Small-Angle Neutron Scattering by the Magnetic Microstructure of Nanocrystalline Ferromagnets Near Saturation

R. D. Shull National Institute of Standards and Technology, Gaithersburg, MD 20899-0001, USA The paper presents a theoretical analysis of elastic magnetic small-angle neutron scattering (SANS) due to the nonuniform magnetic microstructure in nanocrystalline ferromagnets. The reaction of the magnetization to the magnetocrystalline and magnetoelastic anisotropy fields is derived using the theory of micromagnetics. In the limit where the scattering volume is a single magnetic domain, and the magnetization is nearly aligned with the direction of the magnetic field, closed form solutions are given for the differential scattering cross-section as a function of the scattering vector and of the magnetic field. These expressions involve an anisotropy field scattering function, that depends only on the Fourier components of the anisotropy field microstructure, not on the applied field, and a micromagnetic response function for SANS, that can be computed from tabulated values of the materials parameters saturation magnetization and exchange stiffness constant or spin wave stiffness constant. Based on these results, it is suggested that the anisotropy field scattering function SH can be extracted from experimental SANS data. A sum rule for SH suggests measurement of the volumetric mean square anisotropy field. When magnetocrystalline anisotropy is dominant, then a mean grain size or the grain size distribution may be determined by analysis of SH .