Relativistic Douglas-Kroll-Hess calculations of hyperfine interactions within first-principles multireference methods.

A 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 formalism with restricted active space state interaction 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 nonrelativistic 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)Pc2 and Tb(II)(CpiPr5)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).

Hyperfine interactions for small systems including transition-metal elements using self-interaction corrected density-functional theory.

The interactions between the electronic magnetic moment and the nuclear spin moment, i.e., magnetic hyperfine (HF) interactions, play an important role in understanding electronic properties of magnetic systems and in realizing platforms for quantum information science applications. We investigate the HF interactions for atomic systems and small molecules, including Ti or Mn, by using Fermi-Löwdin orbital (FLO) based self-interaction corrected (SIC) density-functional theory. We calculate the Fermi contact (FC) and spin-dipole terms for the systems within the local density approximation (LDA) in the FLO-SIC method and compare them with the corresponding values without SIC within the LDA and generalized-gradient approximation (GGA), as well as experimental data. For the moderately heavy atomic systems (atomic number Z ≤ 25), we find that the mean absolute error of the FLO-SIC FC term is about 27 MHz (percentage error is 6.4%), while that of the LDA and GGA results is almost double that. Therefore, in this case, the FLO-SIC results are in better agreement with the experimental data. For the non-transition-metal molecules, the FLO-SIC FC term has the mean absolute error of 68 MHz, which is comparable to both the LDA and GGA results without SIC. For the seven transition-metal-based molecules, the FLO-SIC mean absolute error is 59 MHz, whereas the corresponding LDA and GGA errors are 101 and 82 MHz, respectively. Therefore, for the transition-metal-based molecules, the FLO-SIC FC term agrees better with experiment than the LDA and GGA results. We observe that the FC term from the FLO-SIC calculation is not necessarily larger than that from the LDA or GGA for all the considered systems due to the core spin polarization, in contrast to the expectation that SIC would increase the spin density near atomic nuclei, leading to larger FC terms.

Tb2O@C2(13333)-C74: A Non-Isolated Pentagon Endohedral Fullerene Containing a Nearly Linear Tb-O-Tb Unit.

Terbium has been added to the list of elements that form oxide clusters inside fullerene cages. Tb2O@C2(13333)-C74 has been isolated as a byproduct of the electric arc synthesis of the azafullerene Tb2@C79N. Cocrystallization of Tb2O@C2(13333)-C74 with Ni(OEP) (where OEP is the dianion of octaethylporphyrin) in toluene yielded black needles of Tb2O@C2(13333)-C74·NiII(OEP)·1.5C7H8 that have been examined by single-crystal X-ray diffraction. The resulting structure shows that a nearly linear Tb-O-Tb unit is contained in a C2(13333)-C74, which has two sites where pentagons share an edge to form pentalene units at opposite ends of the fullerene. Unlike the usual situations where metal atoms in fullerenes that do not obey the isolated pentagon rule are situated within the folds of the pentalene units, the Tb atoms in Tb2O@C2(13333)-C74 are positioned to the side of the pentalene units and near-neighboring hexagons. The magnetic properties of Tb2O@C2(13333)-C74 have been examined starting from the experimental geometry, using ab-initio multiconfigurational methods. The computations predict that Tb2O@C2(13333)-C74 will show strong axiality, which would make it a single-molecule magnet with a large magnetic anisotropy barrier.

Computational Insights into Electronic Excitations, Spin-Orbit Coupling Effects, and Spin Decoherence in Cr(IV)-Based Molecular Qubits.

The great success of point defects and dopants in semiconductors for quantum information processing has invigorated a search for molecules with analogous properties. Flexibility and tunability of desired properties in a large chemical space have great advantages over solid-state systems. The properties analogous to point defects were demonstrated in the Cr(IV)-based molecular family, Cr(IV)(aryl)4, where the electronic spin states were optically initialized, read out, and controlled. Despite this kick-start, there is still a large room for enhancing properties crucial for molecular qubits. Here, we provide computational insights into key properties of the Cr(IV)-based molecules aimed at assisting the chemical design of efficient molecular qubits. Using the multireference ab initio methods, we investigate the electronic states of Cr(IV)(aryl)4 molecules with slightly different ligands, showing that the zero-phonon line energies agree with the experiment and that the excited spin-triplet and spin-singlet states are highly sensitive to small chemical perturbations. By adding spin-orbit interaction, we find that the sign of the uniaxial zero-field splitting (ZFS) parameter is negative for all considered molecules and discuss optically induced spin initialization via non-radiative intersystem crossing. We quantify (super)hyperfine coupling to the 53Cr nuclear spin and to the 13C and 1H nuclear spins, and we discuss electron spin decoherence. We show that the splitting or broadening of the electronic spin sub-levels due to superhyperfine interaction with 1H nuclear spins decreases by an order of magnitude when the molecules have a substantial transverse ZFS parameter.

Electronic structure of mononuclear Cu-based molecule from density-functional theory with self-interaction correction.

We investigate the electronic structure of a planar mononuclear Cu-based molecule [Cu(C6H4S2)2]z in two oxidation states (z = -2, -1) using density-functional theory (DFT) with Fermi-Löwdin orbital (FLO) self-interaction correction (SIC). The dianionic Cu-based molecule was proposed to be a promising qubit candidate. Self-interaction error within approximate DFT functionals renders severe delocalization of electron and spin densities arising from 3d orbitals. The FLO-SIC method relies on optimization of Fermi-Löwdin orbital descriptors (FODs) with which localized occupied orbitals are constructed to create SIC potentials. Starting with many initial sets of FODs, we employ a frozen-density loop algorithm within the FLO-SIC method to study the Cu-based molecule. We find that the electronic structure of the molecule remains unchanged despite somewhat different final FOD configurations. In the dianionic state (spin S = 1/2), FLO-SIC spin density originates from the Cu d and S p orbitals with an approximate ratio of 2:1, in quantitative agreement with multireference calculations, while in the case of SIC-free DFT, the orbital ratio is reversed. Overall, FLO-SIC lowers the energies of the occupied orbitals and, in particular, the 3d orbitals unhybridized with the ligands significantly, which substantially increases the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) compared to SIC-free DFT results. The FLO-SIC HOMO-LUMO gap of the dianionic state is larger than that of the monoanionic state, which is consistent with experiment. Our results suggest a positive outlook of the FLO-SIC method in the description of magnetic exchange coupling within 3d-element-based systems.

Nature of Hyperfine Interactions in TbPc2 Single-Molecule Magnets: Multiconfigurational Ab Initio Study.

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 a 159Tb nucleus in TbPc2 (Pc = phthalocyanine) single-molecule magnets using multiconfigurational 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 pseudospin 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 transverse 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 the experiment. We further find that the transverse 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 transverse quadrupole interactions.

Electrically tuned hyperfine spectrum in neutral Tb(II)(CpiPr5)2 single-molecule magnet.

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 Ln2+ 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 159Tb nucleus in a neutral Tb(ii)(CpiPr5)2 single-molecule magnet (SMM), which exhibits unusually long magnetization relaxation time, using the complete active space self-consistent field (CASSCF) method with spin-orbit interaction included within the restricted active space state interaction (RASSI). Our calculations show that the low-energy states arise from 4f8(6s,5dz2)1, 4f8(5dx2-y2)1, and 4f8(5dxy)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)Pc2 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.

Multireference Ab Initio Studies of Magnetic Properties of Terbium-Based Single-Molecule Magnets.

We investigate how different chemical environments influence 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 calculations including relativistic spin-orbit interaction for representative Tb-based SMMs such as TbPc2 and TbPcNc in three charge states. We calculate the low-energy electronic structure from which we compute the Tb crystal-field (CF) parameters and construct an effective pseudospin Hamiltonian. Our calculations show that the ligand type and fine points of molecular geometry do not affect the gap between the ground-state and first-excited doublets, whereas the latter varies weakly with oxidation number. On the other hand, higher-energy levels have a strong dependence on all these characteristics. For neutral TbPc2 and TbPcNc molecules, the Tb magnetic moment and ligand spin are parallel to each other and the coupling strength between them does not depend much on the ligand type and details of the atomic structure. However, ligand distortion and molecular symmetry play a crucial role in transverse CF 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 insights into the mechanisms of magnetization relaxation in the representative Tb-based SMMs.

Filling the Gap in Extended Metal Atom Chains: Ferromagnetic Interactions in a Tetrairon(II) String Supported by Oligo-α-pyridylamido Ligands.

The stringlike complex [Fe4(tpda)3Cl2] (2; H2tpda = N2, N6-bis(pyridin-2-yl)pyridine-2,6-diamine) was obtained as the first homometallic extended metal atom chain based on iron(II) and oligo-α-pyridylamido ligands. The synthesis was performed under strictly anaerobic and anhydrous conditions using dimesityliron, [Fe2(Mes)4] (1; HMes = mesitylene), as both an iron source and a deprotonating agent for H2tpda. The four lined-up iron(II) ions in the structure of 2 (Fe···Fe = 2.94-2.99 Å, Fe···Fe···Fe = 171.7-168.8°) are wrapped by three doubly deprotonated twisted ligands, and the chain is capped at its termini by two chloride ions. The spectroscopic and electronic properties of 2 were investigated in dichloromethane by UV-vis-NIR absorption spectroscopy, 1H NMR spectroscopy, and cyclic voltammetry. The electrochemical measurements showed four fully resolved, quasi-reversible one-electron-redox processes, implying that 2 can adopt five oxidation states in a potential window of only 0.8 V. Direct current (dc) magnetic measurements indicate dominant ferromagnetic coupling at room temperature, although the ground state is only weakly magnetic. On the basis of density functional theory and angular overlap model calculations, this magnetic behavior was explained as being due to two pairs of ferromagnetically coupled iron(II) ions ( J = -21 cm-1 using JS i·S j convention) weakly antiferromagnetically coupled with each other. Alternating-current susceptibility data in the presence of a 2 kOe dc field and at frequencies up to 1.5 kHz revealed the onset of slow magnetic relaxation below 2.8 K, with the estimated energy barrier Ueff/ kB = 10.1(1.3) K.

Self-assembled PCBM bilayers on graphene and HOPG examined by AFM and STM.

In this work we report fabrication and characterization of phenyl-C61-butyric acid methyl ester (PCBM) bilayer structures on graphene and highly oriented pyrolytic graphite (HOPG). Through careful control of the PCBM solution concentration (from 0.1 to 2 mg ml-1) and the deposition conditions, we demonstrate that PCBM molecules self-assemble into bilayer structures on graphene and HOPG substrates. Interestingly, the PCBM bilayers are formed with two distinct heights on HOPG, but only one unique representative height on graphene. At elevated annealing temperatures, edge diffusion allows neighboring vacancies to merge into a more ordered structure. This is, to the best of our knowledge, the first experimental realization of PCBM bilayer structures on graphene. This work could provide valuable insight into fabrication of new hybrid, ordered structures for applications to organic solar cells.

Engineering and Probing Topological Properties of Dirac Semimetal Films by Asymmetric Charge Transfer.

Dirac semimetals (DSMs) have topologically robust three-dimensional Dirac (doubled Weyl) nodes with Fermi-arc states. In heterostructures involving DSMs, charge transfer occurs at the interfaces, which can be used to probe and control their bulk and surface topological properties through surface-bulk connectivity. Here we demonstrate that despite a band gap in DSM films, asymmetric charge transfer at the surface enables one to accurately identify locations of the Dirac-node projections from gapless band crossings and to examine and engineer properties of the topological Fermi-arc surface states connecting the projections, by simulating adatom-adsorbed DSM films using a first-principles method with an effective model. The positions of the Dirac-node projections are insensitive to charge transfer amount or slab thickness except for extremely thin films. By varying the amount of charge transfer, unique spin textures near the projections and a separation between the Fermi-arc states change, which can be observed by gating without adatoms.

Robust Topological Interfaces and Charge Transfer in Epitaxial Bi2Se3/II-VI Semiconductor Superlattices.

Access to charge transport through Dirac surface states in topological insulators (TIs) can be challenging due to their intermixing with bulk states or nontopological two-dimensional electron gas (2DEG) quantum well states caused by bending of electronic bands near the surface. The band bending arises via charge transfer from surface adatoms or interfaces and, therefore, the choice of layers abutting topological surfaces is critical. Here we report molecular beam epitaxial growth of Bi2Se3/ZnxCd1-xSe superlattices that hold only one topological surface channel per TI layer. The topological nature of conducting channels is supported by π-Berry phase evident from observed Shubnikov de Haas quantum oscillations and by the associated two-dimensional (2D) weak antilocalization quantum interference correction to magnetoresistance. Both density functional theory (DFT) calculations and transport measurements suggest that a single topological Dirac cone per TI layer can be realized by asymmetric interfaces: Se-terminated ZnxCd1-xSe interface with the TI remains "electronically intact", while charge transfer occurs at the Zn-terminated interface. Our findings indicate that topological transport could be controlled by adjusting charge transfer from nontopological spacers in hybrid structures.

Franck-Condon blockade in a single-molecule transistor.

We investigate vibron-assisted electron transport in single-molecule transistors containing an individual Fe4 Single-Molecule Magnet. We observe a strong suppression of the tunneling current at low bias in combination with vibron-assisted excitations. The observed features are explained by a strong electron-vibron coupling in the framework of the Franck-Condon model supported by density-functional theory.

Mapping of single-site magnetic anisotropy tensors in weakly coupled spin clusters by torque magnetometry.

Single-crystal torque magnetometry performed on weakly-coupled polynuclear systems provides access to a complete description of single-site anisotropy tensors. Variable-temperature, variable-field torque magnetometry was used to investigate triiron(III) complex [Fe3La(tea)2(dpm)6] (Fe3La), a lanthanum(III)-centred variant of tetrairon(III) single molecule magnets (Fe4) (H3tea = triethanolamine, Hdpm = dipivaloylmethane). Due to the presence of the diamagnetic lanthanoid, magnetic interactions among iron(III) ions (si = 5/2) are very weak (<0.1 cm(−1)) and the magnetic response of Fe3La is predominantly determined by single-site anisotropies. The local anisotropy tensors were found to have Di > 0 and to be quasi-axial with |Ei/Di| ~ 0.05. Their hard axes form an angle of approximately 70° with the threefold molecular axis, which therefore corresponds to an easy magnetic direction for the molecule. The resulting picture was supported by a High Frequency EPR investigation and by DFT calculations. Our study confirms that the array of peripheral iron(III) centres provides substantially noncollinear anisotropy contributions to the ground state of Fe4 complexes, which are of current interest in molecular magnetism and spintronics.

Topological surface currents accessed through reversible hydrogenation of the three-dimensional bulk.

Hydrogen, the smallest and most abundant element in nature, can be efficiently incorporated within a solid and drastically modify its electronic and structural state. In most semiconductors interstitial hydrogen binds to defects and is known to be amphoteric, namely it can act either as a donor (H+) or an acceptor (H-) of charge, nearly always counteracting the prevailing conductivity type. Here we demonstrate that hydrogenation resolves an outstanding challenge in chalcogenide classes of three-dimensional (3D) topological insulators and magnets - the control of intrinsic bulk conduction that denies access to quantum surface transport, imposing severe thickness limits on the bulk. With electrons donated by a reversible binding of H+ ions to Te(Se) chalcogens, carrier densities are reduced by over 1020cm-3, allowing tuning the Fermi level into the bulk bandgap to enter surface/edge current channels without altering carrier mobility or the bandstructure. The hydrogen-tuned topological nanostructures are stable at room temperature and tunable disregarding bulk size, opening a breadth of device platforms for harnessing emergent topological states.

Robustness of topologically protected surface states in layering of Bi2Te3 thin films.

Bulk Bi2Te3 is known to be a topological insulator. We investigate surface states of Bi2Te3(111) thin films of one to six quintuple layers using density-functional theory including spin-orbit coupling. We construct a method to identify topologically protected surface states of thin film topological insulators. Applying this method to Bi2Te3 thin films, we find that the topological nature of the surface states remains robust with the film thickness and that the films of three or more quintuple layers have topologically nontrivial surface states, which agrees with experiments.

Hyperfine and quadrupole interactions for Dy isotopes in DyPc2 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 161Dy and 163Dy nuclei in anionic DyPc2 (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 161Dy and 163Dy nuclei are much smaller than those for the 159Tb nucleus in TbPc2 single-molecule magnets. The calculated separations of the electronic-nuclear levels are comparable to experimental data reported for 163DyPc2. 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 TbPc2 single-molecule magnets. The magnetic field values of the avoided level crossings for 161DyPc2 and 163DyPc2 are found to be noticeably different, which can be observed from the experiment.

Toward Long-Range Entanglement between Electrically Driven Single-Molecule Magnets.

Over the past two decades, several molecules have been explored as possible building blocks of a quantum computer, a device that would provide exponential speedups for a number of problems, including the simulation of large, strongly correlated chemical systems. Achieving strong interactions and entanglement between molecular qubits remains an outstanding challenge. Here, we show that the TbPc2 single-molecule magnet has the potential to overcome this obstacle because of its sensitivity to electric fields stemming from the hyperfine Stark effect. We show how this feature can be leveraged to achieve long-range entanglement between pairs of molecules using a superconducting resonator as a mediator. Our results suggest that the molecule-resonator interaction is near the edge of the strong-coupling regime and could potentially pass into it given a more detailed, quantitative understanding of the TbPc2 molecule.

Moiré superlattices at the topological insulator Bi2Te3.

We report on the observation of complex superlattices at the surface of the topological insulator Bi2Te3. Scanning tunneling microscopy reveals the existence of two different periodic structures in addition to the Bi2Te3 atomic lattice, which is found to strongly affect the local electronic structure. These three different periodicities are interpreted to result from a single small in-plane rotation of the topmost quintuple layer only. Density functional theory calculations support the observed increase in the DOS near the Fermi level, and exclude the possibility that strain is at the origin of the observed Moiré pattern. Exploration of Moiré superlattices formed by the quintuple layers of topological insulators holds great potential for further tuning of the properties of topological insulators.

Annealing-Induced Bi Bilayer on Bi2Te3 Investigated via Quasi-Particle-Interference Mapping.

Topological insulators (TIs) are renowned for their exotic topological surface states (TSSs) that reside in the top atomic layers, and hence, detailed knowledge of the surface top atomic layers is of utmost importance. Here we present the remarkable morphology changes of Bi2Te3 surfaces, which have been freshly cleaved in air, upon subsequent systematic annealing in ultrahigh vacuum and the resulting effects on the local and area-averaging electronic properties of the surface states, which are investigated by combining scanning tunneling microscopy (STM), scanning tunneling spectroscopy (STS), and Auger electron spectroscopy (AES) experiments with density functional theory (DFT) calculations. Our findings demonstrate that the annealing induces the formation of a Bi bilayer atop the Bi2Te3 surface. The adlayer results in n-type doping, and the atomic defects act as scattering centers of the TSS electrons. We also investigated the annealing-induced Bi bilayer surface on Bi2Te3 via voltage-dependent quasi-particle-interference (QPI) mapping of the surface local density of states and via comparison with the calculated constant-energy contours and QPI patterns. We observed closed hexagonal patterns in the Fourier transform of real-space QPI maps with secondary outer spikes. DFT calculations attribute these complex QPI patterns to the appearance of a "second" cone due to the surface charge transfer between the Bi bilayer and the Bi2Te3. Annealing in ultrahigh vacuum offers a facile route for tuning of the topological properties and may yield similar results for other topological materials.