Hot-electron photoluminescence study of the ( Ga , Mn ) As diluted magnetic semiconductor

We study the spectral shape and the magnetic field induced polarization of hot-electron photoluminescence from the diluted magnetic semiconductor $(\mathrm{Ga},\mathrm{Mn})\mathrm{As}$. It is demonstrated that the holes occupy predominantly the impurity band and not the valence band as required for the Rudermann-Kittel-Kasuya-Yosida-type exchange interaction. We show that the ground state of the impurity band is split by uniaxial stress or electric fields into $F=\ifmmode\pm\else\textpm\fi{}1$ states of antiferromagnetically coupled Mn ions $(J=5∕2)$ and valence band holes $(J=3∕2)$. The polarization of the impurity band holes in a magnetic field is strongly enhanced by antiferromagnetic exchange interaction with Mn ions and saturates at a value much lower than predicted by Rudermann-Kittel-Kasuya-Yosida-like models. The temperature dependence of the hole polarization shows that the ferromagnetic and paramagnetic phases coexist in the whole temperature range below Curie temperature. This observation rather supports percolation based theories of ferromagnetism in $(\mathrm{Ga},\mathrm{Mn})\mathrm{As}$ diluted magnetic semiconductor.