d -wave Hall effect and linear magnetoconductivity in metallic collinear antiferromagnets

In this Letter we theoretically predict a distinct class of anomalous Hall effects occurring in metallic collinear antiferromagnets. The effect is quadratic and d-wave symmetric in an external magnetic field. In addition, the electric current, transverse to the current voltage drop and the magnetic field in the predicted effect are all in the same plane. The studied theoretical model consists of two-dimensional fermions interacting with the N\'eel order through momentum-dependent exchange interaction having a d-wave symmetry. We also find unusual linear magnetoconductivity in this model.