Small-angle neutron scattering modeling of spin disorder in nanoparticles

Abstract

Magnetic small-angle neutron scattering (SANS) is a powerful technique for investigating magnetic nanoparticle assemblies in nonmagnetic matrices. For such microstructures, the standard theory of magnetic SANS assumes uniformly magnetized nanoparticles (macrospin model). However, there exist many experimental and theoretical studies which suggest that this assumption is violated: deviations from ellipsoidal particle shape, crystalline defects, or the interplay between various magnetic interactions (exchange, magnetic anisotropy, magnetostatics, external field) may lead to nonuniform spin structures. Therefore, a theoretical framework of magnetic SANS of nanoparticles needs to be developed. Here, we report numerical micromagnetic simulations of the static spin structure and related unpolarized magnetic SANS of a single cobalt nanorod. While in the saturated state the magnetic SANS cross section is (as expected) determined by the particle form factor, significant deviations appear for nonsaturated states; specifically, at remanence, domain-wall and vortex states emerge which result in a magnetic SANS signal that is composed of all three magnetization Fourier components, giving rise to a complex angular anisotropy on a two-dimensional detector. The strength of the micromagnetic simulation methodology is the possibility to decompose the cross section into the individual Fourier components, which allows one to draw important conclusions regarding the fundamentals of magnetic SANS.

Anomalous magnetic anisotropy and magnetic nanostructure in pure Fe induced by high-pressure torsion straining

“…To analyze the change in the magnetic domain size within nanosized regions, further improvement is necessary using micromagnetics. This method continues to progress with experimental, analytical, and micromagnetic-computational approaches [47][48][49]; the analytical solution for magnetic-field-dependent SANS intensity is only provided for a few special cases such as magnetic vortices in submicron-sized soft magnetic disks [48].…”

Field Dependence of Magnetic Disorder in Nanoparticles

“…Applying SANS with uniaxial polarization analysis (POLARIS) to NP assemblies, a canted magnetic surface shell is reported [36,37], and the temperature dependence of the spin canting in CoFe 2 O 4 NPs is derived [38]. Micromagnetic simulations of isolated magnetic NPs in a nonmagnetic matrix demonstrate how the interplay between various magnetic interactions leads to nonuniform spin structures in NPs, resulting in a strong variation of the magnetic SANS [39,40]. In the context of a polarized SANS study on Fe 3 O 4 =Mn-ferrite core/shell structures, complementary atomistic magnetic simulations considering a drastically reduced exchange coupling between the core and shell spins reveal no remanence for the shell along with a disordered rather than canted surface spin configuration [41].…”

Magnetic Small-Angle Neutron Scattering

“…Future research will therefore concentrate on the analytical and/or numerical micromagnetic computation of the magnetic SANS cross section of a dispersion of magnetic nanoparticles in a nonmagnetic matrix-the classical prototypical sample microstructure in many magnetic SANS experiments. There is ample theoretical (Berger et al, 2008;Gatel et al, 2015;Vivas, Yanes, and Michels, 2017) as well as experimental (Disch et al, 2012;Günther et al, 2014;Krycka et al, 2014) evidence that nanosized magnetic particles are not homogeneously magnetized, and the question thus arises whether the standard expression for the cross section, Eq. (23), is still adequate to describe magnetic SANS.…”

“…Because of their relatively large volume, nanowires exhibit stable ferromagnetic properties and are mostly multidomain structures. The particle-matrix approach is therefore not applicable to nanowires; indeed, micromagnetic simulations (Vivas, Yanes, and Michels, 2017) and experimental data (Günther et al, 2014) demonstrate strong deviations from the uniform-particle form-factor model.…”