  Simultaneous manipulation of charge and spin density distributions in
materials is the key element required in spintronics applications. Here we
study the formation of coupled spin and charge densities arising in scattering
of electrons by domains of local magnetization producing a position-dependent
Zeeman field in the presence of the spin-momentum locking typical for
topological insulators. Analytically and numerically calculated scattering
pattern is determined by the electron energy, domain magnetization, and size.
The spin-momentum locking produces strong differences with respect to the
spin-diagonal scattering and leads to the scattering asymmetry with nonzero
mean scattering angle as determined by only two parameters characterizing the
system. To extend the variety of possible patterns, we study scattering by
diffraction gratings and propose to design them in modern nanostructures based
on topological insulators to produce desired distributions of the charge and
spin densities. These results can be useful for engineering of magnetic
patterns for electron optics to control coupled charge and spin evolution.
