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

Abstract

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\ifmmode^\circ\else\textdegree\fi{}K. The compressional elastic constants ${C}_{11}$ and ${C}_{33}$ display characteristic anomalies at the magnetic transition points ${T}_{N}$ (178\ifmmode^\circ\else\textdegree\fi{}K) and ${T}_{C}$ (87\ifmmode^\circ\else\textdegree\fi{}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 ${K}_{S\ensuremath{\perp}}$. 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 ${K}_{S\ensuremath{\perp}}$ a pronounced softening of the crystal lattice. The limiting Debye temperature extrapolated to 0\ifmmode^\circ\else\textdegree\fi{}K was found to be 190\ifmmode^\circ\else\textdegree\fi{}K. The temperature dependence of the magneto-elastic energy shows a drastic change of 0.71 J ${\mathrm{cm}}^{\ensuremath{-}3}$ at ${T}_{C}$. Apparently, this change is responsible for the first-order phase transition in dysprosium at ${T}_{C}$.