The role of Mn acceptors in determining the Zeeman splitting of the band edges in GaMnAs.*

It has been widely accepted that ferromagnetism in Ga$_{1-x}$Mn$_{x}$As is carrier-induced, and much work has been devoted to the mechanism of coupling between the Mn ions. By comparison considerably less attention has been given to the interaction of Mn ions with electronic bands, and to the Zeeman splitting of the band edges. To address the latter issue, we use magnetic circular dichroism (MCD) to investigate how different Mn acceptor states (neutral A$^{0}$ vs. negatively charged A$^{-})$ affect the magneto-optical properties of Ga$_{1-x}$Mn$_{x}$As. Several series of Ga$_{1-x}$Mn$_{x}$As layers were fabricated for this purpose by low-temperature molecular beam epitaxy, using different Mn concentrations (0.001 $\le $ x $\le $ 0.01), As$_{2}$ fluxes, growth temperatures and co-dopings. Our MCD data show that in highly compensated samples (i.e., those rich in A$^{-}$ centers) the Zeeman splitting of the band edges disappears, thus indicating that the exchange between band carriers and Mn spins takes place entirely via the A$^{0}$ centers.