Third-Order Nonlinear Hall Effect in Altermagnet RuO_{2}

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 RuO_{2} thin films. TNHE emerges when current is applied along [110] or [1[over ¯]10] crystal direction for 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 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 RuO_{2}, which can be generalized to other altermagnets such as d-wave V_{2}X_{2}O (X=Se or Te) and g-wave MnTe and CrSb.