Shift in the absorption edge due to exchange interaction in ferromagnetic semiconductors

We develop the theory of the shift in the band edge caused by a strong exchange interaction between charge carrier spins and the spins of the localized magnetic electrons in ferromagnetic semiconductors. The one-particle Green function is derived by using Matsubara's temperature Green functions, and then an infinite-order correction to the band edge due to the exchange interaction is determined from the poles of the Green function. With the aid of the temperature- and magnetic field-dependent spin polarization of the magnetic moments and the spin correlation functions, the band edge can be calculated as a function of temperature in various magnetic fields. The calculated results are compared to experimental data in the cases of the ferromagnetic semiconductors EuO and Ga_1-xMn_xAs over a wide temperature range. For these materials the values 0.223 and 1.4 eV are evaluated for the exchange interaction parameter, respectively. A new feature is found in the ferromagnetic region, as a result of the exceptionally strong exchange interaction in Ga_1-xMn_xAs, i.e., a blue-shift in the band edge with decreasing temperature or with increasing magnetic field.