Electronic states of a substitutional chromium impurity in GaAs

Abstract

The $X\alpha$ scattered-wave cluster method has been used to investigate the electronic properties associated with various charge configurations of a substitutional chromium impurity in GaAs. The usual spin-restricted formalism is found to provide an inadequate treatment of the strong electron-electron interactions between the $d$-like electrons associated with the chromium impurity and leads to a poor description of the resulting electronic states. Two methods of improving the treatment of the impurity electron-electron interactions are porposed and investigated. In the first approach the spin-polarized electronic states of the various clusters are calculated using a spin-unrestricted formalism. This leads to different energy spectra for electrons of different spin and consequently incorporates some of the broad features of the true many-electron multiplet structure in what is essentially a single-electron description. The second approach consists in treating the electron-electron interactions as a perturbation on the single-particle cluster states obtained from the spin-restricted calculations. The many-electron crystal-field term states are then calculated using a modification of the standard crystal-field theory in the strong-field coupling limit. Both of these approaches are applied to the study of the chromium impurity in the ${\mathrm{Cr}}^{3+}$ and ${\mathrm{Cr}}^{2+}$ charge configurations, and the results are compared and discussed.