Abstract
One of the key challenges in magnetism remains the determination of the nanoscopic magnetization profile within the volume of thick samples, such as permanent ferromagnets. Thanks to the large penetration depth of neutrons, magnetic small‐angle neutron scattering (SANS) is a powerful technique to characterize bulk samples. The major challenge regarding magnetic SANS is accessing the real‐space magnetization vector field from the reciprocal scattering data. In this study, a fast iterative algorithm is introduced that allows one to extract the underlying 2D magnetic correlation functions from the scattering patterns. This approach is used here to analyze the magnetic microstructure of Nanoperm, a nanocrystalline alloy which is widely used in power electronics due to its extraordinary soft magnetic properties. It can be shown that the computed correlation functions clearly reflect the projection of the 3D magnetization vector field onto the detector plane, which demonstrates that the used methodology can be applied to probe directly spin textures within bulk samples with nanometer resolution.
Highlights
Nanostructured magnetic materials attract much interest thanks electrons and X-rays can be used to investigate the interparticle moment coupling in planar 2D assemblies of interacting magnetic nanoparticles.[12,13] for thick, millimeter-sized to the unique magnetic properties that can arise when the struc- 3D samples neither electrons nor X-rays are normally suitable tural units are reduced to access buried magnetic structures due to their small penetrabelow a characteristic intrinsic magnetic length scale of the tion depths, and the internal magnetization profile of most system.[1]
Our approach is used to analyze the magnetic small-angle neutron scattering (SANS) data of Nanoperm and we show that the derived correlation functions nicely reflect the field-dependent, real-space, nanoscale magnetization configuration within the bulk samples predicted by micromagnetic simulation and theory
In writing down Equation 1, it is assumed that the sample is in the approach-to-saturation regime, and that Mð2TÞ % MS, with MS being the saturation magnetization; Θ is the angle between q and H, and MfxðqÞ, MfyðqÞ, and MfzðqÞ are the Fourier transforms of the magnetization components MxðrÞ, MyðrÞ, MzðrÞ of the real-space magnetization vector field, where the asterisk “*” indicates the complex conjugate
Summary
Nanostructured magnetic materials attract much interest thanks electrons and X-rays can be used to investigate the interparticle moment coupling in planar 2D assemblies of interacting magnetic nanoparticles.[12,13] for thick, millimeter-sized to the unique magnetic properties that can arise when the struc- 3D samples neither electrons nor X-rays are normally suitable tural units (e.g., particles, crystallites, or film layers) are reduced to access buried magnetic structures due to their small penetrabelow a characteristic intrinsic magnetic length scale of the tion depths, and the internal magnetization profile of most system.[1]. We introduce a new method to extract the underlying 2D correlation functions from 2D magnetic SANS patterns This approach can be readily applied for the model-free analysis of diffuse magnetic SANS data in various research fields, including multiferroic alloys,[29] permanent magnets,[30] multilayer systems,[31] magnetic steels,[32] nanogranular magnetic films,[33] nanowire arrays,[34,35] ferrofluids,[36] and magnetic nanoparticles.[37,38] the numerical algorithm for the extraction of the 2D magnetic correlation function can be transferred to other experimental techniques where correlation functions are measured, such as spin-echo neutron scattering to study dynamics in the nanoelectron-volt energy range[39,40] and pair distribution function analysis in diffraction for information on atomic disorder,[41] and other complementary X-ray techniques, such as resonant soft X-ray magnetic scattering[42] and X-ray photon correlation spectroscopy.[43] In this study, our approach is used to analyze the magnetic SANS data of Nanoperm and we show that the derived correlation functions nicely reflect the field-dependent, real-space, nanoscale magnetization configuration within the bulk samples predicted by micromagnetic simulation and theory
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