On Ferromagnetism and Related Problems of the Theory of Electrons

In this paper is presented a study of those electrons which hold together a chemically elementary crystal and are responsible for the homoeopolar bonds between neighboring atoms. The starting point of the theory is Slater's form of the secular equations for first order perturbations arising from the interactions of identical atoms composing a system. A rigorous solution of these equations is given in section 4. The investigation is carried through in a unified way for magnetic and non-magnetic materials, with respect to internal energies and to magnetic properties. As anticipated by Heisenberg, the deciding factor is the sign of the Heitler and London interchange integral $J_1$. Substances with large negative $J_1$ are non-magnetic, those with large positive $J_1$, potentially ferromagnetic. For non-magnetic bodies, the theory gives a confirmation of Bloch's conclusions with slight differences of interpretation. On the other hand, the results for magnetic materials are new and entirely different from Bloch's. As to specific heats, it is found that at very low temperatures they have the expression $c=0.208\mathrm{}\mathrm{sR}{\left(\frac{T}{\theta }\right)}^{\frac{3}{2}}$, where $R$ is the gas constant, $s$ the number of valency electrons per atom, and $\theta$ has a close relation to the Curie point. With respect to ferromagnetism, the result is that a crystal satisfying Slater's equations is spontaneously magnetized almost to saturation but that the polarity of this magnetization changes its sense at irregular intervals. This fact suggests that ferromagnetic crystals must have a block structure and that they are coherent, in the sense of the validity of Slater s equations, only within the blocks (compare sections 10 and 11). With this hypothesis the theory accounts for the fundamental facts of ferromagnetism.