Relativistic calculation of the orbital hyperfine splitting in complex microscopic structures

Abstract

Theoretical spectroscopy based on double perturbation theory is typically challenged by systems with large orbital hyperfine splitting. Therefore, we here derive a rigorous, non-perturbative scheme starting from Dirac’s equation which allows to calculate the contribution of the orbital HFI for complex structures including heavy atoms with strong spin-orbit coupling (SOC). Using the PAW formalism, the method has been implemented in the software package Quantum ESPRESSO. We show that the ‘orbital part’ actually scales with SOC strength if orbital quenching is hindered by low local symmetry, i.e. in case of dimers or atoms at surfaces. This holds true in particular when the unpaired electron is localized in quasi-atomic p-like orbitals. Here, the orbital part is by far not negligible, but becomes dominant by surpassing the dipolar contribution by a factor of five.