Hyperfine and quadrupole interactions for Dy isotopes in DyPc molecules.

Nuclear spin levels play an important role in understanding magnetization dynamics and implementation and control of quantum bits in lanthanide-based single-molecule magnets. We investigate the hyperfine and nuclear quadrupole interactions for Dy and Dy nuclei in anionic DyPc (Pc  =  phthalocyanine) single-molecule magnets, using multiconfigurational ab initio methods (beyond density-functional theory) including spin-orbit interaction. The two isotopes of Dy are chosen because the others have zero nuclear spin. Both isotopes have the nuclear spin I  =  5/2, although the magnitude and sign of the nuclear magnetic moment differ from each other. The large energy gap between the electronic ground and first-excited Kramers doublets, allows us to map the microscopic hyperfine and quadrupole interaction Hamiltonian onto an effective Hamiltonian with an electronic pseudo-spin [Formula: see text] that corresponds to the ground Kramers doublet. Our ab initio calculations show that the coupling between the nuclear spin and electronic orbital angular momentum contributes the most to the hyperfine interaction and that both the hyperfine and nuclear quadrupole interactions for Dy and Dy nuclei are much smaller than those for the Tb nucleus in TbPc single-molecule magnets. The calculated separations of the electronic-nuclear levels are comparable to experimental data reported for DyPc. We demonstrate that hyperfine interaction for the Dy Kramers ion leads to tunnel splitting (or quantum tunneling of magnetization) at zero field. This effect does not occur for TbPc single-molecule magnets. The magnetic field values of the avoided level crossings for DyPc and DyPc are found to be noticeably different, which can be observed from the experiment.