29:130 ELECTRICITY AND MAGNETISM II SPRING 2013

MAGNETIC MATERIALS

Just as a dielectric contains electric dipoles that contribute to the electric field, magnetic materials contain magnetic dipoles. Magnetic materials are generally classified in three types:

  • diamagnetic
  • paramagnetic
  • ferromagnetic

Diamagnetic materials.—These contain no permanent dipoles, but only dipoles that are induced by an external magnetic field. The atoms in a substance contain electrons that are free in a sense to move about inside the atom. When a diamagnetic material is placed in a region in which a magnetic fieldchanges in time, currents are inducedfollowing the general law of electromagnetic induction (which we will take up in Chapter 7). This effect can occur in any material. The electrons in the material respond to this B(t) by circulating about the field (current). By Lenz’s law, these currents are in a direction to oppose the changing magnetic field, and thus the induced dipole moment is opposite to B. The term diamagnetic is used to describe any situation in which a magnetic field is excluded from a region.

Paramagnetic materials.— These contain atoms having permanent magnetic dipoles, but which are usually randomly oriented in the absence of a magnetic field. When placed in a magnetic field, the atomic dipoles experience a torque,

N = m x B, that tends to align them along B. The tendency to align is countered by thermal motions, so that the resulting macroscopic dipole moment of the material is proportional to B / T, where T is the absolute temperature. When paramagnetism exists it is usually great enough to mask the diamagnetism which is always present, and which has the opposite sign.

The permanent magnetic moments in paramagnetic materials arise in two ways. First, the orbital motion of the electrons in atoms gives rise to a permanent circulating current, resulting in a magnetic dipole. These internal atomic currents were first postulated by Ampere, and are called “Amperian currents.” Of course, the existence of atoms was not known at the time of Ampere, and these currents must be explained by the laws of quantum mechanics. Secondly, we now know that electrons possess an intrinsic spin magnetic moment. Spin is just another characteristic property of electrons similar to mass or charge. The electron spins are always paired (Pauli principle) but any atom having an unbalanced moment of spinning electrons will be paramagnetic. In materials having atoms with an even number of electrons, there is no net magnetic moment, and the atoms are diamagnetic.

Ferromagnetic materials.—Ferromagnetism is really an extreme case of paramagnetism. If the permanent dipoles resulting from the electron spin are very close together in the medium, there is a quantum mechanical effect, called “exchange” which results in a strong tendency for the spins of adjacent atoms or molecules to line up parallel to each other, even in the absence of a magnetic field.This parallel orientation can extend, in an unmagnetized body, over volumes of a considerable atomic scale. Such a volume containing parallel orientation of magnetic dipoles, is called a “domain.” An ordinary unmagnetized ferromagnetic body contains many domains, each with a strong magnetic moment, but oriented in different directions. In the presence of an external magnetic field, the domains change the orientation of their permanent magnetic moments, lining up with the external magnetic field, until finally when the external magnetic field reaches a certain large value, the moment reaches a limit when all moments are parallel. This limit is called “saturation.” Reversing the external field reverses the moments, but this reorientation is countered by an effect similar to friction, so that by the time the external field is reduced to zero, there can still be a considerable magnetic moment. This is the origin of permanent magnetism. If the external field is reversed alternately between one direction and the other, the magnetic moment lags behind the field, resulting in the phenomenon of hysteresis.

Ferromagnetism tends to decrease with temperature, and the individual domains loose their magnetic moments at a critical temperature known as the
“Curie temperature.” The origin of this temperature effect is thermal agitation which opposes the tendency toward orientation.

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