Dynamical theory of thermal neutron scattering. I. Diffraction from magnetic crystals

Abstract

A general two-beam dynamical theory of the elastic scattering of a thermal neutron from arbitrary magnetic structures is presented. Using a density-matrix formalism, general expressions are developed to compute the scattering cross section as well as the final state of polarization of the emerging neutron. Emphasis is placed on those features of scattering which arise due to the spin of the neutron. Detailed calculations have been carried out for spiral structures, ferromagnetic and antiferromagnetic spin arrangements, and the results are compared with those of kinematical theory. As an illustration, the calculation for the flipping ratio $R$ for the Mn${\mathrm{F}}_2$ (210) peak in the symmetrical Laue configuration indicates that according to dynamical theory $R$ can take arbitrary values when the thickness of the crystal or wavelength of the incident neutron is varied.