Ferromagnet with a noncollinear antiferromagnetic order and anomalous Hall effect

In this paper we introduce a theoretical model of a metallic magnetic system with noncollinear antiferromagnetic order. We introduce a mechanism of indirect interaction of conducting fermions with localized spins based on the tunneling processes of conducting fermions through the localized spins. We demonstrate that interaction of conducting fermions with noncollinear antiferromagnetic order results in odd in momentum spin-momentum locking. The interaction resembles Rashba spin-orbit coupling but breaks the time-reversal symmetry. As a result, we show that a ferromagnet with the noncollinear antiferromagnetic order is an insulator with anomalous Hall effect occurring without any spin-orbit coupling.