Three-dimensional magnetic structures and rare-earth magnetic ordering in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Nd</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">CuO</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Pr</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">CuO</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

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 \ensuremath{\sim}1.3${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ for ${\mathrm{Nd}}^{3+}$ at 0.4 K and \ensuremath{\sim}0.08${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ 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.