Symmetry analysis in neutron diffraction studies of magnetic structures: 5. Polarization effects in the scattering of neutrons by magnetic structures

It is shown that both the cross section of elastic scattering by a magnetic structure and the polarization vector of the scattered neutrons beam are described by a set of complex axial vectors M^L. They depend on the vectors of atomic magnetic moments in a primitive cell of the crystal and the wave-vector star of the magnetic structure. Particularly, the intensity of a magnetic Bragg reflection and the polarization vector of the scattered beam of that reflection are determined only by a vector M^L connected with an arm star contribution of the magnetic structure and corresponding to the wave vector k_L of a star {k}. A single magnetic reflection allows one to determinean arm contribution of the magnetic structure if one uses polarization effects and an expansion of the magnetic structure over the basis functions of the irreducible representation of the crystal space group. In the general case minimal number of necessary reflections for the total determination of a magnetic crystal is equal to the arm number of the wave-vector star. All analyses here have been done for the single domain magnetic structure. The polarization phenomena will not be observed for many cases where there is a uniform distribution of domains.