Magnetization of band electrons

We next develop a model, in some sense a direct extension of the preceding analysis, which includes the important aspects of the band structirre in magnetic phenomena. The starting point for this theory is the density of states derived from the band structure, g(e). We assume that the electronic states can be filled up to the Fermi level ep for a spin-averaged configuration with = N, = N/2. We then perturb this state of the system by moving a few electrons from the spin-down state to the spin-up state, so that Nf N/2, N/2. The energy of the electrons that have 

Expanding the integrals over the density of states as Taylor series in A through the expressions given in Eqs. (G.24) and (G.40), and using the definition of the magnetization number from Eq. (7.11), we obtain 

Through the same procedure of expanding the integrals as Taylor series in A, this expression gives for the band energy 

If we subtract from this expression the value of the exchange energy for m=0, corresponding to the spin-averaged state with N- = N/2, we find that the 

To complete the discussion, we examine the magnetic susceptibility x of a system in which spontaneous magnetization arises when the Stoner criterion is met. We 

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