Magnetic Sans of Bulk Ferromagnets

In chapter 4 we use the results for the Fourier components to compute the unpolarized and spin-polarized SANS cross sections. These expressions serve to highlight certain features of magnetic SANS such as the role of the magnetodipolar and Dzyaloshinskii-Moriya interaction, and are then applied to analyze experimental SANS data on various bulk magnetic materials such as soft and hard magnetic nanocomposites. Furthermore, this chapter contains discussions on the magnetic Guinier law and on the asymptotic power-law exponents found in magnetic SANS experiments, as well as two sections summarizing magnetic SANS results on nanocrystalline rare-earth metals in the paramagnetic temperature regime and on dislocations.

Magnetic Guinier law

Small-angle scattering of X-rays and neutrons is a routine method for the determination of nanoparticle sizes. The so-called Guinier law represents the low-q approximation for the small-angle scattering curve from an assembly of particles. The Guinier law has originally been derived for nonmagnetic particle-matrix-type systems and it is successfully employed for the estimation of particle sizes in various scientific domains (e.g. soft-matter physics, biology, colloidal chemistry, materials science). An important prerequisite for it to apply is the presence of a discontinuous interface separating particles and matrix. Here, the Guinier law is introduced for the case of magnetic small-angle neutron scattering and its applicability is experimentally demonstrated for the example of nanocrystalline cobalt. It is well known that the magnetic microstructure of nanocrystalline ferromagnets is highly nonuniform on the nanometre length scale and characterized by a spectrum of continuously varying long-wavelength magnetization fluctuations, i.e. these systems do not manifest sharp interfaces in their magnetization profile. The magnetic Guinier radius depends on the applied magnetic field, on the magnetic interactions (exchange, magnetostatics) and on the magnetic anisotropy-field radius, which characterizes the size over which the magnetic anisotropy field is coherently aligned into the same direction. In contrast to the nonmagnetic conventional Guinier law, the magnetic version can be applied to fully dense random-anisotropy-type ferromagnets.

On the Guinier law for spin-echo small-angle neutron scattering

It is shown that Guinier analysis of spin-echo small-angle neutron scattering (SESANS) data is dependent on the instrumental setup, in particular the range of scattering vectors accessible by the detector. In the case that Guinier analysis is permissible, the length scale obtained is proportional to the average width of the density autocorrelation function of the scattering particle, and not its radius of gyration.