Exchange integrals in Mn- and Co-doped II-VI semiconductors

Exchange integrals between nearest-neighbor (NN) transition metal ions in II-VI diluted magnetic semiconductors (DMSs) are calculated within a local superexchange model, which includes orbital-dependent transfer, on-site Coulomb repulsion and Hund's exchange between $3d$ electrons, and ligand field effects. This extended model gives a quantitative account for the available experimental data on the NN exchange constants in all II-VI DMS family (wurtzite and zinc-blende) doped by cobalt or manganese. As expected, all obtained exchange integrals are antiferromagnetic. Remarkably, the model input parameters are taken directly from the photoemission spectroscopy. We show that in the case of Co-doped compounds, as compared to Mn-doped ones, the exchange process has at least two salient features. The first one is that the electron transfer between NN $\mathrm{Co}{}^{2+} 3d$ orbitals strongly depends on their symmetry positions in the crystal lattice. The second one is related to a peculiar virtual process, involving empty and occupied $\mathrm{Co}{}^{2+} 3d$ orbitals, which leads to an additional ferromagnetic contribution to the exchange constant. We argue that our systematic study of the superexchange opens a pathway toward an understanding of other exchange mechanisms occurring in DMSs.

Figure 1

Analogous cluster of (a) zinc-blende and (b) wurtzite DMS. A, B, and C (red) denote cationic sites possibly occupied by transition metal ions, and 1, 2, 3,$...$ (gray) denote anionic sites. A-B and A-C pairs are equivalent in the zinc-blende structure but not in the wurtzite structure: The C surrounding anion tetrahedron is rotated by $60{}^{\circ }$ compared to the A and B ones.