Machine-learning-based architecting of magnetoresistance phase diagrams in anomalous Hall systems

The nontrivial magnetoresistance in anomalous Hall systems (AH-MR) plays a crucial role in understanding electron dynamics in condensed matter systems. Unlike conventional Hall resistance reflecting the cyclotron motion of electrons under magnetic fields, anomalous Hall magnetoresistance typically stems from Berry-curvature-induced anomalous velocity or electron scattering events in anomalous Hall systems. Therefore, multiple parameters-such as carrier density, electrical conductivity and anomalous Hall conductivity-offer the capability for tailoring AH-MR associated phenomena including quantum anomalous Hall effect, colossal magnetoresistance and topological phase transition. However, the high-dimensional nature of these parameters hinders the global understanding of AH-MR and related electronic transport behavior. Here we employ machine learning algorithms to architect AH-MR phase diagrams by analyzing over 2000 000 AH-MR curves generated from a two-band model with five adjustable parameters. We found these curves can be clustered into 13 distinct AH-MR states using the mean-shift algorithm and established topological networks to describe transitions between them, offering designing transition paths to switch AH-MR states by tuning selected electronic parameters. Our experimental AH-MR results on gated Fe₅GeTe₂ nanoflakes-serving as a validation dataset-verify the reliability of the obtained topological relationships and landscape phase diagrams. Such a machine-learning-assisted approach of high-dimensional data processing offers a powerful methodology for investigating spin-dependent transport phenomena.