# Magnetoelastic behavior of europium oxide. II. Magnetostriction and the λ anomaly

## Abstract

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 λ100=-22×10-6 and λ111=55×10-6. These yield the magnetoelastic coupling constants b1(0)-32λ100(c11-c12)=(31±6)×106 and b2(0)-3λ111c44=-(86±10)×106 dyn/cm2. 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 λ(T)=λ(0)[I^52(L-1(m))] and λ(T)=λ(0)m2, respectively. This suggests that the magnetoelastic Hamiltonian contains one-ion (B1,B2) and two-ion (D1,D2) magnetoelastic constants, B1D112b1 and B2D212b2. Since classical dipole-dipole interactions in EuO theoretically give D1d=-6.4×106 and D2d+4.3×106, we estimate for pseudodipolar effects D121×106 and D2p=-47×106 dyn/cm2. The forced (volume) magnetostriction λf 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 λf versus σ2, leads to results which are inconsistent with other determinations for dTcdP 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 λ anomaly in thermal expansivity by applied magnetic fields is also presented. The peak is rounded and its magnitude reduced by a factor of 1/2 at 18 kOe. © 1968 The American Physical Society.