Influence of a narrow conduction band on a Heisenberg spin system

We consider an idealized model, represented by a Heisenberg spin system, which is influenced by a narrow conduction band via ans-d-exchange interaction. By calculating and decoupling the equation of motion of double-time Green's functions by RPA, we derive the magnon dispersion law. The result is a separation of the spectrum into two magnon bands of different shape, similar to the band structure found by Hubbard in his system. We discuss our result by variation of the system parameters, as there are interactions, polarization, temperature, and external field.