Low-dimensional magnetism in the high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>superconductor<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>L</mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ba</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Cu</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>7</mml:mn><mml:mo>−</mml:mo><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>(<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>L</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">G</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mo>,</mml:mo><mml:mspace/><mml:mi mathvariant="normal">H</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mo>,</mml:mo><mml:mspace/><mml:mi mathvariant="normal">E</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:math>): Heat-capacity study

Heat capacities have been measured for the high-${T}_{c}$ superconductors $L{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}y}$ ($L=\mathrm{G}\mathrm{d},\phantom{\rule{0ex}{0ex}}\mathrm{H}\mathrm{o},\phantom{\rule{0ex}{0ex}}\mathrm{E}\mathrm{r},\phantom{\rule{0ex}{0ex}}\mathrm{Y}$) between 0.15 and 100 K. While the superconducting phase-transition temperatures of these compounds are nearly the same at ${T}_{c}=92$ K, the heat-capacity data indicate magnetic ordering in the system of rare earths at ${T}_{m}=2.21$ K for $\mathrm{Gd}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}y}$ and at ${T}_{m}=0.60$ K for $\mathrm{Er}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}y}$. In both cases, the cooperative heat-capacity peak resmbles that of the two-dimensional (2D) Ising model. In addition, broad heat-capacity anomalies, which cannot be attributed to crystalline field splittings, are found. A semiquantitative fit can be obtained by assuming that two-thirds of the rare earths constitute a 2D Ising system and the rest of them form a 1D Ising-like system. The heat capacity of the $\mathrm{Ho}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}y}$ shows a very flat maximum at \ensuremath{\sim}5 K. The separation of the two lowest-lying singlet levels of ${\mathrm{Ho}}^{3+}$ ions is estimated to be \ensuremath{\sim}7 K.

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