Investigations on the EPR Parameters of $KMgF_3$:$Cr^{+}$

The electron paramagnetic resonance parameters (i.e., g factor, hyperfine structure constant and superhyperfine parameters) of $KMgF_3$:$Cr^{+}$ are theoretically investigated from the perturbation formulae of these parameters for an octahedral $3 d^5$ cluster. As for the calculations of g factor and hyperfine structure constant, both the contributions from the crystal-field and charge transfer mechanisms are included based on the cluster approach. The metal to ligand charge transfer contribution to the g-shift Δg ( ≈ g-2.0023) is the same (negative) in sign and much larger in magnitude as compared to the crystal-field one. The conventional argument that the charge transfer contributions to zero-field splittings are negligible for $3 d^5$ ions in fluorides is no longer suitable for Δg analysis of $KMgF_3$:$Cr^{+}$ due to the dominant second-order charge transfer perturbation term. The charge transfer contribution to hyperfine structure constant exhibits the same sign and about 4% of the crystal-field one. The unpaired spin densities of the fluorine 2s, 2pσ and 2pπ orbitals are quantitatively acquired from the relationships with the relevant molecular orbital coefficients using the uniform model. The present treatments are superior to the previous calculations of directly fitting the experimental superhyperfine parameters.