Microscopic Analysis of the Valence Band and Impurity Band Theories of (Ga,Mn)As

We analyze microscopically the valence and impurity band models of ferromagnetic (Ga,Mn)As. We find that the tight-binding Anderson approach with conventional parametrization and the full potential $\mathrm{\text{local}}\mathrm{\text{−}}\mathrm{\text{density approximation}}+\mathrm{U}$ calculations give a very similar band structure whose microscopic spectral character is consistent with the physical premise of the $\mathit{k}·\mathit{p}$ kinetic-exchange model. On the other hand, the various models with a band structure comprising an impurity band detached from the valence band assume mutually incompatible microscopic spectral character. By adapting the tight-binding Anderson calculations individually to each of the impurity band pictures in the single Mn impurity limit and then by exploring the entire doping range, we find that a detached impurity band does not persist in any of these models in ferromagnetic (Ga,Mn)As.

Figure 1

(a),(b) Total (solid line) and partial Mn $d$-orbital [gray (red) filled areas] DOSs calculated using the TBA (CPA) and compared with the $\mathrm{LDA}+\mathrm{U}$ (supercell) results for ${\mathrm{Mn}}_{\mathrm{Ga}}$ dopings of 3%, 6%, 12%, and 100%. (c),(d) Same for the ${\mathrm{TBA}}^d$ compared with the LDA results. $E_F$ is indicated by the dashed vertical line.

Figure 2

Partial As $p$-orbital (a) and Mn $d$-orbital (b) DOSs at $E_F$ in the depicted TBA models. The remaining contribution to the total DOS is primarily due to Ga and Mn $p$ orbitals with their relative weights given nearly precisely by the $\mathrm{Ga}/\mathrm{Mn}$ ratio [14]. (c) The $p\mathrm{\text{−}}d$ coupling strength in the TBA models compared with the LDA (triangles) and $\mathrm{LDA}+\mathrm{U}$ (circles) results. (d)–(f) Total DOSs showing the merging of the IB into the VB in the depicted tight-binding models.