The Ferromagnetism of Nickel. II. Temperature Effects

With the model proposed in an earlier paper, the temperature variation of the ferromagnetism of nickel is discussed. By application of Fermi statistics to the electrons in the $d$ bands, the free energy is computed as a function of temperature and magnetic moment. At each temperature, the value of magnetic moment for which the free energy is a minimum is the value which will actually be found, and this decreases with increasing temperature, going to zero at the Curie point, in satisfactory agreement with experiment. The value of the free energy itself at the minimum, as a function of temperature, is compared with experimental values derived from the observed electronic specific heat of nickel, and the agreement is again satisfactory. To get agreement of both quantities with experiment, it is necessary to use a smaller exchange integral than was suggested in the earlier paper, but plausible reasons are suggested for thinking that this should be done anyway. It is found that even at the absolute zero not quite all of the spins are parallel to each other, the minimum in the free energy curve coming at a little less than the maximum possible magnetic moment. It is suggested that this small effect becomes much more pronounced as iron is approached in the series of ferromagnetic elements, explaining the fact that alloys of iron and cobalt show the highest saturation moments of any ferromagnetic substances, the moment then decreasing in iron and even more in alloys of iron with lighter elements.