Hyperfine and quadrupole interactions for Dy isotopes in DyPc 2 molecules

Abstract

Nuclear spin levels play a vital 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 161 Dy and 163 Dy nuclei in anionic DyPc 2 (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 that corresponds to the ground Kramers doublet. Our ab initio calculations illustrate 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 161 Dy and 163 Dy nuclei are much smaller than those for the 159 Tb nucleus in TbPc 2 single-molecule magnets. The calculated separations of the electronic-nuclear levels are comparable to experimental data reported for 163 DyPc 2 . 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 2 single-molecule magnets. The magnetic field values of the avoided level crossings for 161 DyPc 2 and 163 DyPc 2 are found to be noticeably different, which can be observed from the experiment.