Altermagnets are a novel class of magnetic materials with cutting-edge advantages. Identifying altermagnets, i.e., exploring their distinguishing fingerprints, is vital but challenging. The as-reported spontaneous anomalous Hall effect is not universally present in all altermagnets due to magnetic symmetry constraints, and the second-order nonlinear Hall effect is prohibited by spatial-inversion symmetry. Here, we report the experimental discovery of a third-order nonlinear Hall effect (TNHE) in ${\text{RuO}}_2$ thin films. TNHE emerges when current is applied along [110] or $[\overline{1}10]$ crystal direction for ${\text{RuO}}_2(001)$, as the second-order currents induce a magnetization by breaking orthogonal mirror and rotation symmetries of this altermagnet. These symmetry-breaking conditions also enforce a twofold angular dependence of TNHE concerning current direction in the ${\text{RuO}}_2(001)$ plane. Moreover, temperature-dependent measurements and scaling law analysis reveal that TNHE is governed primarily by the third-order skew scattering mechanism. Our findings establish TNHE as a transport fingerprint of altermagnet ${\text{RuO}}_2$, which can be generalized to other altermagnets such as $d$-wave ${\mathrm{V}}_2{\mathrm{X}}_2\mathrm{O}$ ($\mathrm{X}=\text{Se}$ or Te) and $g$-wave MnTe and CrSb.

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• Magnetotransport
• Spintronics