Origin of Magnetic Circular Dichroism in GaMnAs: Giant Zeeman Splitting versus Spin Dependent Density of States

We present a unified interpretation of experimentally observed magnetic circular dichroism (MCD) in the ferromagnetic semiconductor (Ga,Mn)As, based on theoretical arguments, which demonstrates that MCD in this material arises primarily from a difference in the density of spin-up and spin-down states in the valence band brought about by the presence of the Mn impurity band, rather than being primarily due to the Zeeman splitting of electronic states.

Figure 1

(a) MCD spectra taken at $B=5.0\mathrm{T}$ and $T=1.7$, 20, 40, and 70 K on a ${\mathrm{Ga}}_{0.984}{\mathrm{Mn}}_{0.016}\mathrm{As}$ layer grown at $280°\mathrm{C}$. The dash-dotted vertical line marks the onset of the sharp rise of MCD. (b) MCD spectra taken at 5.0 T for similar temperatures on a ${\mathrm{Cd}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ sample with $x=0.037$. The inset shows a schematic illustration of the spin split valence and conduction bands in CdMnTe, together with spin conserving transitions allowed for ${\sigma }^{+}$ and ${\sigma }^{-}$ circular polarizations (right and left arrows, respectively).

Figure 2

MCD signal (lowest line), ${\alpha }^{-}$ (topmost line), and ${\alpha }^{+}$ (middle line) calculated for a 1D doped system which is (a) uncompensated, (b) partially compensated, and (c) fully compensated. The corresponding allowed transitions are shown schematically in the insets. The sharp peaks seen at $E_g$ reflect the 1D density of states (DOS) which diverge at the band edges.

Figure 3

Absorption spectra of GaMnAs with $x=0.0003$ taken at 5 T and $T=2\mathrm{K}$ for circular polarizations ${\sigma }^{+}$ and ${\sigma }^{-}$. The corresponding MCD calculated from the ${\sigma }^{+}$ and ${\sigma }^{-}$ absorption curves as $({\alpha }^{-}-{\alpha }^{+})d/2$ is also plotted. The MCD is dominated by a single broad peak centered at 1.565 eV, corresponding to the energy range where $d\alpha /dE$ is negligible.

Figure 4

(a) MCD spectra taken at $T=1.8\mathrm{K}$ and $B=5.0\mathrm{T}$ for several GaMnAs samples. Samples $A$, $B$, and $D$ have $x=0.014$, while sample $C$ has $x=0.002$. For other details, see text. (b) MCD spectra taken on sample $B$ at $T=1.8\mathrm{K}$ and $B=0$, 0.5, 2, and 5 T. The horizontal line marks $\mathrm{MCD}=0$. Inset: Magnetic field dependence of MCD for sample $B$ observed at $T=1.8\mathrm{K}$ at photon energy 1.405 eV, showing a small but finite hysteresis loop.