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

Anna Ciechan; Piotr Bogusławski

doi:10.1038/s41598-021-83258-1

paper

Theory of the $s p - d$ coupling of transition metal impurities with free carriers in ZnO

arXiv:2102.12338 · doi:10.1038/s41598-021-83258-1

Abstract

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 $N_{0} β$ vary about 10 times when going from V to Cu, (ii) not only the value but also the sign of $N_{0} β$ 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, $N_{0} β$ 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 $N_{0} α$ 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 $N_{0} α$ .

arXiv comment16 pages, 11 figures, 1 table

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

Abstract

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Theory of the $s p - d$ coupling of transition metal impurities with free carriers in ZnO