Magnetic Sans of Nanoparticles and Complex Systems

This chapter provides an overview on the magnetic SANS of nanoparticles and complex systems, which include ferrofluids, magnetic steels, and spin glasses and amorphous magnets. The underlying assumptions of the conventional particle-matrix-based model of magnetic SANS, which assumes uniformly magnetized domains, characteristic e.g., for superparamagnets, are discussed and we provide a complete specification of the micromagnetic boundary-value problem. First attempts to provide analytical expressions for the vortex-state-related magnetic SANS of thin circular discs are considered.

Real-Space Analysis

Spin-misalignment correlations in real space are the subject of this chapter. The correlation function and correlation length of the spin-misalignment SANS cross section are introduced, their properties are discussed within the context of micromagnetic theory, and selected experimental data on Nd-Fe-B-based permanent magnets and nanocrystalline elemental soft (Cobalt and Nickel) and hard (Gadolinium and Terbium) magnets are reviewed.

Introduction

In this chapter the basic properties of the neutron and the different neutron scattering cross sections are introduced, the nuclear and the magnetic SANS cross sections are derived, and the various origins of magnetic SANS are discussed in relation to the microstructure of polycrystalline magnetic materials.

Basics of Static Micromagnetism

Chapter 3 introduces the continuum expressions for the magnetic energy contributions, which are employed for describing the mesoscale magnetic microstructure of magnetic materials. It is then shown how the static equations of micromagnetics, the so-called Brown's equations, can be solved in the high-field regime and how the Fourier components of the magnetization are related to the magnetic SANS cross section.

Magnetic Sans of Bulk Ferromagnets

In chapter 4 we use the results for the Fourier components to compute the unpolarized and spin-polarized SANS cross sections. These expressions serve to highlight certain features of magnetic SANS such as the role of the magnetodipolar and Dzyaloshinskii-Moriya interaction, and are then applied to analyze experimental SANS data on various bulk magnetic materials such as soft and hard magnetic nanocomposites. Furthermore, this chapter contains discussions on the magnetic Guinier law and on the asymptotic power-law exponents found in magnetic SANS experiments, as well as two sections summarizing magnetic SANS results on nanocrystalline rare-earth metals in the paramagnetic temperature regime and on dislocations.

Micromagnetic Simulations

In this chapter we report the progress made in using full-scale micromagnetic simulations for the understanding of the fundamentals of magnetic SANS. These studies take into account the nonlinearity of Brown's static equations of micromagnetics. Prototypical sample microstructures, the implementation of the different energy contributions, and the state-of-the-art regarding simulations on multiphase nanocomposites and nanoparticle assemblies are discussed.

Basics of Sans

In this chapter the general aspects of SANS are addressed. This includes discussions of the experimental setup, instrumental resolution, the influence of inelastic contributions due to phonon and magnon scattering to the elastic SANS cross section, the basics of nuclear SANS, the magnetic SANS cross sections, and their relation to the particle-matrix model.