Analysis of the small-angle neutron scattering of nanocrystalline ferromagnets using a micromagnetics model

In ferromagnets with a nonuniform magnetocrystalline and/or magnetoelastic anisotropy, such as nanocrystalline ~nc-! or cold-worked ~cw-! polycrystalline materials, the static magnetic microstructure gives rise to strong elastic magnetic small-angle neutron scattering ~SANS!. The paper explores a method for analyzing field-dependent SANS data from such materials in terms of a model based on the theory of micromagnetics. Samples of cw Ni and of electrodeposited nc Ni and nc Co were characterized by x-ray scattering and magnetometry, and were investigated by SANS both with and without polarization of the neutron beam. The variation of the differential scattering cross section with the scattering vector and with the applied magnetic field is well described by the model. Also, experimental results for the exchange stiffness constant A and for the spin-wave stiffness constant D obtained from the analysis are found to agree with literature data obtained by inelastic neutron scattering on single-crystal specimens. The model supplies an ‘‘anisotropy field scattering function’’ that contains information on the magnitude of the magnetic anisotropy in the material, and on the characteristic length scales on which the anisotropy changes direction. The results suggest that the anisotropy may be strongly nonuniform in each crystallite, possibly due to twinning, and that some magnetic moments in the Ni samples are strongly pinned at defects.