Defect-induced spin textures in magnetic solids

Vacancy defects in isotropic noncollinear antiferromagnets produce long-range spin textures. By developing a magnetic elasticity theory, we demonstrate that a vacancy-induced readjustment in the spin configuration decays algebraically with distance. The power-law exponent depends on the multipole moment of a local spin deformation, which in turn is determined by the lattice symmetry and an equilibrium spin configuration in the absence of defects. The role of these two factors is highlighted for the ${J}_{1}$--${J}_{2}$ Heisenberg model on a kagome lattice. A vacancy in this model generates spin deformations that decay as $1/{r}^{2}$ for the $q=0$ ground state and as a $1/r$ for the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ magnetic structure. The analytic conclusions are confirmed by extensive numerical simulations. We also compute the fractional magnetic moments associated with vacancies and other lattice defects. Our results shed light on relative fragility of different magnetic structures with respect to spin glass formation at higher doping levels.