The collective electron theory of ferromagnetism is extended to include in the expression for the energy associated with the magnetization a term in the fourth power of the magnetization. A second adjustable parameter, similar to the
kθ'/ϵ
0
of the Stoner treatment, is thus introduced. Detailed comparison with experiment of a number of properties of nickel, nickel-cobalt and nickel-copper alloys, is carried out. A high degree of co-ordination of the properties of nickel is obtained by a suitable choice of the two parameters, which are thereby determined within fairly close limits. The temperature variation of electronic specific heat and spontaneous magnetization of nickel is quantitatively covered, as is the magnetocaloric temperature change accompanying changes in external field. The spontaneous magnetization, temperature curves of cubic cobalt and four nickel-copper alloys are similarly covered, and a simple interpretation can be given of the adherence to the law of corresponding states of nickel-cobalt alloys and the deviation therefrom of the nickel-copper alloys. The model accounts qualitatively for the field-magnetization isothermals and for the variation of the magnetocaloric temperature change with magnetization. A detailed examination shows that the differences between theory and observation, where they exist, are due to effects not covered by the collective electron theory. The main discrepancies can be accounted for on the assumption that a small fraction of the volume of the material is made up of groups of atoms of varying size with a Langevin distribution of their magnetic axes. These groups may be called small domains. The problem is complicated by the fact that the field values computed theoretically are critically dependent on the parameters, of which a sufficiently close estimate cannot be made. However, for particular values of both
kθ'/ϵ
0
and
A
a good fit with experiment over a wide temperature range is obtained when it is assumed that the domains are of sizes varying from 10
3
atoms upwards, the largest proportion of domains being of 10
4
to 10
5
atoms, and the volume occupied by such domains probably being much less than 10% of the total volume of material. It is shown that the hitherto unexplained large temperature variation, derived from the experimental results, in the value of —1/
σ
(∂
E
/∂
σ
)
T
corresponding to the Weiss molecular field coefficient, is an almost direct consequence of the basic physical premises of the collective electron treatment.
Collective electron ferromagnetism III. Nickel and nickel-copper alloys