Optical band edge of diluted magnetic semiconductors

Abstract

Applying the dynamical coherent potential approximation to a simple model, we have theoretically studied the behavior of the optical band edge in diluted magnetic semiconductors (DMS). For ${A}_{1\ensuremath{-}x}^{II}{\mathrm{Mn}}_{x}{B}^{VI}$-type DMS, the present study reveals that the linear relationship between spin splitting due to the exchange interaction $\ensuremath{\Delta}{E}_{\mathit{ex}}$ and averaged magnetization $\ensuremath{\mid}x⟨Sz⟩\ensuremath{\mid}$ widely holds for different values of $x$. The ratio, $\ensuremath{\Delta}{E}_{\mathit{ex}}∕x⟨{S}_{z}⟩$, however, does not agree with the exchange integral, but depends on both the exchange strength and the band offset. Furthermore, the present study reveals that in the low dilution of ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$, the optical band edge exists not at the band edge of the impurity band but near the bottom of the host band. The optical band edge behaves as if the exchange interaction is ferromagnetic although the antiferromagnetic exchange interaction actually operates at the Mn site. We conclude that the spin-dependent shift of the carrier states between the impurity band and the host band accompanied by the change of magnetization causes the anomalous behavior of the optical band edge (the reversal of the apparent sign of the exchange integral) that was reported in the magnetoreflection measurement of ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$.