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We study helical structures in spin-spiral single crystals. In the continuumapproach for the helicity potential energy the simple electronic band splitsinto two non-parabolic bands. For the Fermi energy greater than the splittingbetween the bands, the lower band is described by a surface with a saddle shapein the direction of the helicity axis. Using the Boltzmann equation with therelaxation due to acoustic phonons, we discover the dependence of the currenton the angle between the electric field and helicity axis leading to the bothparallel and perpendicular to the electric field components in theelectroconductivity. In addition, we find that the transition rates depend onan electron spin allowing the transition between the bands. The electricconductivities exhibit nonlinear behaviors with respect to chemical potential.We explain this effect as the interference of the band anisotropy, spinconservation, and interband transitions. The proposed theory with the sphericalmodel in the effective mass approximation for conduction electrons canelucidate nonlinear dependencies that can be identified in experiments. Thereis the excellent agreement between the theoretical and experimental data forparallel resistivity depending on temperature at the phase transition fromhelical to ferromagnetic state in a MnP single crystal. In addition, we predictthat the perpendicular resistivity abruptly drops to zero in the ferromagneticphase.

The theory of transport in helical spin-structure crystals