Effects of oxygen on the magnetic order of the rare-earth ions in R${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$ (R=Dy, Er, Nd)

Neutron diffraction has been used to study the effects of oxygen on the magnetic order of the rare-earth ions in R${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathit{x}}$ (R=Dy, Er, Nd). For fully oxygenated superconducting (${\mathit{T}}_{\mathit{c}}$=92 K) ${\mathrm{ErBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$, two-dimensional (2D) short-range magnetic correlations are observed just above the ordering temperature ${\mathit{T}}_{\mathit{N}}$=0.62 K, while at ${\mathit{T}}_{\mathit{N}}$ long-range correlations develop in the a-b plane, inducing 3D long-range order. Below ${\mathit{T}}_{\mathit{N}}$ the sublattice magnetization is found to obey Onsager’s exact solution of the 2D S=1/2 Ising model. For oxygen-reduced (x≊0.6) superconducting ${\mathrm{ErBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6.6}$ the 3D ordering temperature is lowered to ${\mathit{T}}_{\mathit{N}}$≃0.48 K. For insulating ${\mathrm{ErBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathit{x}}$ (x≊0) neither 2D nor 3D long-range order develops, as only 2D short-range correlations are observed. For ${\mathrm{DyBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ (${\mathit{T}}_{\mathit{c}}$≃92 K) 3D long-range order occurs at ${\mathit{T}}_{\mathit{N}}$≃0.93 K, with spins coupled antiferromagnetically along all three crystallographic axes. As we reduce the oxygen concentration the 3D magnetic ordering temperature decreases.