Magnetostriction and the two-spin correlation function in EuO

The longitudinal and transverse magnetostrictions along the [100] direction of EuO were measured at temperatures between the Curie point $T_C=69.25\mathrm{} \mathrm{and} 245$ K in magnetic fields $H$ up to 145 kOe. The volume magnetostriction was obtained from these measurements. The data indicate that above $T_C$ the isotropic magnetostriction (independent of the direction of $\overrightarrow{H}$ is much larger than the anisotropic magnetostriction. The isotropic magnetostriction is attributed to the volume dependence of the dominant nearest-neighbor exchange constant $J$. The results are compared with the theory of Callen and Callen. Assuming only nearest-neighbor exchange interactions, this theory relates the isotropic magnetostriction to the $H$ dependence of the two-spin correlation function $〈{\overrightarrow{\mathrm{S}}}_i·{\overrightarrow{\mathrm{S}}}_j〉$ for nearest neighbors. An alternative theoretical approach, based on thermodynamic and statistical-mechanical arguments is presented and is shown to lead to equivalent results. Based on these theoretical results for the magnetostriction, numerical predictions are obtained using high-temperature series expansions. These numerical results point to the inadequacy of the molecular-field approximation, particularly near $T_C$. The overall agreement between theory (evaluated using series expansions) and experiment is very good. However, there are small discrepancies near $T_C$, consistent with other data which show that for EuO the model of a Heisenberg ferromagnet with nearest-neighbor exchange interactions is good, but not exact. Susceptibility and magnetization data (obtained for the purpose of interpreting the magnetostriction data) are also compared with results of series expansions for zero and finite fields. The zero-field susceptibility is in good agreement with theory, except near $T_C$ where small deviations appear. The field variation of the susceptibility $\chi$ in intermediate fields, for which $\frac{\chi \mathrm{}\left(H\right)\mathrm{}}{\chi \mathrm{}\left(0\right)\mathrm{}}\gtrsim 0.9$, is in good agreement with predictions based on "double series" in powers of $\frac{J}{kT}$ and $\frac{{\mu }_{B}H}{kT}$.