  Theory of interference-induced quantum corrections to conductivity is
developed for two dimensional systems with chiral spin textures including
skyrmions. The effect of exchange interaction between electrons and spin
textures on weak localization of electronic waves is studied. The spin
dephasing rates are calculated as functions of the spin texture size. The
anomalous magnetoresistance is shown to be governed by the size and
magnetization spatial distribution of the spin textures. The effect of average
magnetization-induced spin splitting on weak localization is analyzed. The
sign-alternating weak-antilocalization magnetoresistance is demonstrated for
skyrmion crystals. We argue that analysis of the low-field magnetoresistance
serves as an independent tool for an experimental detection of chiral spin
textures and, in particular, skyrmions.
