Competing impurities and reentrant magnetism in   La(2-x)Sr(x)Cu(1-z)Zn(z)O(4) revisited. The role of the Dzyaloshinskii-Moriya   and XY anisotropies
  We study the order-from-disorder transition and reentrant magnetism in 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. Doping with nonmagnetic impurities, such as Zn, is considered according to classical percolation theory, whereas the effect of Sr, which introduces charge carriers into the CuO(2) planes, is described as a dipolar frustration of the antiferromagnetic order. We calculate several magnetic, thermodynamic, and spectral properties of the system, such as the antiferromagnetic order parameter, the Neel temperature, the spin-stiffness, and the anisotropy gaps, as well as their evolution with both Zn and Sr doping. We explain the nonmonotonic and reentrant behavior experimentally observed for T_N by Hucker et al. in Phys. Rev. B 59, R725 (1999), as resulting from the reduction, due to the nonmagnetic impurities, of the dipolar frustration induced by the charge carriers (order-from-disorder). Furthermore, we find a similar nonmonotonic and reentrant behavior for all the other observables studied. Most remarkably, our results show that while for x=2% and z=0 the Dzyaloshinskii-Moriya gap \Delta_{DM}=0, for z=15% it is approximately \Delta_{DM} = 7.5 cm^(-1). The later is larger than the lowest low-frequency cutoff for Raman spectroscopy (~ 5 cm^(-1)), and could thus be observed in one-magnon Raman scattering. 
L. Adamska, M. B. Silva Neto, and C. Morais Smith