  We study helical structures in spin-spiral single crystals. In the continuum
approach for the helicity potential energy the simple electronic band splits
into two non-parabolic bands. For the Fermi energy greater than the splitting
between the bands, the lower band is described by a surface with a saddle shape
in the direction of the helicity axis. Using the Boltzmann equation with the
relaxation due to acoustic phonons, we discover the dependence of the current
on the angle between the electric field and helicity axis leading to the both
parallel and perpendicular to the electric field components in the
electroconductivity. In addition, we find that the transition rates depend on
an electron spin allowing the transition between the bands. The electric
conductivities exhibit nonlinear behaviors with respect to chemical potential.
We explain this effect as the interference of the band anisotropy, spin
conservation, and interband transitions. The proposed theory with the spherical
model in the effective mass approximation for conduction electrons can
elucidate nonlinear dependencies that can be identified in experiments. There
is the excellent agreement between the theoretical and experimental data for
parallel resistivity depending on temperature at the phase transition from
helical to ferromagnetic state in a MnP single crystal. In addition, we predict
that the perpendicular resistivity abruptly drops to zero in the ferromagnetic
phase.
