Observation of the Berry curvature quadrupole induced nonlinear anomalous Hall effect at room temperature

The anomalous Hall effect (AHE) describes the appearance of a transverse voltage when a longitudinal voltage is applied in the presence of broken time-reversal symmetry. The AHE plays a prominent role in the study of topological quantum materials in which it results from the electronic Berry curvature. More recently, it has been recognized that certain magnetic point group symmetries can significantly enrich the anomalous Hall response by higher-order terms, which are induced by Berry curvature multipoles. Here we report the observation of the 3rd order AHE at room temperature in epitaxially grown thin films of the kagome antiferromagnet FeSn. When a longitudinal a.c. drive current at frequency \omega is applied, the 3rd order AHE appears as a transverse voltage response at 3\omega from cryogenic conditions to above room temperature in the presence of a magnetic field. Our scaling analysis of the charge carrier scattering time reveals the almost purely topological origin of 3rd order anomalous Hall response at room temperature. Conducting a symmetry analysis, model and ab-initio calculations, and magnetic Monte Carlo simulations, we demonstrate this intrinsic contribution can be attributed to the Berry curvature quadrupole moment, which arises in the spin-canted state of FeSn. Our measurements establish the 3rd order nonlinear AHE as a sensitive electrical transport probe to investigate antiferromagnetic phase transitions in a variety of materials. Because Berry curvature multipole effects are predicted to exist for 90 magnetic point groups, our work opens a new field to study a variety of topological magnetic materials through their nonlinear anomalous Hall response. Observing the 3rd order nonlinear AHE at room temperature in an epitaxially grown material platform, we demonstrate a new type of Hall effect with potential technological applications as frequency multiplier elements.