Quantum question about the anomalous Hall effect is answered

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.”