Rigorous results for electronic excitation spectrum of a ferromagnetic semiconductor

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Abstract
The electronic excitation spectrum of a ferromagnetic semiconductor is calculated exactly up to linear terms in g/W (g=s-f coupling constant, W=bandwidth) for the strong-coupling limit (g>>W). It turns out that at absolute zero the conduction band is split into three sub-bands, two of which belong to the spin down-spectrum with centres of gravity at the energies 1/2g(S+1) and -1/2gS, respectively. The widths of these spin down-bands are spin-dependent, (2S/(2S+1))W0 and (1/(2S+1))W0 (W0 is the bandwidth in the limit of g=0). The spin up-spectrum consists of only one, non-deformed band of width W0. The usual picture that the conduction band of a ferromagnetic semiconductor is split into two spin-polarised subbands is therefore obviously incorrect. It is shown that this assumption also contradicts the exact results which can be found for the atomic limit and for the temperature behaviour of the centre of gravity of the band.