Freeon Theory of Ferromagnetism

The freeon theory of ferromagnetism is based on the negative-U, Hiickel-Hubbard Hamiltonian (NUHH). However the conventional positive-U, Hiickel-Hubbard (PUHH) Hamiltonian employs a positive U which is a measure of the repulsion of a bare pair of electrons on a single site. From whence comes NUHH There are three positions to take with respect to NUHH  

1) The Ising, small-bipolaron (ISB) theory of cuprate superconductivity (Section 8) employs NUHH where, just as in BCS theory, it is a consequence of vibronic interaction which overrides the positive U. 

2) Ferromagnetism cannot be explained by a site theory and requires a delocalized band theory. Support for this point of view is provided by UHF band calculations which produce a surplus of up spins over down spins for a number of the ferromagnetic materials. 

3) Adopt the cavalier attitude of Weiss and claim that the use of NUHH in a theory of ferromagnetism is supported by a sufficient number of facts that one can be certain that it contains an important part of the truth and that 

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The mean-field equation will be derived from two models the uniform interaction model and the Ising model. Neither of the two derivations depend explicitly on spin. They will be applied to the freeon theory of ferromagnetism Section 6 and freeon theory of high-Tc superconductivity in Section 7. 

In this section we give the freeon theory of ferromagnetism. As pointed about above ferromagnetism is a second order-phase change which is well-defined by mean-field theory. In Section 6.2 we give the uniform interaction derivation of mean-field theory and in Section 6.3 we compare prediction with observation. 

Note that the undoped cuprate is an antiferromagnet and that doping converts it into a superconductor. We have shown above that antiferromagnetic behavior arises from the z = +1 side of the extended Hiickel-Hubbard spectrum in Fig. 4.1. In the ISB theory the superconducting behavior comes from the z = -1 side of Fig. 4.1 just as does the freeon theory of ferromagnetism. 

In Section 4.4 the freeon ferromagnetic Hamiltonian is used to the develop the freeon theory of spin-waves. 

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