  In this work we manifest that an electrostatic disorder in conducting systems
with broken time reversal symmetry universally leads to a chiral ordering of
the electron gas giving rise to skyrmion-like textures in spatial distribution
of the electron spin density. We describe a microscopic mechanism underlying
the formation of the equilibrium chiral spin textures in two-dimensional
systems with spin-orbit interaction and exchange spin splitting. We have
obtained analytical expressions for spin-density response functions and have
analyzed both local and non-local spin response to electrostatic perturbations
for systems with parabolic-like and Dirac electron spectra. With the proposed
theory we come up with a concept of controlling spin chirality by electrical
means.
