Quantitative Analysis of Inelastic Scattering in Two-Crystal and Three-Crystal Neutron Spectrometry; Critical Scattering from RbMnF3

Abstract

The use of the neutron spectrometer in the quantitative determination of neutron scattering cross sections is discussed in detail. The explicit analytical dependence of the total detection efficiency of the three-crystal spectrometer on incident and scattered neutron energies as well as on instrumental parameters is presented, and measurement of the energy sensitivity of the analyzer-detector system is described. A comprehensive treatment of two-crystal inelastic scattering is given, and a practical method is developed for carrying out the inelastic analysis of two-crystal data using the experimental elastic resolution function. The quasielastic approximation is discussed, several mechanisms which extend its range of validity are described, and its applicability is shown to depend on a parameter which is a dimensionless combination of the variables in the problem. These techniques are applied to the measurement of the spinpair correlation function, in the neighborhood of the critical point, for the ideal Heisenberg antiferromagnet RbMn${\mathrm{F}}_3$. The predictions of dynamic-scaling theory, recently proposed by Halperin and Hohenberg, are extensively tested and find strong support in experiment. The energy widths of the scattering, measured in the region $T\ge T_N$, are compared with theoretical calculations for the Heisenberg antiferromagnet by Résibois and Piette and by Huber and Krueger. The measurement, by means of the two-crystal diffractometer, of the static correlation function at the critical point is discussed in detail, and direct evidence is presented for departure from the classical Ornstein-Zernike behavior. The parameter $\eta$, which measures this departure, is determined by means of three independent experiments and, after the inelasticity of the scattering is taken into full account, is found to be 0.055 ± 0.010. Measurement of the critical indices above $T_N$ gives $\gamma =1.366\mathrm{}\pm 0.024$ and $\nu =0.701\mathrm{}\pm 0.011$, and the static scaling relation $\gamma =(2-\eta )\nu$ is verified. Below $T_N$, we find $\beta =0.32\mathrm{}\pm 0.02$ and ${\nu }^{\prime }=0.54\mathrm{}\pm 0.03$; these values are consistent with the static scaling relation $2\beta =(1+\eta ){\nu }^{\prime }$, whereas the symmetry relation $\nu ={\nu }^{\prime }$ is violated.