Symplectic connection third-order Hall effect in a room-temperature ferromagnet

Abstract: Third-order nonlinear Hall effects (THE) have recently attracted considerable experimental interest as powerful probes for quantum geometric properties in emergent quantum materials, encompassing quadrupole moments of quantum metric and Berry curvature. Here, we report a fundamentally new THE in room-temperature van der Waals ferromagnet Fe3GaTe2 from second-order Berry connection polarizability, which manifests a higher-order characterization of band geometry called symplectic connection. Our observations show that the third-order transverse response in Fe3GaTe2 is odd to magnetization, vanishes above the Curie temperature and remains independent of driving current directions. Scaling law analysis combined with first-principles calculations establishes this response as the symplectic-connection-induced THE. This discovery opens the door to probing high-order quantum geometric properties beyond Berry curvature and quantum metric through nonlinear transport, unveiling the potential of exploring nonlinear Hall phenomena in broad classes of magnets without breaking inversion symmetry. Moreover, the room-temperature manipulation of THE holds promises for device applications based on harnessing the quantum-geometric connection structure.