Phenomenological model of the magnetic properties of ${\mathrm{La}}_{2\mathrm{-}\mathrm{x}}$${\mathrm{Sr}}_{\mathrm{x}}$${\mathrm{CuO}}_{4\mathrm{-}\mathrm{y}}$

We model ${\mathrm{La}}_{2\mathrm{-}\mathrm{x}}$ ${\mathrm{Sr}}_{\mathrm{x}}$ ${\mathrm{CuO}}_{4\mathrm{-}\mathrm{y}}$ for small x by assuming $p_{\pi }$ oxygen holes are Coulombically bound to Sr (or La vacancy) acceptor defects in 2d hydrogenic orbitals. The holes exchange couple to the antiferromagnetically ordered copper moments. The defects are polarized due to the copper spin canting induced by the Dzyaloshinski-Moriya interaction. Within linear spin-wave analysis we obtain a defect contribution to the magnetization jump at a critical applied field $H_c$, and we deduce a critical defect concentration for suppression of the long-range magnetic order which is sensitive to dimensionality, defect position, and defect-defect interactions. We quantitatively account for the nonmetal-metal transition. We qualitatively explain the observed resistivity drop at $H_c$ (for which we propose an experimental test), some anomalous muon-spin-resonance data, and the dependence of $T_N$ on oxygen vacancies.