We investigate the intrinsic nonlinear Hall effect (INHE) in $\mathcal{PT}$-symmetric antiferromagnetic nodal-line semimetals, highlighting a significant enhancement characterized by a logarithmic divergence in the INH conductivity as the Fermi energy intersects the nodal line within a finite energy range. Through analytical derivations and numerical calculations, we demonstrate that the INH conductivity logarithmically depends on the gap opening at the nodal line. We further reveal that current-induced spin-orbit torque, which rotates the Néel vector and opens a gap at the nodal line, results in a nonanalytical transverse response, where the amplitude of high-harmonic generation decreases as the inverse cube of the harmonic order. Our finding not only serves as a pathway to an enhanced nonlinear Hall response without the necessity of fine tuning the chemical potential but also suggests a different nonanalytical response that may contribute to the experiment identification of topological nodal-line semimetals and potential applications in ultrafast nonlinear devices.

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• Anomalous Hall effect
• Electrical properties
• Spintronics
• Transport phenomena
• Antiferromagnets
• Nodal-line semimetals
• Tight-binding model
• k dot p method