Anomalous Hall effect in metallic collinear antiferromagnets with charge density wave order

In this paper we propose two theoretical models of a metallic N & eacute;el ordered antiferromagnet with chargedensity wave order which shows the anomalous Hall effect. In our models a combination of the N & eacute;el order and the charge-density wave order results in spin splitting of the conducting fermions. In addition, spin-orbit coupling is required to drive the anomalous Hall effect. In the first model we analyzed the effects of the Rashba spin-orbit coupling, and of the intrinsic d-wave spin-orbit coupling in the second model.