Relativistic Douglas-Kroll-Hess Calculations of Hyperfine Interactions within First Principles Multireference Methods

Relativistic magnetic hyperfine interaction Hamiltonian based on the Douglas-Kroll-Hess (DKH) theory up to the second order is implemented within the ab initio multireference methods including spin-orbit coupling in the Molcas/OpenMolcas package. This implementation is applied to calculate relativistic hyperfine coupling (HFC) parameters for atomic systems and diatomic radicals with valence s or d orbitals by systematically varying active space size in the restricted active space self-consistent field (RASSCF) formalism with restricted active space state interaction (RASSI) for spin-orbit coupling. The DKH relativistic treatment of the hyperfine interaction reduces the Fermi contact contribution to the HFC due to the presence of kinetic factors that regularize the singularity of the Dirac delta function in the nonrelativitic Fermi contact operator. This effect is more prominent for heavier nuclei. As the active space size increases, the relativistic correction of the Fermi contact contribution converges well to the experimental data for light and moderately heavy nuclei. The relativistic correction, however, does not significantly affect the spin-dipole contribution to the hyperfine interaction. In addition to the atomic and molecular systems, the implementation is applied to calculate the relativistic HFC parameters for large trivalent and divalent Tb-based single-molecule magnets (SMMs) such as Tb(III)Pc$_2$ and Tb(II)(Cp$^\text{iPr5}$)$_2$ without ligand truncation using well-converged basis sets. In particular, for the divalent SMM which has an unpaired valence 6s/5d hybrid orbital, the relativistic treatment of HFC is crucial for a proper description of the Fermi contact contribution. Even with the relativistic hyperfine Hamiltonian, the divalent SMM is shown to exhibit strong tunability of HFC via an external electric field (i.e., strong hyperfine Stark effect).Comment: 40 pages, 4 figure

Biquadratic magnetic interaction in parent ferropnictides

We discuss an effective spin Hamiltonian with biquadratic interaction for ferropnictide superconductors from the point of view of band structure theory and available experimental data. This model is consistent with electronic structure calculations and captures many observed magnetic properties, including the anisotropy of the exchange coupling, thin domain walls, and the crossover from first to second-order phase transition under doping. The parameters of the model are analyzed as a function of the local spin moment using first-principles calculations. Calculations show the biquadratic coupling is negative in stoichiometric KFe2Se2, and the phase diagram is extended into this region. We also consider magnetic short-range order and discuss the limitations of this model in comparison with experiment