Magnetic Circular Dichroism from the Impurity Band in III-V Diluted Magnetic Semiconductors

The magnetic circular dichroism of III-V diluted magnetic semiconductors, calculated within a theoretical framework suitable for highly disordered materials, is shown to be dominated by optical transitions between the bulk bands and an impurity band formed from magnetic dopant states. The real-space Green’s functions incorporate spatial correlations in the disordered conduction band and valence-band electronic structure, and include extended and localized states on an equal basis. Our findings reconcile unusual trends in the experimental magnetic circular dichroism in III-V diluted magnetic semiconductors with the antiferromagnetic $p\mathrm{\text{−}}d$ exchange interaction between a magnetic dopant spin and its host.

Figure 1

Absorption coefficient (${\alpha }_0$) for GaAs as function of photon energy ($\hslash \omega$) with the Fermi level at 0.1 eV (solid line), 0 eV (dotted line), and $-0.1\mathrm{eV}$ (dashed line) relative to the valence-band maximum. The step increase near 1.9 eV shows the onset of the split-off band. The inset shows an example of $M_0(E,E+\hslash \omega )$ as a function of $E$ with $\hslash \omega =2\mathrm{eV}$. The three peaks from highest to lowest correspond to the cases where the initial states are in the heavy-hole (HH), the light-hole (LH), and the split-off (SO) valence bands.

Figure 2

Absorption coefficients, $\Delta {\alpha }^{+}$ (dashed line), $\Delta {\alpha }^{-}$ (dash-dotted line), and ${\alpha }^{-}-{\alpha }^{+}$ (solid line), as functions of photon energy $\hslash \omega$ with the Fermi level at (a) 0.1 eV, (b) 0.05 eV, (c) 0 eV, and (d) $-0.1\mathrm{eV}$ relative to the valence-band maximum.

Figure 3

The optical transition strength, $\Delta M^{+}(E,E+\hslash \omega )$ (dashed line), and $\Delta M^{-}(E,E+\hslash \omega )$ (solid line), as functions of $E$ with $\hslash \omega =2\mathrm{eV}$. The four peaks correspond to the four distinct processes shown by the arrows in the energy diagram at the center. States in the shaded region are occupied if the Fermi level lies in the impurity band.

Figure 4

The absorption-coefficient differences, $\Delta {\alpha }^{+}$ (dashed line), $\Delta {\alpha }^{-}$ (dash-dotted line), and ${\alpha }^{-}-{\alpha }^{+}$ (solid line), with $\hslash \omega =2\mathrm{eV}$ as a function of the Fermi level relative to the valence-band maximum.