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Introduction to Magnetism W. Weber

Abstract This lecture gives an overview of the main phenomena that determine the magnetism of matter and the properties of magnetic materials. After an introduction, the second section presents the following topics: orbital and spin magnetic moment, dia- and paramagnetism of free atoms, and Pauli-paramagnetism of free electrons. The third section deals with ferromagnetism. The Heisenberg-exchange interaction and its consequences for the magnetization as a function of the applied magnetic field and the temperature are discussed in the molecular field approximation. In particular, the ferromagnetic phase transition and spin waves are described before we finish this section by discussing briefly itinerant ferromagnetism. The fourth section introduces the important concepts of magnetic anisotropy (shape and magneto-crystalline anisotropy) and magnetic domains. Then, we discuss magnetization reversal by the application of a magnetic field, and how it is influenced by the nucleation of domains and domain wall motion. In a last subsection of this section, we discuss the magnetic behavior of small particles. The fifth section deals with the magnetism of thin films and multilayers. We mostly concentrate on two important phenomena observed in multilayers: indirect exchange coupling (RKKY interaction) and giant magnetoresistance.

1.1 Introduction 1.1.1 Definition of the Magnetic Moment It is not possible to define a magnetic moment in analogy to the electric dipole moment: p D Ql, with l the displacement vector between the charges CQ and Q. It is therefore not possible to write m D QM l, with QM the magnetic charge,

W. Weber Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504, UdS - CNRS, 23 rue du Loess, BP 43, F-67034 Strasbourg Cedex 2, France e-mail: [email protected]

E. Beaurepaire et al. (eds.), Magnetism and Synchrotron Radiation, Springer Proceedings in Physics 133, DOI 10.1007/978-3-642-04498-4_1, c Springer-Verlag Berlin Heidelberg 2010 

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W. Weber

Fig. 1.1 Magnetic moment due to an eddy current

a so-called magnetic monopole. Up to now, magnetic monopoles have not been discovered, which is expressed by one of Maxwell’s equations: r B D 0, that is, there is no source of a magnetic field. To give a definition of the magnetic dipole moment, we exploit the fact that a bar magnet and a small coil through which a current is driven have similar properties. Both produce, if viewed from a point sufficiently far away from them, a magnetic field of similar shape. Thus, let us define the magnetic dipole moment m by considering an eddy current (Ampere’s definition): m D I  F, where the direction of the vector F indicates the sense of the current I and its absolute value the area that is encircled by the current (Fig. 1.1). The unit of the magnetic moment is A m2 .

1.1.2 Energy of the Moment in an External Magnetic Field We emphasize that the magnetic field H (unit is A m1 ) derives from a vector potential and is therefore an axial vector, while