Since the discovery of the Hall effect in 1879, it has given rise to a series of landmark advances in condensed matter physics. These include the quantum Hall effect and the fractional quantum Hall effect, recognized with Nobel Prizes in 1985 and 1998, respectively, as well as the experimental realization of the quantum anomalous Hall effect in 2013, which demonstrated how the interplay between topology and ferromagnetism can produce dissipationless edge currents.

Despite this long history, research on the Hall effect—particularly the anomalous Hall effect—has largely concentrated on the Hall resistance, derived from the transverse voltage. By contrast, the magnetoresistance, obtained from the longitudinal voltage, is important for helping scientists understand exotic quantum phenomena such as the giant magnetoresistance effect. However, the magnetoresistance has received far less attention in past decades largely because of the complexity for interpreting the data. Only in recent years has a theoretical model—a two-band framework incorporating anomalous Hall conductivity—been developed that can effectively capture its behavior. Even so, the resulting expression for magnetoresistance remains complicated, limiting deeper understanding.

Writing in National Science Review, a team from Nanjing University now offers a solution. Using machine learning, the researchers analyzed over two million magnetoresistance curves generated from the above-mentioned two-band model. By applying the mean-shift algorithm, they classified the curves into 13 distinct magnetoresistance states and established topological networks that describe transitions among them. These networks make it possible to design transition paths for switching magnetoresistance states by tuning selected electronic parameters. Experimental magnetoresistance measurements on a gated ferromagnetic material confirmed the reliability of the obtained phase diagrams. This machine-learning-assisted approach to high-dimensional data processing provides a powerful new methodology for investigating transport phenomena.

Human activity and climate change are estimated to increase the amount of seabed methane leakage. Much of the methane could be consumed by microbes, yet it is unclear how quickly such communities establish. Through six-year seabed monitoring, researchers found that an animal-microbe “biofilter” removing up to100% of the dissolved methane can develop in just 2–3 years, not the decades once thought. Fast-growing methane-oxidizing microbes feed burrowing animals, which churn the seafloor like tiny gardeners to help the microbes feast on the greenhouse gas. This discovery improves our understanding of seafloor methane removal capacity, which is critical to assess the effects of global warming and anthropogenic disturbance in the deep sea.