Microscopic origin of the anomalous Hall effect in noncollinear kagome magnets

The anomalous Hall effect is commonly considered a signature of ferromagnetism. However, recently, an enormous anomalous Hall conductivity was measured in the compensated kagome magnets Mn3Sn and Mn3Ge. The occurrence of this effect is allowed by the magnetic point group of these materials; however, its emergence is still lacking a microscopic explanation. Herein we show that the spin-orbit coupling and an out-of-plane tilting of the texture are equivalent for several kagome magnets. Consequently, a coplanar system with spin-orbit coupling behaves as if it were virtually noncoplanar. We show via tight-binding model calculations that the Hall effect can mainly be interpreted as a topological Hall effect generated by the opening angle of the virtually tilted texture. Furthermore, upon tilting the fixed texture out of the kagome plane, we find a critical tilting angle for which the Hall conductivity vanishes for all energies. In this case, the Hamiltonian is invariant under a combined time-reversal and mirror symmetry, because the virtual texture is coplanar.