Anomalous Thermal Expansion and Magnetostriction of Single-Crystal Dysprosium

The temperature and field dependences of the magnetostriction and thermal expansion of single-crystal dysprosium metal were measured in the paramagnetic, spiral, and ferromagnetic regions. In the paramagnetic temperature range from the Néel point to room temperature, the thermal expansion is normal and the six lowest order magnetostriction coefficients vary as ${\mathrm{H}}^2$. As the temperature is lowered and the spins align, the magnetostriction becomes immense (0.62% at 80°K) and terms in the thermal expansion attributed to thermal vibrations are dwarfed by those arising from the magnetoelastic energy (≈350 ${\mathrm{cm}}^{-1\mathrm{}}$ ${\mathrm{atom}}^{-1\mathrm{}}$). Consequently, large discontinuities in the length of the hexagonal $a$ and $c$ axes occur when the spiral spin structure changes into the aligned configurations. Because the basal plane is the plane of easy magnetization in dysprosium, the basal-plane shearing magnetostriction is measurable over a wide range in temperature. Good agreement for this coefficient is found between the measured magnetostriction and that predicted by the single-ion magnetoelastic coupling theory [$\lambda \mathrm{}\left(T\right)=\lambda \mathrm{}\left(0\right)\mathrm{}{\hat{I}}_{\frac{5}{2}}\left({\mathcal{L}}^{-1\mathrm{}}\mathrm{}\right(m\left)\right)$]. The magnetostriction is proportional to $m^3$ at low temperatures and to $\frac{3m^2}{5}$ at high temperatures with the exceptionally large proportionality constant of $\lambda \mathrm{}\left(0\right)=8.5\mathrm{}\times {10}^{-3\mathrm{}}$.