The conduction band of an antiferromagnetic non-metal spin polarons

4 The conduction band of an antiferromagnetic non-metal spin polarons 

In this section we discuss the properties of an electron in the conduction band of an antiferromagnetic insulator. This may be a simple Mott insulator, but, since the experimental evidence is related to them, we first discuss materials like EuSe, where the europium ion has seven 4f-electrons and electrons can be introduced into the conduction band by doping with GdSe the ion Gd2 + has the same number of f-electrons but one more electron in an outer shell, so a Gd ion acts as a donor. 

The interaction between an electron spin in an s- or d-like conduction band and a given 4f-moment can be written as 

Here is the Hund s-rule energy coupling the spin of the conduction electron and the moment S on the europium ion in a ferromagnetic sense. Q is the atomic volume and ps is the wave function of the conduction electrons. 

A spin polaron should move at low temperatures with a fixed wave vector k, like any other pseudoparticle, and be scattered by phonons and magnons. The effective mass is expected to be of the form mey /0, where y l. To obtain this result, we compute the transfer integral when the polaron moves through one atomic distance. The spin will contribute a term proportional to 

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