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An emerging phase of matter among the class of topological materials is nodalline semimetal, possessing symmetry-protected one-dimensional gapless lines atthe (or close to) the Fermi level in $k$-space. When the $k$-dispersion of thenodal line is weak, van Hove singularities generated by the almost flat nodallines may be prone to instabilities introduced by additional perturbations suchas spin-orbit coupling or magnetism. Here, we study Cr-based ferromagneticchalcospinel compound CuCr$_2$Se$_4$ (CCS) via first-principles electronicstructure methods and reveal the true origin of its dissipationless anomalousHall conductivity, which was not well understood previously. We find that CCShosts nodal lines protected by nonsymmorphic symmetries, located in thevicinity of Fermi level, and that such nodal lines are the origin of thepreviously observed distinct behavior of the anomalous Hall signature in thepresence of electron doping. The splitting of nodal line via spin-orbitcoupling produces a large Berry curvature, which leads to a significantresponse in anomalous Hall conductivity. Upon electron doping via chemicalsubstitution or gating, or rotation of magnetization via external magneticfield, steep change of anomalous Hall behavior occurs, which makes CCS apromising compound for low energy spintronics applications.

Anomalous Hall signatures of nonsymmorphic nodal lines in doped chromium chalcospinel CuCr$_2$Se$_4$