Magnetic and Thermal Properties of Dysprosium Aluminum Garnet. I. Experimental Results for the Two-Sublattice Phases

In a magnetic field along a $〈111〉$ axis, dysprosium aluminum garnet (DAG) closely resembles a two-sublattice Ising antiferromagnet, and it undergoes a transition to the paramagnetic state without spin flopping. To investigate the nature of this transition, high-resolution measurements have been made of the isothermal magnetization and the specific heat $C_H$ as a function of temperature from 1.1 to 4.2 °K in magnetic fields up to 14 kOe. A number of additional measurements have also been made down to 0.5 °K and between 4.2 and 8 °K. Small lattice contributions to the specific heat were estimated from separate measurements on yttrium and lutetium aluminum garnets. The magnetic measurements were made on a small spherical crystal and the thermal measurements were made on a large ellipsoidal single crystal with a demagnetizing factor $N=5.35\mathrm{}$. The two sets of data are shown to be consistent if the expected shape dependence is taken into account, and the principal results are converted to correspond to the ideal case of $N=0\mathrm{}$. The analysis indicates that the transition is of first order below 1.66 °K, with a region of coexistence between the antiferromagnetic and paramagnetic phases, depending on sample shape. The corresponding latent heat was measured directly and compared with the predictions of the magnetic Clausius-Clapeyron equation. Between 1.66 and 2.53 °K the transition is higher than first order and unusual in form, with fairly sharp but finite maxima in the specific heat and only mild inflections in the magnetic isotherms. A complete phase diagram was constructed, and the principal thermodynamic functions (internal energy, entropy, and enthalpy) were derived. Possible applications of DAG to low-temperature heat engines are discussed briefly. The phase diagram corresponding to $N=0\mathrm{}$ shows a general similarity to the phase diagram for ${\mathrm{He}}^3$-${\mathrm{He}}^4$ mixtures, but the analogy is complicated by long-range dipolar forces, known to be significant in the present case.