Dependence of powder neutron scattering on the dimensionality of magnetic order

The peak profiles of coherent scattering obtained in powder diffraction experiments that reflect the dimensionality of the ordered system are discussed. The well known expression that generates the powder diffraction pattern of a two-dimensionally ordered system is generalized to include couplings along the third dimension. Attention is concentrated on the magnetic systems, and the interactions between the adjacent layers are allowed to be either ferromagnetic or antiferromagnetic. A two-dimensionally ordered system gives Bragg peaks with characteristic sawtooth profiles at the (hk) positions. As the correlations between the ordered layers develop, new Bragg peaks at the (khl) positions appear and their widths are closely related to the correlation length along the third axis. A finite correlation length gives a width which is broader than the instrumental resolution, and its intrinsic width is inversely proportional to the correlation length. In the limit for long-range correlation along the third axis, symmetric peaks with their widths consistent with the instrumental resolution are then obtained. Neutron magnetic diffraction patterns taken at low temperatures on various high-Tc oxides are used as examples to illustrate the expression obtained.