Orbital and spin contributions to magnetic hyperfine fields of the 3d transition metal ions

Highlights: • Orbital and spin contributions to magnetic hyperfine fields of most of the 3d transition metal free ions are presented. • The developed scheme is tested on Fe²⁺ free ion as well as in FeF₂. • Good agreement with previously measured and estimated in the literature is found for the orbital and spin contributions. A scheme is presented to estimate the magnetic hyperfine field due to orbital and spin current densities of 3d transition metal free ion and in a crystal field. Orbital and spin contributions to magnetic hyperfine fields of most of the 3d transition metal free ions are presented. The application of the formulae offered is tested on the ground state of the free ion ${\mathrm{Fe}}^{2+}$ and when this ion is in the compound ${\mathrm{FeF}}_2$. The estimated orbital and spin contributions to magnetic hyperfine fields of ${\mathrm{Fe}}^{2+}$ free ion are in good agreement with previously measured and estimated in the literature. The values of estimated orbital and spin contributions to magnetic hyperfine fields of ${\mathrm{Fe}}^{2+}$ in ${\mathrm{FeF}}_2$ compound depend on the effective $〈r_{\mathrm{eff}}^{-3}〉$ values of the $〈r^{-3}〉$. The $〈r_{\mathrm{eff}}^{-3}〉=3.0$ a.u. produces values of orbital and spin contribution to magnetic hyperfine fields that are also in good agreement with the measured and estimated ones in the literature.