Physics of Magnetism

10

Caloric Effects in Magnetic Materials

10.1. THE SPECIFIC-HEAT ANOMALY

It has been shown in Chapter 4 that the magnetic susceptibility of ferromagnets, ferrimag­

nets, and antiferromagnets behaves anomalously when the temperature in the paramagnetic

range approaches the magnetic-ordering temperature. In this section, it will be shown that

the anomalies in magnetic behavior close to the ordering temperature are accompanied by

anomalies in the specific heat.

Let us first consider the effect of an external field H on a magnetic material for which

the magnetization is equal to zero before a magnetic field is applied. The work necessary

to magnetize a unit volume of the material is given by

The total work required to magnetize a unit volume of the material is

In analogy with Eq. (10.1.1), one finds that the spontaneous magnetization of a ferromag­

netic material gives rise to an additional contribution to the internal energy per unit volume

of the material

where is the molecular field or Weiss field introduced in Chapter 4. After
substituting for and performing the integration from 0 to M, one obtains

The additional specific heat due to the spontaneous magnetization is then given in the

molecular field approach by

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