  While the anomalous Hall effect takes place typically in ferromagnets with
finite magnetization, large anomalous Hall conductivity in noncollinear
antiferromagnetic systems has been recently observed and attracted much
attention. In this study, we predict the anomalous Hall effect in perovskite
CaCrO$_3$ as a representative of 'collinear' antiferromagnetic materials. Our
result shows that the C-type antiferromagnetic ordering generates the sizable
anomalous Hall conductivity. Based on symmetry analyses, we show that the
antiferromagnetic order parameter belongs to the same irreducible
representation as the ferromagnetic order parameter in the nonsymmorphic space
group, allowing the non-vanishing Berry curvatures in k space. By performing
first-principles density-functional theory calculations, we find that the
Berry-curvature 'hot spots' lie along the gapped nodal lines where spin-orbit
coupling induces the spin splitting of Cr-3d bands near the Fermi energy and
enhances the anomalous Hall effect in CaCrO$_3$.
