The Heisenberg Theory of Ferromagnetism of The Crystal constituted by the Atoms with Spin One

Huzio NAKANO

 Department if Physics, Osaka University

(Received March 6, 1953)


Abstract

  The Heisenberg theory of ferromagnetism of the crystal whose atoms have the spin one is developed. It is proved that the hamiltonian of the crystal constituted by the atoms having the spin $ larger than l can be expressed by -ZJ'::E.Sf, ·Sj in terms of the spin vector Sf, and Sj, of the nearest neighboring atoms in the same way as in the case $=l/Z, as far as the Hund rule prevails in each constituent atom in the molecular fields. The Curie points of a few lattice types are obtained in the stage of the first, the second and the third approximation. These are all higher than those_ corresponding to the case $= l/Z. Especially in the second approximation the Curie point To is given by the formula, Tc=l1 Jf[3k(1- / 1_11)] in terms of the exchange integral J between the nearest 'V Z2 neighboring atoms, the coordination number z and the aoltzmann constant k. The condition for -appearing of ferromagnetism in this approximation is that z=6.

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