Theory of the sp-d coupling of transition metal impurities with free carriers in ZnO.

The [Formula: see text] exchange coupling between the spins of band carriers and of transition metal (TM) dopants ranging from Ti to Cu in ZnO is studied within the density functional theory. The [Formula: see text] corrections are included to reproduce the experimental ZnO band gap and the dopant levels. The p-d coupling reveals unexpectedly complex features. In particular, (i) the p-d coupling constants [Formula: see text] vary about 10 times when going from V to Ni, (ii) not only the value but also the sign of [Formula: see text] depends on the charge state of the dopant, (iii) the p-d coupling with the heavy holes and the light holes is not the same; in the case of Fe, Co and Ni, [Formula: see text]s for the two subbands can differ twice, and for Cu the opposite sign of the coupling is found for light and heavy holes. The main features of the p-d coupling are determined by the p-d hybridization between the d(TM) and p(O) orbitals. In contrast, the s-d coupling constant [Formula: see text] is almost the same for all TM ions, and does not depend on the charge state of the dopant. The TM-induced spin polarization of the p(O) orbitals contributes to the s-d coupling, enhancing [Formula: see text].