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Magnetoelastic Behavior of Europium Oxide. II. Magnetostriction and the λ Anomaly

1968; American Institute of Physics; Volume: 171; Issue: 2 Linguagem: Inglês

10.1103/physrev.171.555

1536-6065

B. E. Argyle, Nahonori Miyata,

Ferroelectric and Piezoelectric Materials

Magnetostriction of single-crystal EuO was determined in the temperature range 4.2-150\ifmmode^\circ\else\textdegree\fi{}K in applied magnetic fields up to 20 kOe. Linear magnetostriction coefficients extrapolated to 0\ifmmode^\circ\else\textdegree\fi{}K are ${\ensuremath{\lambda}}_{100}=\ensuremath{-}22\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ and ${\ensuremath{\lambda}}_{111}=55\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. These yield the magnetoelastic coupling constants ${b}_{1}(0)\ensuremath{\equiv}\ensuremath{-}\frac{3}{2}{\ensuremath{\lambda}}_{100}({c}_{11}\ensuremath{-}{c}_{12})=(31\ifmmode\pm\else\textpm\fi{}6)\ifmmode\times\else\texttimes\fi{}{10}^{6}$ and ${b}_{2}(0)\ensuremath{\equiv}\ensuremath{-}3{\ensuremath{\lambda}}_{111}{c}_{44}=\ensuremath{-}(86\ifmmode\pm\else\textpm\fi{}10)\ifmmode\times\else\texttimes\fi{}{10}^{6}$ 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 $\ensuremath{\lambda}(T)=\ensuremath{\lambda}(0)[{\stackrel{^}{I}}_{\frac{5}{2}}({\mathcal{L}}^{\ensuremath{-}1}(m))]$ and $\ensuremath{\lambda}(T)=\ensuremath{\lambda}(0){m}^{2}$, respectively. This suggests that the magnetoelastic Hamiltonian contains one-ion (${B}_{1}, {B}_{2}$) and two-ion (${D}_{1}, {D}_{2}$) magnetoelastic constants, ${B}_{1}\ensuremath{\approx}{D}_{1}\ensuremath{\approx}\frac{1}{2}{b}_{1}$ and ${B}_{2}\ensuremath{\approx}{D}_{2}\ensuremath{\approx}\frac{1}{2}{b}_{2}$. Since classical dipole-dipole interactions in EuO theoretically give ${{D}_{1}}^{d}=\ensuremath{-}6.4\ifmmode\times\else\texttimes\fi{}{10}^{6}$ and ${{D}_{2}}^{d}\ensuremath{\approx}+4.3\ifmmode\times\else\texttimes\fi{}{10}^{6}$, we estimate for pseudodipolar effects ${{D}_{1}}^{p}\ensuremath{\approx}21\ifmmode\times\else\texttimes\fi{}{10}^{6}$ and ${{D}_{2}}^{p}=\ensuremath{-}47\ifmmode\times\else\texttimes\fi{}{10}^{6}$ dyn/${\mathrm{cm}}^{2}$. The forced (volume) magnetostriction ${\ensuremath{\lambda}}_{f}$ 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 ${\ensuremath{\lambda}}_{f}$ versus ${\ensuremath{\sigma}}^{2}$, 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 Gr\"uneisen parameter. Data exhibiting suppression of the $\ensuremath{\lambda}$ anomaly in thermal expansivity by applied magnetic fields is also presented. The peak is rounded and its magnitude reduced by a factor of \ensuremath{\approx}\textonehalf{} at 18 kOe.