The Stoner Model for Band Magnetism

The Stoner model, which we discuss in its simplest form, describes the formation of a net magnetic moment for itinerant electrons in a narrow band by adding to the basic Hamiltonian (11) of band theory a perturbing term accounting for total energy increase in case the itinerant electrons spins are not polarized (as in an atom for states not maximizing the spin). 

Therefore, considering Bloch states, a positive exchange term coupling opposite spins is added to the Hamiltonian (11)  

When a magnetic field H is apphed, two energies are available for electrons  

An exchange splitting of the band levels is produced for every k, which is proportional to the magnetization A = I(n+ - n ). 

To derive the magnetic susceptibility the argument then follows lines which are similar to the treatment of Pauli paramagnetism. Essentially (see Fig. 13), the two populations must have the same pp, and this causes a disequilibrium leading to a net magnetic moment (n+ - n ). The paramagnetic susceptibility is given as  

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