Phenomenology of Magnetism at the Microscopic Scale
- PDF / 3,921,217 Bytes
- 37 Pages / 504.6 x 720 pts Page_size
- 103 Downloads / 255 Views
This chapter presents some simple models which account for the three main types of magnetism previously introduced: that of substances without magnetic atoms (diamagnetism), that of substances with magnetic atoms without interactions (paramagnetism), andfinally that ofsubstances with magnetic atoms which strongly interact with their surroundings (je"o, antife"o,ferrimagnetism, etc.). The models described in this chapter only apply to substances in which the electrons responsible for magnetism are well localised. They do not apply to substances in which magnetism originates from itinerant electrons. For the latter, other models have been proposed ( Landau diamagnetism, Pauli paramagnetism, and Stoner- Wohlfarth ferromagnetism): these "itinerant electron" models of magnetism are presented in chapter8.
1. THE CLASSICAL MODEL OF DIAMAGNETISM: CASE OF LOCAL/SED ELECTRONS We have seen in chapter 3 that a diamagnetic substance is one in which the atoms have no permanent magnetic moment. Correspondingly it exhibits a magnetic susceptibility that is generally weak, and virtually temperature independent. The simplest way to account for this property is to consider the classical model of an electron moving on a circular orbit. The situation is identica! to that of a current loop. When a magnetic field is applied perpendicular to the plane of the orbit, the current is modified in such a way that the flux variation originating from the loop itself is equal and opposite to that due to the applied field (Lenz's rule). The result is an orbita} magnetic moment variation opposite to the applied field. This magnetic moment change is the same whatever the sign of the electron displacement on its orbital, i.e. the sign of the initial orbita} magnetic moment with respect to the applied field: the variation is alway opposite to the magnetic field (fig. 4.1).
106
MAGNETISM - FUNDAMENT ALS
~m
l
m
)
m
/
V
I --:...-----"" ~V
Figure 4.1 - Effect of a magnetic field on two electrons moving in opposite directions on the same circular orbit As an electron on an orbit is equivalent to a superconductor current lloop, i.e. without resistance, the current variation, and accordingly the magnetic moment variation, remain unchanged as long as the applied field is maintained. Let us assume that two electrons with opposite spins move on the same orbit in opposite directions. The total orbital and spin angular momenta, anei accordingly the total magnetic moment, are zero. Under the application of a field, the orbital magnetic moment changes being opposite to the field for both electrons, the system acquires a magnetic moment opposite to the field. Let us look more quantitatively at the magnetic moment variation in the case of one electron (charge - e, and mass ffie) moving at speed v on a circular orbit of radius r (fig. 4.1)_ We will see farther (eq. 7.3) that the orbital magnetic moment is: (4_1)
mo = -erv/2
According to the Lenz's rule, the electromotive force u resulting from the flux variation in the current loop, when a field B is app
Data Loading...
