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 transition metal (TM) dopants ranging from Ti to Cu in ZnO is studied within density functional theory. $+U$ corrections are included reproduce experimental gap dopant levels. $p-d$ reveals unexpectedly complex features. In particular, (i) constants $N_0\beta$ vary about 10 times when going V Cu, (ii) not only value but also sign depends on charge state dopant, (iii) with heavy holes light same; case Fe, Co Ni, $N_0\beta$s for two subbands can differ twice, opposite found holes. main features determined by hybridization $d$(TM) $p$(O) orbitals. contrast, $s-d$ constant $N_0\alpha$ almost same all TM ions, does depend dopant. TM-induced spin polarization orbitals contributes coupling, enhancing $N_0\alpha$.