Magnetic Small Angle Neutron Scattering A Probe for Mesoscale Magnetism Analysis 1st Edition by Andreas Michels 0192597981 9780192597984

1 INTRODUCTION

1.1 Outline of the book

1.2 Basic properties of the neutron and numerical relations

1.3 Definitions of scattering cross sections

1.4 Elastic differential SANS cross section

1.4.1 Nuclear SANS cross section

1.4.2 Magnetic SANS cross section

1.5 Diffraction versus refraction

1.6 Origin of magnetic SANS: relation to magnetic microstructure

1.6.1 Origins of inhomogeneous magnetization states

1.6.2 Example: uniform versus nonuniform sphere

2 BASICS OF SANS

2.1 Description of the SANS setup

2.2 Elementary considerations of resolution

2.3 Inuence of inelastic SANS

2.4 Summary of the basics of nuclear SANS

2.4.1 Coherent and incoherent nuclear scattering

2.4.2 Spin-polarized nuclei and polarized neutrons

2.4.3 Nuclear SANS cross section

2.5 Magnetic SANS: general considerations

2.6 Unpolarized SANS cross sections

2.6.1 k0 ⊥ H0

2.6.2 k0 || H0

2.7 SANSPOL cross sections

2.7.1 k0 ⊥ H0

2.7.2 k0 || H0

2.8 POLARIS cross sections

2.8.1 k0 ⊥ H0

2.8.2 k0 || H0

2.8.3 POLARIS equations with non-ideal neutron optics

2.9 Magnetic SANS at saturation

2.9.1 Unpolarized SANS cross sections at saturation

2.9.2 SANSPOL cross sections at saturation

2.9.3 POLARIS cross sections at saturation

2.9.4 Relation to particle-matrix approach

3 BASICS OF STATIC MICROMAGNETISM

3.1 Magnetic energy contributions

3.1.1 Exchange energy

3.1.2 Dzyaloshinskii{Moriya energy

3.1.3 Magnetocrystalline anisotropy

3.1.4 Magnetoelastic anisotropy

3.1.5 Zeeman interaction

3.1.6 Magnetodipolar interaction

3.2 Balance of torques

3.3 Connecting micromagnetics and SANS

3.3.1 The general case of a ferromagnet with anisotropy-field and magnetostatic uctuations

3.3.2 The case of a single-phase ferromagnet

4 MAGNETIC SANS OF BULK FERROMAGNETS

4.1 Historical overview of magnetic SANS theory

4.2 Closed-form results for the spin-misalignment scattering

4.2.1 Unpolarized neutrons (k0 ⊥ H0)

4.2.2 Unpolarized neutrons (k0 || H0)

4.2.3 Polarized neutrons (POLARIS) (k0 ⊥ H0)

4.2.4 Polarized neutrons (POLARIS) (k0 || H0)

4.2.5 Third-order magnetic SANS effect

4.3 Basic features of magnetic SANS

4.3.1 Angular anisotropy

4.3.2 Effect of magnetodipolar interaction

4.3.3 Effect of Dzyaloshinskii–Moriya interaction

4.3.4 Magnetic Guinier law

4.3.5 Asymptotic power-law exponent

4.3.6 Polarization dependence of magnetic SANS

4.4 Selected experimental results

4.4.1 Fe-based soft magnetic nanocomposites

4.4.2 Nd–Fe–B-based hard magnetic nanocomposites

4.4.3 Spin-flip SANS of nanocrystalline cobalt

4.5 SANS on systems with random paramagnetic susceptibility

4.6 Magnetic SANS on dislocations

5 MAGNETIC SANS OF NANOPARTICLES AND COMPLEX SYSTEMS

5.1 Nanoparticles

5.1.1 Description by the conventional particle-matrix approach

5.1.2 SANS of superparamagnetic particles

5.1.3 The micromagnetic problem

5.1.4 SANS by magnetic vortices in thin submicron-sized soft ferromagnetic cylinders

5.2 Complex systems

5.2.1 Ferrouids

5.2.2 Magnetic steels

5.2.3 Spin glasses, amorphous metals, and critical SANS

5.2.4 Some further applications of magnetic SANS

6 REAL-SPACE ANALYSIS

6.1 Magnetization profile around a spherical inclusion

6.2 Correlation function of the spin-misalignment SANS cross section

6.3 Basic properties of the correlation function of the spin-misalignment SANS

6.4 Total correlation function

6.5 Selected experimental results

6.5.1 Nanocrystalline Nd–Fe–B-based permanent magnets

6.5.2 Nanocrystalline soft magnets

6.5.3 Nanocrystalline hard magnets

7 MICROMAGNETIC SIMULATIONS

7.1 Brief overview of micromagnetic SANS simulations

7.2 Sample microstructures

7.3 Simulation methodology and implementation of energy contributions

7.3.1 Methodology

7.3.2 Energy contributions

7.4 Decrypting the SANS cross section

7.4.1 Nanocomposite bulk magnets

7.4.2 Magnetic nanoparticles

7.5 Summary and outlook on simulation studies

Appendix A Caveat on the separation of nuclear and magnetic SANS from unpolarized SANS data

Appendix B Magnetic materials parameters

Appendix C Fourier—Hankel—Abel cycle

Appendix D Fourier transform of the local saturation magnetization in a material containing ferromag

Appendix E Three- and two-dimensional Fourier transforms in polar coordinates

E.0.1 Three-dimensional case

E.0.2 Two-dimensional case

Appendix F Magnetic units

Appendix G Fundamental constants

Appendix H Glossary of symbols

References

Index