Weak localization in systems with chiral spin textures and skyrmion crystals

A 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 might assist the experimental detection of chiral spin textures and, in particular, skyrmions.

Figure 1

The dependence of the scattering rates for singlet (${\tau }_s^{-1}$) and triplet (${\tau }_{t0,t1}^{-1}$) channels on a spin texture radius for the spin spatial distribution Eq. (11) with $\alpha =\pi /2$. The inset shows two time-inverted electron trajectories with scattering by both impurities and a spin texture.

Figure 2

The magnetic field dependence of the weak-localization conductivity correction at ${\tau }_{\varphi }/{\tau }_0=30$ for (a) a different spin texture radius $k_{F}a$ (at $\alpha =\pi /2$) and (b) a different spin inclination angle $\alpha$ (at $k_{F}a=3$).

Figure 3

The magnetic-field dependence of the conductivity correction for different spin-flip rates $1/{\tau }_{12}$. The 2D electron spin polarization $\delta =0.3$.

Figure 4

The dependence of $\mathrm{\Delta }\sigma \left(B\right)$ for skyrmion crystals with different values of the topological magnetic field $B_T$.