Valence-band ordering and magneto-optic exciton fine structure in ZnO

Using first-principles linear muffin-tin orbital density functional band structure calculations, the ordering of the states in the wurtzite ZnO valence-band maximum, split by crystal-field and spin-orbit coupling effects, is found to be Gamma(7(5)) > Gamma(9(5)) > Gamma(7(1)), in which the number in parentheses indicates the parent state without spin-orbit coupling. This results from the negative spin-orbit splitting, which in turn is due to the participation of the Zn 3d band. The result is found to be robust even when effects beyond the local density approximation on the Zn 3d band position are included. Using a Kohn-Luttinger model parametrized by our first-principles calculations, it is furthermore shown that the binding energies of the excitons primarily derived from each valence band differ by less than the valence-band splittings even when interband coupling effects are included. The binding energies of n = 2 and n = 1 excitons, however, are not in a simple 1/4 ratio, Our results are shown to be in good agreement with the recent magneto-optical experimental data by Reynolds et al. [Phys. Rev. B 60, 2340 (1999)], in spite of the fact that on the basis of these data these authors claimed that the valence-band maximum would have Gamma(9) symmetry. The differences between our and Reynolds' analysis of the data are discussed and arise from the sign of the Lande g factor for holes, which is here found to be negative for the upper Gamma(7) band.