Orbital and spin contributions to magnetic hyperfine fields of tri-positive rare earth ions

An alternative approach in the estimation of the magnetic field generated by atomic current densities is presented and applied to both the orbital and spin magnetic hyperfine fields of tri-positive rare earth ions. The application of the formulae offered is tested on the free ions Dy³⁺, Er³⁺ and Yb³⁺ in their ground states. The estimated magnetic hyperfine fields are in full agreement with those found in the literature. Our calculated magnetic hyperfine fields produced in the ground states of Er³⁺ ion in Er₂Ge₂O₇ and Yb³⁺ ion in YbNi₅ are also in good agreement with experimental and estimated data found in the literature