Neutron spin-flip scattering of nanocrystalline cobalt

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.

Magnetic field dependent small-angle neutron scattering on a Co nanorod array: evidence for intraparticle spin misalignment

The structural and magnetic properties of a cobalt nanorod array have been studied by means of magnetic field dependent small-angle neutron scattering (SANS). Measurement of the unpolarized SANS cross section dΣ/dΩ of the saturated sample in the two scattering geometries where the applied magnetic field H is either perpendicular or parallel to the wavevector ki of the incoming neutron beam allows one to separate nuclear from magnetic SANS, without employing the usual sector-averaging procedure. The analysis of the SANS data in the saturated state provides structural parameters (rod radius and centre-to-centre distance) that are in good agreement with results from electron microscopy. Between saturation and the coercive field, a strong field dependence of dΣ/dΩ is observed (in both geometries), which cannot be explained using the conventional expression of the magnetic SANS cross section of magnetic nanoparticles in a homogeneous nonmagnetic matrix. The origin of the strong field dependence of dΣ/dΩ is believed to be related to intradomain spin misalignment, due to magnetocrystalline and magnetoelastic anisotropies and magnetostatic stray fields.