Neutron Scattering From Rare-Earth Materials

Neutron scattering has played a crucial role in advancing our understanding of rare-earth materials. It has provided a detailed description of the rich array of exotic magnetic structures; it has confirmed the accuracy of theoretical wave functions for the 4f electrons; and it has provided fundamental data on the collective magnetic excitations in these materials. The fundamental property of the neutron which has been exploited in this work is the magnetic interaction which exists between the magnetic moment of the neutron and atomic magnetic moments on individual rare-earth atoms. This interaction produces scattering of neutrons in a manner closely analogous to the scattering of X rays by atomic charge distributions. In a material exhibiting long-range magnetic order, Bragg diffraction peaks will appear at scattering angles determined by the periodicity of the magnetic structure. The Bragg intensities are determined by the magnitude and relative directions of the atomic moments. The rare-earth metals and alloys are characterized by sinusoidal modulation of magnetic moment components which can be combined in various ways to produce a variety of magnetic structures. The periodicity of these modulations is frequently not related simply to the underlying periodicity of the chemical structure. The major features of these structures are explained by the combined, and sometimes competing, exchange and crystal-field interactions. At a more fundamental level, neutron diffraction also gives information on the spatial distribution of a magnetic moment in a rare-earth atom. This moment comes from the 4f electron shell, and accurate measurements of the neutron scattering amplitudes have been used to check the accuracy of atomic wave function calculations for the 4f electrons. It was found that relativistic Dirac-Fock calculations are in excellent agreement with the experimental results. Collective excitations of ordered magnetic systems are described in terms of spin waves, which are sinusoidal modulations in space and time of the direction of the ordered moments. Inelastic neutron scattering is used to measure the energy and wave length of these collective excitations. Analysis of these data gives direct information on the interatomic interactions responsible for the magnetib properties of these materials.