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, ferrimagnets, 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 ferromagnetic 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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