Magnetic order in two-dimensional nanoparticle assemblies

Abstract

This thesis involves a fundamental study of two-dimensional arrays of magnetic nanoparticles using non-contact Atomic Force Microscopy, Magnetic Force Microscopy, and Atomic Force Spectroscopy. The goal is to acquire a better understanding of the interactions between magnetic nanoparticles and the resulting configuration of their magnetic moments. We have studied two systems: 20-nm magnetite (Fe3O4) and 21-nm cobalt ferrite (CoFe2O4) nanoparticles, capped with oleic acid and oleylamine, deposited using drop-casting technique on HOPG (Highly Oriented Pyrolytic Graphite). We present an analytical model to interpret the experimental spectroscopy curves (frequency shift as a function of the tip-sample distance) in terms of force, to enable a quantitative interpretation of the experimental results. In addition, a numerical model based on the Metropolis Monte Carlo method has been developed to calculate the configuration of magnetic moments with minimum energy. The energy consists of dipolar energy and anisotropy energy. The simulations have shown that local energy minima are present that correspond to different configurations of magnetic moments. Because of the thermal energy, the system may jump in between these energy minima. Considering a specific configuration of moments, MFM images were simulated taking the dipolar interactions between the nanoparticles and the tip into account. Spectroscopy curves were calculated for two cases: namely with and without the influence of the tip. The magnetite nanoparticles present a relatively large magnetic moment and exhibit strong dipole-dipole interactions and small, negligible, anisotropy. The observed repulsion between the tip and the nanoparticles at the side of the nanoparticle islands shows that dipolar coupling between the particles causes blocking of their magnetic moments. The experimental observations agree well with the numerical calculations, which show that the magnetic moments arrange themselves in flux-closure structures. However, the magnetite nanoparticle 2D systems can be considered soft-magnetic: their moments are strongly influenced by the field of the tip. This has been observed experimentally and confirmed by simulations for the considered magnetic moment of the tip. The cobalt-ferrite nanoparticles present a similar magnetic moment as the magnetite nanoparticles. The anisotropy, however, increases significantly with decreasing temperature, which leads to blocking of the moments even in the strong field of the tip. As a consequence, attractive and repulsive areas were observed in the MFM image above the islands of nanoparticles at low temperatures. In our simulation we have assumed arbitrary orientations of the easy axes of the particles. Simulation results reveal short-range order of the magnetic moments, consistent with the experimental results.