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] .