Magnetic anisotropy and superconductivity in a model for high- Tc copper oxides

Abstract

The phase diagram for the CuO 2-based superconductors is found to be consistent with an extended Hubbard Hamiltonian with competing positive-and negative- U interactions on a 2D lattice where sites are plaquettes formed by clusters of Cu and O atoms. The negative- U effective interactions are implied by the XY anisotropy in the Cu-Cu spin couplings and local hole pairing corresponds to vortex-antivortex spin configurations. The phase progression observed with the variation of dopant fraction x can be obtained via gradual implementation of canonical transformation that maps the properties of the positive- U Hubbard model at half-filling into those of the negative- U model away from half-filling. In the strong-coupling limit this process is described in terms of percolation-driven dilute magnetism for both spins ( U>0) and pseudospins ( U<O) appearing in the model. Other predictions of the model are: (i) An inverse spin-spin correlation length of the form ξ −1 x = ξ −1 o + η −1 x for x→O as seen in La 2- x Sr xCuO 4. (ii) An x-dependent reduction of spin fluctuations at low temperatures that conforms with NMR studies of La 2-xSr xCuO 4. And, (iii) a reduced superconducting transition locus T c(x)/ T cmax in agreement with the universal shape and location revealed by analysis of experimental data.