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

The s,p-d 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 +U 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 N0 beta vary about 10 times when going from V to Ni, (ii) not only the value but also the sign of N0 beta 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, N0 beta 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 N0 alpha 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 N0 alpha.