Magnetic and Thermal Properties of Gd(OH)3

Measurements of the low-temperature specific heat have shown that Gd${\mathrm{}\left(\mathrm{OH}\right)\mathrm{}}_3$ undergoes a co-operative transition at 0.94 ± 0.02 K. To determine the interactions giving rise to this transition, a series of accurate susceptibility and magnetic-specific-heat measurements were made at temperatures high compared to the transition, and analyzed using asymptotically exact series expansions. The susceptibility measurements were made using an audiofrequency mutual-inductance method at temperatures between 1.4 and 4.2 K and 14.7 and 20.0 K. The magnetic specific heat was determined using two different techniques. One was the conventional calorimetric method, and measurements were made at temperatures between 0.4 and 15 K. An estimate of the lattice specific heat and a comparison with calorimetric measurements of the diamagnetic isomorph La${\mathrm{}\left(\mathrm{OH}\right)\mathrm{}}_3$ are given. In the other method, the magnetic specific heat was determined from the field dependence of the adiabatic differential susceptibility, using the method of Casimir and du Pré (CdP). For this, a special 4.5-MHz tunnel-diode oscillator was used, together with a sensitive temperature controller and a superconducting solenoid. Measurements were made in fields up to 15 kOe at temperatures between 5 and 68 K. Using an iterative procedure, the leading terms in the susceptibility expansion were found to be ${\chi }_T^{\parallel }=\frac{\lambda }{(T-{\theta }_{\parallel }^{\infty }+\frac{B_{2\parallel }}{T}+\frac{B_{3\parallel }}{T^2}+\cdots )}$ with $\lambda =7.815\mathrm{}\pm 0.008$ emu K/mole, ${\theta }_{\parallel }^{\infty }=0.02\mathrm{}\pm 0.10$ K, $B_{2\parallel }=2.05\mathrm{}\pm 0.10$ ${\mathrm{K}}^2$, and $B_{3\parallel }=-0.59\mathrm{}\pm 0.10$ ${\mathrm{K}}^3$, where $\parallel$ denotes measurements parallel to the crystal $c$ axis and the superscript $\infty$ denotes correction to an infinitely long sample shape. For the magnetic specific heat, the leading terms were found to be $\frac{C_M}{R}=\frac{C_2}{T^2}+\frac{C_3}{T^3}+\cdots$, with $C_2=4.09\mathrm{}\pm 0.05$ ${\mathrm{K}}^2$ and $C_3=-4.2\mathrm{}\pm 0.7$ ${\mathrm{K}}^3$. The unusually small error in $C_2$ reflects the fact that the CdP method determines