Magnetic Ordering in Dy(OH)3and Ho(OH)3

Measurements are reported on the low-temperature (1-16 K) magnetic susceptibilities and specific heats of the hexagonal compounds Dy${\mathrm{}\left(\mathrm{OH}\right)\mathrm{}}_3$ and Ho${\mathrm{}\left(\mathrm{OH}\right)\mathrm{}}_3$. Dy${\mathrm{}\left(\mathrm{OH}\right)\mathrm{}}_3$ is shown to be highly anisotropic below 4 K, with the magnetic moment strongly constrained to lie along the $c$ axis. At 3.48 K, the spin system undergoes a phase transition to a ferromagnetic ordered state; this transition is dominated by the long-range magnetic dipole-dipole interactions. The effective Hamiltonian of the spin system is shown to be accurately represented by an Ising Hamiltonian, a scalar form which is particularly tractable to theoretical analysis. Above 4 K, the susceptibility and the specific-heat behavior are strongly influenced by the presence of low-lying energy levels and it is shown that the specific-heat behavior predicted on the basis of spectroscopically observed states agrees accurately with the experimental results. Ho${\mathrm{}\left(\mathrm{OH}\right)\mathrm{}}_3$ is very similar to Dy${\mathrm{}\left(\mathrm{OH}\right)\mathrm{}}_3$. Below 4 K the spins align parallel to the $c$ axis. At 2.54 K, Ho${\mathrm{}\left(\mathrm{OH}\right)\mathrm{}}_3$ undergoes a transition to a ferromagnetic ordered state under the dominance of magnetic dipole-dipole interactions. Above 4 K the susceptibility and specific heat are strongly influenced by the presence of low-lying excited states, and again this behavior is accurately accounted for on the basis of the spectroscopically observed states.