they hit impurities and scatter in a different direction. The time it takes before this disruption happens is called the electron’s lifetime.

The second relevant quantum feature is an internal magnetic property of electrons, called spin, which can point in one of two directions, up or down. Isobe and Nagaosa noted that in materials that display the anomalous Hall effect, electrons with a spin pointing up have a different lifetime to those with a spin pointing down. In particular, the pair has now demonstrated how this difference is captured mathematically in the energy description of such systems. “This provides a renewed perspective on the problem,” says Isobe.

Isobe’s goal for the future is to apply this mathematical description to real-world experiments. “Is this renewed perspective really useful for explaining real materials?” Isobe asks. “That’s the next question to address.”

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  • 1. Isobe, H. & Nagaosa, N. Anomalous Hall effect from a non-Hermitian viewpoint. Physical Review B 107, L201116 (2023). doi: 10.1103/PhysRevB.107.L201116