Anomalous Hall effect in conical helimagnet crystals

Spin-spiral texture can substantially change charge transport properties in helimagnets. We find the anomalous Hall effect (AHE) exhibiting the dramatic behavior with respect to chemical potential, μ, in conical magnetic structures. The direct conductivity demonstrates kinks, and the Hall current exhibits minima and maxima changing the direction. We analytically derive the expression for energy bands and eigenstates for the most general case. Because of the conical potential, the energy bands are split into two nonparabolic bands where the lower band can have one- or two-minima shapes in the k_z-direction (z is a direction of the spiral axis). We prove that the origin of the anomalous Hall effect is not topological and is due to the anisotropy of the energy bands resulting from the conical potential. We also investigate the dependence of transport properties on conical angle, $ heta$, and find that the effects are most pronounced at θ = π/2 (a helical state). Electric current is calculated using the Boltzmann equation where the relaxation is caused by electron-acoustic phonon interaction. The transition probability is a 2×2 matrix with nonvanishing off-diagonal elements indicating the strong interband transitions. The origin of interband transitions is because of the nature of the conical potential where conduction electron spins interact with localized magnetic moments. To verify the proposed theory, we calculate the temperature dependence of resistivity for MnSe and MnP crystals and find the discontinuity at the phase transition between conical and paramagnetic phases. The calculations are in the excellent agreement with the experimental data. In addition, we predict the discontinuity behavior for the anomalous Hall resistivity at the phase transition where the resistivity drops to zero in the paramagnetic phase at T = T_C.