Calorimetric Study of Several Rare-Earth Gallium Garnets

Specific-heat measurements on the gallium garnets (GaG) of Nd, Sm, Gd, Er, Dy, Ho, and Yb between 0.35 and 4.2°K are presented. The transition to the ordered state for the garnets of Nd, Sm, and Er is studied in detail, the transition temperature $T_N$ being, respectively, 0.516, 0.967, and 0.789°K. Another Sm sample had a transition at $T_N=0.921\mathrm{}$°K. From this study, the exchange coupling parameter $J_{\mathrm{cc}}$ between the rare-earth ions situated on the $c$ sites is derived in different ways, namely, from $T_N$, the magnetic energy, and the high-temperature specific-heat "tail." These determinations are found to be reasonably consistent. The entropy and magnetic energy are found to be approximately those of a Heisenberg system with spin ½. For GdGaG, the rounded specific-heat maximum is interpreted in terms of a Schottky anomaly. The specific-heat anomaly can be well fitted by a calculated curve assuming a cubic crystalline field. Unexpectedly, the splitting is much larger than that obtained for the diluted garnet from ESR data. For HoGaG, the specific heat shows the population of the first excited singlet at $\frac{E}{k}=7.4\mathrm{}$°K and a second-order hyperfine splitting at temperatures below 1°K. For YbGaG, the specific heat increases as the temperature decreases, and from the temperature region where the magnetic contribution is proportional to $T^{-2\mathrm{}}$, the transition to an ordered state is expected at about 0.3°K. The DyGaG shows a maximum specific heat at about 0.36°K, but no satisfactory analysis could be carried out on this compound.