Quantum metric third-order nonlinear Hall effect in a non-centrosymmetric ferromagnet.

Berry curvature in the imaginary part of quantum geometry has been confirmed to play a role in the nonlinear Hall effect of Weyl semimetals. However, exploration of the influence of the real component of the quantum geometry, the quantum metrics, on nonlinear Hall transport has primarily focused on second-order effects at lower temperatures, rather than higher-order transport. In this study, we observed a significant third-order nonlinear Hall effect induced by quantum metric in non-centrosymmetric ferromagnetic FeGeTe 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, 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 third-order equation. Our findings lay the groundwork for the development of room-temperature, low-power quantum spintronic devices leveraging the third-order nonlinear Hall effect.