Low-dimensional magnetism in the high-TcsuperconductorLBa2Cu3O7−y(L=Gd,Ho,Er): Heat-capacity study

Heat capacities have been measured for the high-$T_c$ superconductors $L{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-y}$ ($L=\mathrm{G}\mathrm{d},\mathrm{H}\mathrm{o},\mathrm{E}\mathrm{r},\mathrm{Y}$) between 0.15 and 100 K. While the superconducting phase-transition temperatures of these compounds are nearly the same at $T_c=92\mathrm{}$ K, the heat-capacity data indicate magnetic ordering in the system of rare earths at $T_m=2.21\mathrm{}$ K for $\mathrm{Gd}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-y}$ and at $T_m=0.60\mathrm{}$ K for $\mathrm{Er}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-y}$. 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 $\mathrm{Ho}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-y}$ shows a very flat maximum at ∼5 K. The separation of the two lowest-lying singlet levels of ${\mathrm{Ho}}^{3+}$ ions is estimated to be ∼7 K.