The importance to the mechanism of ferromagnetim 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 unsatistisfactory because his model is phenomenological and moreover does not involve antiferromagnetism and spin wave mode. Our paper considers this

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... interaction on a more rigorous basis. By a certain approximation, there appear long range eychange 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. § I. Introduction Since Heisenberg,!> there have been many discussions on the origin of the ferro-and antiferromagnetism; however, no satisfactory theory has so far been offered. The simplest theory is that of Heisenberg using atomic wave functions, a standpoint which may be suitable for non metallic substances. Even in such a case, however, there exist certain ambiguities, as was pointed out by Slater. 2 > It is generally accepted that Heisenberg's model can not be adopted for metallic ferromagnetism where the situation is more difficult. It is conceivable that there are two different standpoints for the origins of ferro-and antiferromagnetism. One regards the exchange interaction between the inner shell electrons as very important to the origin of ferro-and antiferromagnetism, and considers the role of conduction electron to be negligible. The other regards the exchange interaction between the conduction electron and the inner shell electron as essential. The former interaction may be essential for transition metals, e. g., Ni, Fe, Co, Cr, Mn, etc., but for rare earth metals, this interaction almost completely vanishes and the latter interaction seems to increase in importance. Even for transition metals, the latter interaction exists and plays an important role in many phenomena; for example, in the relaxation process of microw;tve resonance absorption ; 3 > 4 > in the anomalous electrical resistance of transition metals,"> and in the temperature dependence of the anisotropy energy of Ni, 6 > as was previously discussed by the author. This interaction (s-d interaction) was first discussed by Zener. 7 > However his treatment is only phenomenological and on many points unsatisfactory, because his