Antitoroidal magnets and anomalous Hall effect

Abstract: In this paper we introduce a theoretical model of a metallic magnetic system with an antitoroidal 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 an antitoroidal 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 antitoroidal order is an insulator with anomalous Hall effect occurring without any spin-orbit coupling.