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Register a new userNature of hyperfine interactions in TbPc$_2$ single-molecule magnets: Multireference ab-initio study
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Lanthanide-based single-ion magnetic molecules can have large magnetic hyperfine interactions as well as large magnetic anisotropy. Recent experimental studies reported tunability of these properties by changes of chemical environments or by application of external stimuli for device applications. In order to provide insight onto the origin and mechanism of such tunability, here we investigate the magnetic hyperfine and nuclear quadrupole interactions for $^{159}$Tb nucleus in TbPc$_2$ (Pc=phthalocyanine) single-molecule magnets using multireference ab-initio methods including spin-orbit interaction. Since the electronic ground and first-excited (quasi)doublets are well separated in energy, the microscopic Hamiltonian can be mapped onto an effective Hamiltonian with an electronic pseudo-spin $S=1/2$. From the ab-initio-calculated parameters, we find that the magnetic hyperfine coupling is dominated by the interaction of the Tb nuclear spin with electronic orbital angular momentum. The asymmetric $4f$-like electronic charge distribution leads to a strong nuclear quadrupole interaction with significant non-axial terms for the molecule with low symmetry. The ab-initio calculated electronic-nuclear spectrum including the magnetic hyperfine and quadrupole interactions is in excellent agreement with experiment. We further find that the non-axial quadrupole interactions significantly influence the avoided level crossings in magnetization dynamics and that the molecular distortions affect mostly the Fermi contact terms as well as the non-axial quadrupole interactions.
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We investigate how different chemical environment influences magnetic properties of terbium(III) (Tb)-based single-molecule magnets (SMMs), using first-principles relativistic multireference methods. Recent experiments showed that Tb-based SMMs can have exceptionally large magnetic anisotropy and that they can be used for experimental realization of quantum information applications, with a judicious choice of chemical environment. Here, we perform complete active space self-consistent field (CASSCF) calculations including relativistic spin-orbit interaction (SOI) for representative Tb-based SMMs such as TbPc$_2$ and TbPcNc in three charge states. We calculate low-energy electronic structure from which we compute the Tb crystal-field parameters and construct an effective pseudospin Hamiltonian. Our calculations show that ligand type and fine points of molecular geometry do not affect the zero-field splitting, while the latter varies weakly with oxidation number. On the other hand, higher-energy levels have a strong dependence on all these characteristics. For neutral TbPc$_2$ and TbPcNc molecules, the Tb magnetic moment and the ligand spin are parallel to each other and the coupling strength between them does not depend much on ligand type and details of atomic structure. However, ligand distortion and molecular symmetry play a crucial role in transverse crystal-field parameters which lead to tunnel splitting. The tunnel splitting induces quantum tunneling of magnetization by itself or by combining with other processes. Our results provide insight into mechanisms of magnetization relaxation in the representative Tb-based SMMs.
Molecular spin qubits with long spin coherence time as well as non-invasive operation methods on such qubits are in high demand. It was shown that both molecular electronic and nuclear spin levels can be used as qubits. In solid state systems with dopants, an electric field was shown to effectively change the spacing between the nuclear spin qubit levels when the electron spin density is high at the nucleus of the dopant. Inspired by such solid-state systems, we propose that divalent lanthanide (Ln) complexes with an unusual electronic configuration of Ln$^{2+}$ have a strong interaction between the Ln nuclear spin and the electronic degrees of freedom, which renders electrical tuning of the interaction. As an example, we study electronic structure and hyperfine interaction of the $^{159}$Tb nucleus in a neutral Tb(II)(Cp$^{rm{iPr5}}$)$_2$ single-molecule magnet (SMM) using the complete active space self-consistent field method with spin-orbit interaction included within the restricted active space state interaction. Our calculations show that the low-energy states arise from $4f^8(6s,5d_{z^2})^1$, 4$f^8$(5$d_{x^2-y^2}$)$^1$, and $4f^8(5d_{xy})^1$ configurations. We compute the hyperfine interaction parameters and the electronic-nuclear spectrum within our multiconfigurational approach. We find that the hyperfine interaction is about one order of magnitude greater than that for Tb(III)Pc$_2$ SMMs. This stems from the strong Fermi contact interaction between the Tb nuclear spin and the electron spin density at the nucleus that originates from the occupation of the $(6s,5d)$ orbitals. We also uncover that the response of the Fermi contact term to electric field results in electrical tuning of the electronic-nuclear level separations. This hyperfine Stark effect may be useful for applications of molecular nuclear spins for quantum computing.
Magnetization, AC susceptibility and $mu$SR measurements have been performed in neutral phthalocyaninato lanthanide ([LnPc$_2]^0$) single molecule magnets in order to determine the low-energy levels structure and to compare the low-frequency spin excitations probed by means of macroscopic techniques, such as AC susceptibility, with the ones explored by means of techniques of microscopic character, such as $mu$SR. Both techniques show a high temperature thermally activated regime for the spin dynamics and a low temperature tunneling one. While in the activated regime the correlation times for the spin fluctuations estimated by AC susceptibility and $mu$SR basically agree, clear discrepancies are found in the tunneling regime. In particular, $mu$SR probes a faster dynamics with respect to AC susceptibility. It is argued that the tunneling dynamics probed by $mu$SR involves fluctuations which do not yield a net change in the macroscopic magnetization probed by AC susceptibiliy. Finally resistivity measurements in [TbPc$_2]^0$ crystals show a high temperature nearly metallic behaviour and a low temperature activated behaviour.
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 $^{161}$Dy and $^{163}$Dy nucleus 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 $S_{rm eff}=1/2$ 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 $^{161}$Dy and $^{163}$Dy nucleus are much smaller than those for $^{159}$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 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 experiment.
Density Functional Theory (DFT) calculations show a weak interaction between hydrogen and helium in iron, in contrast to previous reports of a strong trapping of hydrogen at helium. The strong preference of He and H to occupy regions with low electronic density (such as vacancies) explains this discrepancy, with vacancy-He and vacancy-H binding forces concealing the repulsive interaction between He and H. Furthermore, Rate Theory simulations based on our DFT-calculated V$_n$He$_m$H$_p$ cluster energetics predict, as it is observed in some experiments, that synergetic effects could be expected between H and He in iron under irradiation.
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