Anomalous Hall effect has been understood in terms of the geometric nature of Bloch bands and impurity scattering, and has been observed in a wide variety of magnetic materials, including ferromagnets and antiferromagnets. Recently, a large anomalous Hall effect was reported in the noncollinear antiferromagnetic metal $\mathrm{NbMnP}$, whose magnetic order is a mixture of even- and odd-parity magnetic components. Such a magnetic structure is expected to exhibit the anomalous Hall effect and the nonlinear Hall effect from the symmetry breaking of the antiferromagnetic ordering. Here, we theoretically investigate the intrinsic anomalous and nonlinear Hall effect in $\mathrm{NbMnP}$ induced by the quantum geometry of the Bloch band using the first-principles calculation and the Wannier interpolation method. We found that the intrinsic Hall response of $\mathrm{NbMnP}$ is predominantly governed by the strongly enhanced Berry curvature and Berry-connection-polarization dipole on a specific mirror plane. These enhanced geometric quantities originate from the spin-orbit-coupling-induced gap openings along the nodal lines. Our results indicate that $\mathrm{NbMnP}$ serves as a model system for investigating transport phenomena originating from nodal lines in parity-mixed antiferromagnets.

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• Electrical conductivity
• Magnetism
• First-principles calculations
• Wannier function methods