Magnetic properties of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Gd</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>crystals

Magnetic-susceptibility and magnetization measurements on single crystals of the ${\mathrm{CuO}}_{2}$-planar compound ${\mathrm{Gd}}_{2}$${\mathrm{CuO}}_{4}$ indicate copper moment ordering near 260 K, producing an internal field at the gadolinium site that induces substantial anisotropy in the magnetic response. Dilute substitutions for gadolinium and copper leave the essential physics unaffected. We suggest that copper ordering also occurs in ${\mathrm{Eu}}_{2}$${\mathrm{CuO}}_{4}$ on the basis of substitutional studies but is not detected in other rare-earth-based compounds in this series. Rare-earth size appears to play an important role.