Neutron scattering from the Heisenberg ferromagnets EuO and EuS. II. Static critical properties

Abstract

Neutron scattering has been used to study the magnetic ordering process in the isotropic exchange coupled ferromagnets EuO and EuS. Quantities investigated include the critical coefficients $B$ and ${F}^{+}$ and the critical exponents $\ensuremath{\beta}$, $\ensuremath{\nu}$, and $\ensuremath{\gamma}$ describing respectively the temperature dependence of the reduced magnetization below ${T}_{C}$ and the temperature dependence of the inverse spin correlation range and reduced static susceptibility above ${T}_{C}$. All of the above-mentioned parameters are found to be in satisfactory agreement with theoretical predictions; a predicted scaling relation between $\ensuremath{\beta}$, $\ensuremath{\nu}$, and $\ensuremath{\gamma}$ is also confirmed. An approximate procedure for unfolding from the scattering below ${T}_{C}$ that part associated with the longitudinal static susceptibility was developed and applied to EuO to obtain an indication of the distance over which longitudinal spin fluctuations are correlated in the ordered state. The results are consistent with the view that the range of spin correlations below ${T}_{C}$ is about half as large as at an equivalent temperature about ${T}_{C}$. In all but one case, agreement between the neutron scattering results and those obtained by other experimental methods is within the limits of the errors. The exception is the critical exponent $\ensuremath{\gamma}$ for which the neutron value is significantly larger than that derived from bulk measurements.