Monte Carlo study of two-dimensional Ising dipolar antiferromagnets as a model for rare-earth ordering in theR-Ba-Cu-O compounds (R=rare earth)

The two-dimensional Ising model with dipolar interactions is studied using Monte Carlo simulation. In the case of a pure dipolar interaction, estimates are obtained for the reduced transition temperature, ${\mathrm{\theta }}_{\mathit{n}}$=2${\mathit{a}}^3$ ${\mathit{k}}_{\mathit{B}}$ ${\mathit{T}}_{\mathit{n}}$/${\mathrm{\mu }}_{\mathit{e}\mathit{f}\mathit{f}}^2$ for two particular spin alignments in which the spins are aligned parallel to and perpendicular to the plane, respectively. A comparison with measurements made on R${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ (R=Nd,Dy, and Er) and R${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_4$ ${\mathrm{O}}_8$ (R=Dy and Er) show that the calculated Ne´el temperature falls consistently below that observed experimentally. The model is generalized to include an isotropic intraplanar nearest-neighbor exchange interaction and the Ne´el temperature calculated as a function of the strength of the exchange coupling for configurations in which the spins are aligned perpendicular to the plane. From this estimates of the exchange coupling are obtained for some of these materials. The results obtained from these calculations confirm that the long-range character of the dipolar interaction does not affect the universality class of the two-dimensional Ising antiferromagnet. Extensions of the present analysis are discussed.