03MagneticSusceptibilities.pdf

3 Magnetic Susceptibilities The previous chapters concentrated on the origins of magnetic moments in individual ions or atoms and collective excitations of spin systems coupled by the exchange interaction. In this chapter, we will discuss the magnetic properties of macroscopic media composed of very large numbers of indivi- dual moments and the dependence of these properties on the magnetic field.1 Specifically, we are interested in the net magnetization (magnetic dipole mo- ment per unit volume) that exists either spontaneously or in response to an applied magnetic field. If the relationship between the induced magnetization and the applied field is linear, we can write M = M0 + χ · H, (3.1) where χ is called the magnetic susceptibility tensor of the medium. For isotropic media, the susceptibility reduces to a scalar constant times the iden- tity matrix, and M and H are collinear. 3.1 Diamagnetism According to Lenz’s law, currents are induced in conductors when a magnetic field is applied. These currents persist only as long as the applied field is changing and circulate in such a way as to produce a magnetic field that opposes the applied field. In addition to these currents from the conduction electrons, the application of a magnetic field produces perturbations in the orbitals of bound electrons resulting in microscopic currents opposing the applied field. In contrast to the macroscopic currents, however, the microscopic currents persist as long as the field is applied. 1 General introductory treatments of the theory of magnetism and magnetic sus- ceptibilities are given by Brailsford [1], Ashcroft and Mermin [2], and Kittel [3]. Effective field theories in magnetism are discussed in detail by Smart [4]. D.D. Stancil, A. Prabhakar, Spin Waves, DOI