The effect of band nonparabolicity on the range function of RKKY interaction

Using an analytical method, we provide the exact derivation of the spatial dependence of the RKKY exchange integral in a system with nonparabolic dispersion. We prove that the RKKY exchange integral shows a sign reversal, being a superposition of oscillations with two different periods. We show that our results describe the magnetic behaviour of semimagnetic semiconductors with planar doping (δ-doping).