1 Basis of Nanomagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1 Introduction: The Importance of Nanomagnetism . . . . . . . . . . . . . . . . 5
1.2 The Origin of Nanomagnetic Behavior . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.1 Sample Dimensions and Characteristic Lengths . . . . . . . . . . . 8
1.2.2 Broken Translation Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.3 Nanoscopic Samples and Magnetization Reversal . . . . . . . . . 20
1.3 Dimensionality and Critical Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . 20
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2 Magnetic Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2 Interactions in Magnetic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.2.1 Exchange Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.2.2 Magnetostatic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2.3 Magnetic Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2.4 Magnetoelastic Energy and Magnetostriction . . . . . . . . . . . . . 37
2.3 Elements of Micromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.3.1 Equation of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.4 Magnetic Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.4.1 Domain Wall Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.4.2 Domain Wall Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.5 Random Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3 Magnetism of Small Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.2 Particle Size and Magnetic Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.3 Superparamagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.3.1 Superparamagnetism: The Langevin Function . . . . . . . . . . . . 78
3.4 Surface Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.5 The Stoner-Wohlfarth Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.5.1 Inhomogeneous Magnetization Reversal . . . . . . . . . . . . . . . . . 91
3.5.2 Precessional Magnetization Reversal . . . . . . . . . . . . . . . . . . . . 94
3.5.3 Current-Induced Magnetization Reversal . . . . . . . . . . . . . . . . 97
3.6 Interaction Between Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4 Magnetism of Thin Films and Multilayers . . . . . . . . . . . . . . . . . . . . . . . . 109
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.1.1 Thin Films: Planar Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.1.2 Thin Films: Laterally Structured Systems . . . . . . . . . . . . . . . . 112
4.
About the Author:
Alberto Passos Guimarães studied physics at the University of Rio de Janeiro and obtained his Ph.D. at the University of Manchester, England. He was a visiting scientist at MIT, Cambridge, and at the Physics Institute in Uppsala, Sweden. He has worked in the field of magnetism for several years, initially studying the magnetic properties of rare-earth intermetallic compounds with Mossbauer Spectroscopy and zero-field nuclear magnetic resonance (NMR), and also studied the Magnetocaloric Effect in intermetallic compounds. In recent years he has turned his attention to nanoscale systems, such as small particles, nanowires, nanorings and nanodisks studied with different experimental techniques and micromagnetic simulation. He is the author of Magnetism and Magnetic Resonance in solids (1998) and From Lodestone to Supermagnets: Understanding Magnetic Phenomena (2005), and has also been active in the popularization of science.
He is now Emeritus Researcher at the Brazilian Center for Research in Physics (CBPF) and he is a member of the Brazilian Academy of Sciences.
