Low-Temperature Elasticity and Magneto-Elasticity of Dysprosium Single Crystals

The five independent adiabatic elastic constants of dysprosium have been determined by means of an ultrasonic-pulse technique at a frequency of 10 MHz, between 4.2 and 300°K. The compressional elastic constants $C_{11}$ and $C_{33}$ display characteristic anomalies at the magnetic transition points $T_N$ (178°K) and $T_C$ (87°K). The shear constants $C_{44}$ and $C_{66}$ are very little affected at $T_N$; however, they exhibit typical anomalies at $T_C$. The temperature dependence of the directional compressibility $K_{S\mathrm{II}}$ parallel to the hexagonal $c$ axis is qualitatively a mirror image of the perpendicular compressibility $K_{S\perp }$. Both are only slightly affected at $T_N$, but show drastic anomalies at $T_C$. At this transition, $K_{S\mathrm{II}}$ exhibits a hardening and $K_{S\perp }$ a pronounced softening of the crystal lattice. The limiting Debye temperature extrapolated to 0°K was found to be 190°K. The temperature dependence of the magneto-elastic energy shows a drastic change of 0.71 J ${\mathrm{cm}}^{-3\mathrm{}}$ at $T_C$. Apparently, this change is responsible for the first-order phase transition in dysprosium at $T_C$.