Unraveling Nanoscale Magnetic Ordering in Fe3O4 Nanoparticle Assemblies via X-rays

Mesoscale self-organization of polydisperse magnetic nanoparticles at the water surface

In this study, we investigated the self-ordering process in Langmuir films of polydisperse iron oxide nanoparticles on a water surface, employing in situ x-ray scattering, surface pressure-area isotherm analysis, and Brewster angle microscopy. X-ray reflectometry confirmed the formation of a monolayer, while grazing incidence small-angle x-ray scattering revealed short-range lateral correlations with a characteristic length equal to the mean particle size. Remarkably, our findings indicated that at zero surface pressure, the particles organized into submicrometer clusters, merging upon compression to form a homogeneous layer. These layers were subsequently transferred to a solid substrate using the Langmuir-Schaefer technique and further characterized via scanning electron microscopy and polarized neutron reflectometry. Notably, our measurements revealed a second characteristic length in the lateral correlations, orders of magnitude longer than the mean particle diameter, with polydisperse particles forming circular clusters densely packed in a hexagonal lattice. Furthermore, our evidence suggests that the lattice constant of this mesocrystal depends on the characteristics of the particle size distribution, specifically the mean particle size and the width of the size distribution. In addition, we observed internal size separation within these clusters, where larger particles were positioned closer to the center of the cluster. Finally, polarized neutron reflectometry measurements provided valuable insights into the magnetization profile across the layer.

Using small-angle scattering to guide functional magnetic nanoparticle design

Magnetic nanoparticles offer unique potential for various technological, biomedical, or environmental applications thanks to the size-, shape- and material-dependent tunability of their magnetic properties. To optimize particles for a specific application, it is crucial to interrelate their performance with their structural and magnetic properties. This review presents the advantages of small-angle X-ray and neutron scattering techniques for achieving a detailed multiscale characterization of magnetic nanoparticles and their ensembles in a mesoscopic size range from 1 to a few hundred nanometers with nanometer resolution. Both X-rays and neutrons allow the ensemble-averaged determination of structural properties, such as particle morphology or particle arrangement in multilayers and 3D assemblies. Additionally, the magnetic scattering contributions enable retrieving the internal magnetization profile of the nanoparticles as well as the inter-particle moment correlations caused by interactions within dense assemblies. Most measurements are used to determine the time-averaged ensemble properties, in addition advanced small-angle scattering techniques exist that allow accessing particle and spin dynamics on various timescales. In this review, we focus on conventional small-angle X-ray and neutron scattering (SAXS and SANS), X-ray and neutron reflectometry, gracing-incidence SAXS and SANS, X-ray resonant magnetic scattering, and neutron spin-echo spectroscopy techniques. For each technique, we provide a general overview, present the latest scientific results, and discuss its strengths as well as sample requirements. Finally, we give our perspectives on how future small-angle scattering experiments, especially in combination with micromagnetic simulations, could help to optimize the performance of magnetic nanoparticles for specific applications.

The benefits of a Bayesian analysis for the characterization of magnetic nanoparticles

Magnetic nanoparticles offer a unique potential for various biomedical applications, but prior to commercial usage a standardized characterization of their structural and magnetic properties is required. For a thorough characterization, the combination of conventional magnetometry and advanced scattering techniques has shown great potential. In the present work, we characterize a powder sample of high-quality iron oxide nanoparticles that are surrounded with a homogeneous thick silica shell by DC magnetometry and magnetic small-angle neutron scattering (SANS). To retrieve the particle parameters such as their size distribution and saturation magnetization from the data, we apply standard model fits of individual data sets as well as global fits of multiple curves, including a combination of the magnetometry and SANS measurements. We show that by combining a standard least-squares fit with a subsequent Bayesian approach for the data refinement, the probability distributions of the model parameters and their cross correlations can be readily extracted, which enables a direct visual feedback regarding the quality of the fit. This prevents an overfitting of data in case of highly correlated parameters and renders the Bayesian method as an ideal component for a standardized data analysis of magnetic nanoparticle samples.