Quantum Metric Third-Order Nonlinear Hall Effect in A Non-Centrosymmetric Ferromagnet

Although Berry curvature in the imaginary part of quantum geometry has been confirmed to play a role in the nonlinear Hall effect of Weyl semimetals, exploration of the real component's influence on nonlinear Hall transport has primarily focused on second-order effects at lower temperatures. However, the potential impact of quantum metric on higher-order transport, particularly the room-temperature quantum metric nonlinear Hall effect, remains largely unexplored. In this study, we observed a significant third-order nonlinear Hall effect induced by quantum metric in non-centrosymmetric ferromagnetic Fe5GeTe2 at room temperature. This effect was confirmed through distinct scaling behaviors regardless of scattering time and a third-order signal dependent on the electron spin state. Notably, our Hall device exhibited an ultrahigh third-order conductivity of 72 μm·S·V-2, surpassing previous studies in Berry curvature-induced third-order nonlinear Hall effects by approximately tenfold, thus enhancing the device's third-order current conversion efficiency. Moreover, we extended the second-order quantum metric dipole scaling to derive a novel third-order equation (χ_xxy^("3" ω) = η_"2" σ^"2" +η_"0" ), offering a fresh perspective for studying third-order nonlinear Hall effects in emerging material platforms. Our findings lay the groundwork for the development of room-temperature, low-power quantum spintronic devices leveraging the third-order nonlinear Hall effect.