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The importance to the mechanism of ferromagnetism of exchange interaction between conduction electrons and unfilled inner shell electrons (called s-d interaction) has been pointed out by Zener. Especially for rare earth metals, this interaction seems to be the only mechanism which can cause ferro- and antiferromagnetism. However Zener's works are unsatisfactory because his model is phenomenological and moreover does not involve antiferromagnetism and spin wave mode. Our paper considers this s-d interaction on a more rigorous basis. By a certain approximation, there appear long range exchange type interactions between d-electron spins and, in certain conditions both ferro- and antiferromagnetism appear. The excitations of spin wave modes are the same as those in the ordinary modes of the short range exchange force, viz, the energy of the spin wave excitations is proportional to q2 for ferromagnetism and q for antiferromagnetism in the region of small wave vector q. The T3/2 law for the temperature dependence of the magnetization of ferromagnetism is applicable up to very high temperatures, and this result is in good agreement with the results of experiments on metallic ferromagnetism.
T. Kasuya (1956) studied this question.