Low-Temperature Studies of CuFe$_{2}$S$_{3}$ and CuFeS$_{2}$ by $^{63,65}$Cu NMR in the Internal Magnetic Field

Abstract

The resonance $^{63,65}$Cu NMR spectra in the internal magnetic field in cubanite CuFe$_{2}$S$_{3}$ and chalcopyrite CuFeS$_{2}$ were studied experimentally at 77 K. Using a cluster approach, ab initio evaluation of the electric field gradient (EFG) at the nuclei of copper in both compounds was performed. The calculations were carried out by the self-consistent restricted method of Hartree–Fock with open shells (SCF-LCAO-ROHF). The largest clusters for which calculations were made had a formula of Cu$_{7}$Fe$_{14}$S$_{29}^\mathrm{n}$ for cubanite and Cu$_{9}$Fe$_{10}$S$_{28}^\mathrm{n}$ for chalcopyrite, where n is the cluster charge. The best-fit values of the quadrupole parameters (quadrupole frequency $\nu _\mathrm{Q}$ and the asymmetry parameter of the EFG tensor $\eta$)—determined experimentally ($\nu _\mathrm{Q} \approx$ 7.30 MHz and $\eta \approx$ 0.82) and by calculation ($\nu _\mathrm{Q} \approx$ 7.38 MHz and $\eta \approx$ 0.87)—were obtained for a cluster Cu$_{7}$Fe$_{14}$S$_{29}^{10}$ for cubanite. Similarly, the best-fit values of the quadrupole parameters—determined experimentally ($\nu _\mathrm{Q} \approx$ 1.29 MHz and $\eta \approx$ 0.34) and by calculation ($\nu _\mathrm{Q} \approx$ 1.40 MHz and $\eta \approx$ 0.50)—were obtained for a cluster Cu$_{9}$Fe$_{10}$S$_{28}^{-4}$ for chalcopyrite. For these clusters, maps of the electron density distribution in the neighborhood of quadrupole nucleus of copper were built. Based on the analysis of the resulting electron density distribution, it is supposed that the bond in these compounds is not quite covalent. Evaluations of the hyperfine interaction constants were made and maps of the spin density distribution in the neighborhood of quadrupole nucleus of copper were built. The energy level diagram calculated in the high-spin ROHF approximation defined chalcopyrite as a compound with a very narrow LUMO–HOMO gap rather well and is consistent with the notion of this compound as a semiconductor.