Berry curvature, as the imaginary component of quantum geometry, plays a crucial role in condensed matter physics. The spatial distribution of Berry curvature can be characterized by its dipole and multipole moments, which can induce the nonlinear anomalous Hall effect (NLAHE). To date, the NLAHE has been experimentally reported in various materials, yet studies on room-temperature NLAHE remain limited. In this work, we report the observation of the third-order NLAHE in the ferromagnetic metal ${\mathrm{Fe}}_3{\mathrm{GaTe}}_2$. The third-order NLAHE exhibits hysteresis as a function of external magnetic field, and the coercive field is the same as that of the anomalous Hall effect. Also, the third-order NLAHE remains observable up to the Curie temperature $\left(\sim 350\mathrm{K}\right)$. The scaling analysis suggests that the third-order NLAHE may arise from the Berry curvature quadrupole. Our work not only provides an approach for investigating magnetic materials via nonlinear electric transports, but also opens up possibilities for the future development of room-temperature third-order nonlinear electronic devices.

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• Anomalous Hall effect
• Berry curvature
• Electrical properties
• Hall effect
• Magnetism
• Magnetotransport
• Ferromagnets
• Resistivity measurements