Competing Impurities in an Antiferromagnetic Background.

We study the order-from-disorder transition and reentrant magnetism in a doped crystal La$_{2-x}$Sr$_{x}$Cu$_{1-z}$Zn$_{z}$O$_{4}$ within the framework of a long-wavelength nonlinear sigma model that properly incorporates the Dzyaloshinskii- Moriya and XY anisotropies. The effect of doping La$_{2}$CuO$_{4}$ with nonmagnetic impurities, such as Zn, is considered according to classical percolation theory, while the effect of the Sr-doped charge carriers is described as a dipolar frustration of the antiferromagnetic order. We derive the expressions for several magnetic, thermodynamic, and spectral properties of the system, such as the N\'{e}el temperature, the spin-stiffness, and the anisotropy gaps, as well as their evolution with both Zn and Sr doping for cases of ballistic and diffusive vacancies. We solve the problem analytically in the limits of low and high temperatures. The connection to several experiments will be discussed [Phys. Rev. B59, R725 (1999), Science 295, 1691 (2002), Phys. Rev. Lett. 93, 027001 (2004)].