Three-dimensional magnetic structures and rare-earth magnetic ordering in ${\mathrm{Nd}}_2$${\mathrm{CuO}}_4$ and ${\mathrm{Pr}}_2$${\mathrm{CuO}}_4$

The three-dimensional (3D) magnetism present in ${\mathrm{Nd}}_2$ ${\mathrm{CuO}}_4$ and ${\mathrm{Pr}}_2$ ${\mathrm{CuO}}_4$ has been examined in neutron-scattering experiments. Antiferromagnetic long-range order of the ${\mathrm{Cu}}^{2+}$ moments develops below ${\mathit{T}}_{\mathit{N}}$=255 K in both compounds. In ${\mathrm{Nd}}_2$ ${\mathrm{CuO}}_4$ a series of magnetic phase transitions in which the ${\mathrm{Cu}}^{2+}$ spins reorient has also been observed below ${\mathit{T}}_{\mathit{N}}$, while in ${\mathrm{Pr}}_2$ ${\mathrm{CuO}}_4$ the 3D ${\mathrm{Cu}}^{2+}$ spin structure is stable. No changes in the crystalline structure of ${\mathrm{Nd}}_2$ ${\mathrm{CuO}}_4$ associated with the spin-reorientation transitions were found. Induced ordering of the rare-earth magnetic moments has been observed in both compounds. The ${\mathrm{Nd}}^{3+}$ (${\mathrm{Pr}}^{3+}$) magnetic moments align parallel (antiparallel) to ${\mathrm{Cu}}^{2+}$ moments which are nearest neighbors along the c axis, and the ordered moments of the rare-earth ions were determined to be ∼1.3${\mathrm{\mu }}_{\mathit{B}}$ for ${\mathrm{Nd}}^{3+}$ at 0.4 K and ∼0.08${\mathrm{\mu }}_{\mathit{B}}$ for ${\mathrm{Pr}}^{3+}$ at 8 K. The temperature-dependent ${\mathrm{Pr}}^{3+}$ moment is shown to be proportional to the ${\mathrm{Cu}}^{2+}$ moment times the bulk susceptibility. In this paper we also discuss the role of the XY anisotropy in the 3D ordering.