Magnetostriction of single-crystal EuO was determined in the temperature range 4.2-150°K in applied magnetic fields up to 20 kOe. Linear magnetostriction coefficients extrapolated to 0°K are ${\lambda }_{100}=-22\mathrm{}\times {10}^{-6\mathrm{}}$ and ${\lambda }_{111}=55\mathrm{}\times {10}^{-6\mathrm{}}$. These yield the magnetoelastic coupling constants $b_1\mathrm{}\left(0\right)\mathrm{}\equiv -\frac{3}{2}{\lambda }_{100}(c_{11}-c_{12})=(31\mathrm{}\pm 6)\times {10}^6$ and $b_2\mathrm{}\left(0\right)\mathrm{}\equiv -3\mathrm{}{\lambda }_{111}{c}_{44}=-(86\mathrm{}\pm 10)\times {10}^6$ dyn/${\mathrm{cm}}^2$. Their decrease with increasing temperature appears to be explained by a 1:1 admixture of longitudinal single-ion and two-ion spin correlation as described by $\lambda \mathrm{}\left(T\right)=\lambda \mathrm{}\left(0\right)\left[{\hat{I}}_{\frac{5}{2}}\right({\mathcal{L}}^{-1\mathrm{}}\mathrm{}\left(m\right)\left)\right]$ and $\lambda \mathrm{}\left(T\right)=\lambda \mathrm{}\left(0\right)\mathrm{}{m}^2$, respectively. This suggests that the magnetoelastic Hamiltonian contains one-ion ($B_1, B_2$) and two-ion ($D_1, D_2$) magnetoelastic constants, $B_1\approx D_1\approx \frac{1}{2}{b}_1$ and $B_2\approx D_2\approx \frac{1}{2}{b}_2$. Since classical dipole-dipole interactions in EuO theoretically give ${D_1}^d=-6.4\mathrm{}\times {10}^6$ and ${D_2}^d\approx +4.3\mathrm{}\times {10}^6$, we estimate for pseudodipolar effects ${D_1}^p\approx 21\times {10}^6$ and ${D_2}^p=-47\mathrm{}\times {10}^6$ dyn/${\mathrm{cm}}^2$. The forced (volume) magnetostriction ${\lambda }_f$ was obtained versus applied magnetic field and is plotted versus the internal magnetic field. These results, which reflect the behavior of short-range order (isotropic spin-spin correlations) in the presence of a magnetic field, are qualitatively similar to predictions of the two-particle cluster calculation by E. R. Callen and H. B. Callen. The Landau-Belov phenomenological theory, which is often used to estimate the pressure derivative of the transition temperature from data of ${\lambda }_f$ versus ${\sigma }^2$, leads to results which are inconsistent with other determinations for $\frac{d{T}_c}{\mathrm{dP}}$ in EuO and with the theoretical and experimental results in a previous paper, showing that EuO exhibits a temperature-independent magnetic Grüneisen parameter. Data exhibiting suppression of the $\lambda$ anomaly in thermal expansivity by applied magnetic fields is also presented. The peak is rounded and its magnitude reduced by a factor of ≈½ at 18 kOe.

• Received 5 October 1967

DOI:https://doi.org/10.1103/PhysRev.171.555