The quantum theory of the spontaneous magnetization of ferrimagnetics, anti-ferromagnetics and thin films with arbitrary spin at high temperatures

Abstract

Using Van Vleck's modification of the Heisenberg theory of ferro-magnetism for substances with arbitrary spin per atom, a generalization of the theory is given for the case of ferrimagnetics, anti-ferromagnetics and thin films with an arbitrary number of sub-lattices and with arbitrary spin per atom. The exchange part of the energy operator is formulated by means of “rotated” spin operators. The theory contains the quantum-mechanical generalization of non-quantum theories given by Neel and later generalized by Yafet and Kittel. It also contains the theory of thin films proposed recently by the author. The magnetization laws are completely analogous to the relations derived from the theory of molecular fields. The constants of the molecular fields are interpreted by means of exchange integrals. For the special case of spin S=1/2the theory agrees with the results of the work of Vlasov and Ismuchametov for ferrimagnetics and anti-ferromagnetics and with the author's for thin films.