It is well known that when a current-carrying material is subjected to an external magnetic field, a voltage can develop perpendicular to the current direction—a phenomenon called the Hall effect. The measured perpendicular voltage is the Hall voltage. When this voltage arises without an external magnetic field, it is termed the anomalous Hall effect.
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.
