The first-principles all-electron Hartree-Fock cluster procedure is applied to the spinels ${\mathrm{ZnAl}}_2$${\mathrm{O}}_4$ and ${\mathrm{ZnFe}}_2$${\mathrm{O}}_4$ for the pure spinels, ${\mathrm{Zn}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ substituted for ${\mathrm{Al}}^{3+}$ in ${\mathrm{ZnAl}}_2$${\mathrm{O}}_4$, and when ${\mathrm{Zn}}^{2+}$ is substituted for ${\mathrm{Fe}}^{3+}$ in ${\mathrm{ZnFe}}_2$${\mathrm{O}}_4$. Electric-field gradients (EFG’s) are calculated for the nuclei at the B sites using clusters which involve the B site cation and its six nearest-neighbor oxygens. The rest of the solid is included by considering all sites outside the cluster as point ions. The calculated EFG’s agree well with the available nuclear quadrupole interaction data. For the impurity systems, the possibility of impurity-induced lattice relaxation is not included. However, the concordance found between theoretical and experimental ${}_{}{}^{67}{}_{}{}^{}\mathrm{Zn}$ nuclear quadrupole coupling constants (${\mathit{e}}^2$qQ) indirectly suggests that the relaxation due to the presence of the defect is relatively small. For ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ and ${}_{}{}^{67}{}_{}{}^{}\mathrm{Zn}$ at the B site, the ratios of the main component ${\mathit{V}}_{\mathit{zz}}$ of the EFG’s, ${\mathit{V}}_{\mathit{zz}}$[${\mathrm{ZnAl}}_2$${\mathrm{O}}_4$]/${\mathit{V}}_{\mathit{zz}}$[${\mathrm{ZnFe}}_2$${\mathrm{O}}_4$], agree very well with the experimentally determined ratios ${\mathit{e}}^2$qQ[${\mathrm{ZnAl}}_2$${\mathrm{O}}_4$]/${\mathit{e}}^2$qQ[${\mathrm{ZnFe}}_2$${\mathrm{O}}_4$]. This is significant because these ratios are independent of the nuclear quadrupole moment Q. Combined with the good agreement found between theoretical and experimental results for ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ and ${}_{}{}^{67}{}_{}{}^{}\mathrm{Zn}$, the present calculations suggest a value for Q${(}^{57}$Fe)≊0.20 b.

Electron densities are calculated at ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ and ${}_{}{}^{67}{}_{}{}^{}\mathrm{Zn}$. The ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ magnetic hyperfine field is calculated, and very good agreement is obtained with the experimental result for ${\mathrm{ZnFe}}_2$${\mathrm{O}}_4$. Correcting the Hartree-Fock results for many-body and relativistic effects is important. The magnetic moment of ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ in ${\mathrm{ZnFe}}_2$${\mathrm{O}}_4$, estimated from the Mulliken population analysis, is found to be 4.8${\mathrm{\mu }}_{\mathit{B}}$, somewhat larger than the experimental moment of 4.2${\mathrm{\mu }}_{\mathit{B}}$. Charge densities at the zinc nucleus are calculated at the A sites for the pure spinels, and for the B sites when zinc is a substitutional defect. Our calculations suggest that for ${}_{}{}^{67}{}_{}{}^{}\mathrm{ssbauer}$ spectroscopy contributions to the center shift from the second-order Doppler effect are significant in oxide spinels. © 1996 The American Physical Society.

• Received 6 July 1995

DOI:https://doi.org/10.1103/PhysRevB.53.7684