Single-molecule quantum dot as a Kondo simulator

Engineering Spin Interaction Channels of FePc on Au(111)

We demonstrate the reversible control of interactions between a local molecular spin, hosted within an iron phthalocyanine (FePc) molecule, and the conduction electrons of a supporting Au(111) surface. Using the tip of a scanning tunneling microscope, we deliberately and reversibly manipulate the adsorption configuration of the molecule relative to the underlying substrate lattice. Different rotation configurations lead to noticeable changes in the differential conductance measured on the FePc molecules. In one configuration, a Kondo resonance is observed, while in others, spin excitations are revealed. To further explore the impact of the local environment, we designed a series of molecular assemblies in which neighboring molecules surrounding the target molecule are incrementally increased. In this structured approach, we observed a step-by-step transition of the spin excitation state to a Kondo resonance, ultimately resulting in a pure Kondo feature.

Differences in Kondo Splitting of Surface Quantum Systems Induced by Two Distinct Magnetic Tips: A Joint Method of DFT and HEOM

The interactions between a magnetic tip and local spin impurities initiate unconventional Kondo phenomena, such as asymmetric suppression or even splitting of the Kondo peak. However, a lack of realistic theoretical models and comprehensive explanations for this phenomenon persists due to the complexity of the interactions. This research employs a joint method of density functional theory (DFT) and hierarchical equation of motion (HEOM) to simulate and contrast the modulation of the spin state and Kondo behavior in the Fe/Cu(100) system with two distinct magnetic tips. A cobalt tip, possessing a larger magnetic moment, incites greater atomic displacement of the iron atom, more notable alterations in electronic structure, and enhanced charge transfer with the environment compared with the control process utilizing a nickel tip. Furthermore, the Kondo resonance undergoes asymmetric splitting as a result of the ferromagnetic correlation between the iron atom and the magnetic tip. The Co tip's higher spin polarization results in a wider spacing between the splitting peaks. This investigation underscores the precision of the DFT + HEOM approach in predicting complex quantum phenomena and explaining the underlying physical principles. This provides valuable theoretical support for developing more sophisticated quantum regulation experiments.

Quantum Mpemba Effect in a Quantum Dot with Reservoirs

We demonstrate the quantum Mpemba effect in a quantum dot coupled to two reservoirs, described by the Anderson model. We show that the system temperatures starting from two different initial values (hot and cold) cross each other at finite time (and thereby reverse their identities; i.e., hot becomes cold and vice versa) to generate thermal quantum Mpemba effect. The slowest relaxation mode believed to play the dominating role in Mpemba effect in Markovian systems does not contribute to such anomalous relaxation in the present model. In this connection, our analytical result provides necessary condition for producing quantum Mpemba effect in the density matrix elements of the quantum dot, as a combined effect of the remaining relaxation modes.

Manipulation of the Magnetic State of a Porphyrin-Based Molecule on Gold: From Kondo to Quantum Nanomagnet via the Charge Fluctuation Regime

By moving individual Fe-porphyrin-based molecules with the tip of a scanning tunneling microscope in the vicinity of the elbow of the herringbone-reconstructed Au(111) containing a Br atom, we reversibly and continuously control their magnetic state. Several regimes are obtained experimentally and explored theoretically: from the integer spin limit, through intermediate magnetic states with renormalized magnetic anisotropy, until the Kondo-screened regime, corresponding to a progressive increase of charge fluctuations and mixed valency due to an increase in the interaction of the molecular Fe states with the substrate Fermi sea. Our study demonstrates the potential of utilizing charge fluctuations to generate and tune quantum magnetic states in molecule-surface hybrids.

Dynamical Screening of Local Spin Moments at Metal-Molecule Interfaces

Transition-metal phthalocyanine molecules have attracted considerable interest in the context of spintronics device development due to their amenability to diverse bonding regimes and their intrinsic magnetism. The latter is highly influenced by the quantum fluctuations that arise at the inevitable metal-molecule interface in a device architecture. In this study, we have systematically investigated the dynamical screening effects in phthalocyanine molecules hosting a series of transition-metal ions (Ti, V, Cr, Mn, Fe, Co, and Ni) in contact with the Cu(111) surface. Using comprehensive density functional theory plus Anderson's Impurity Model calculations, we show that the orbital-dependent hybridization and electron correlation together result in strong charge and spin fluctuations. While the instantaneous spin moments of the transition-metal ions are near atomic-like, we find that screening gives rise to considerable lowering or even quenching of these. Our results highlight the importance of quantum fluctuations in metal-contacted molecular devices, which may influence the results obtained from theoretical or experimental probes, depending on their possibly material-dependent characteristic sampling time-scales.

Tweezer-like magnetic tip control of the local spin state in the FeOEP/Pb(111) adsorption system: a preliminary exploration based on first-principles calculations

The magnetic interactions between the spin-polarized scanning tunnelling microscopy (SP-STM) tip and the localized spin impurities lead to various forms of the Kondo effect. Although these intriguing phenomena enrich Kondo physics, detailed theoretical simulations and explanations are still lacking due to the rather complex formation mechanisms. Here, by combining density functional theory (DFT), complete active space self-consistent field (CASSCF) theory, and hierarchical equations of motion (HEOM) methods, we perform first-principles-based simulation to elaborate the regulation process of the magnetic Co-tip on the spin state and transport behaviour of FeOEP/Pb(111) system. Compared with the non-magnetic tip, the stronger interaction between the magnetic tip and FeOEP molecule results in a more drastic deformation of the molecular structure with more electron transfer from the local environment to Fe-3d orbitals. The magnetic anisotropy of FeOEP changes very drastically from positive values in the tunnelling region to negative values in the contact region. The ferromagnetic electron correlation between the magnetic tip and the molecule induces an asymmetric Kondo line-shape near the Fermi level. This work highlights that the DFT + CASSCF + HEOM approach can not only predict complex quantum phenomena and explain underlying physical mechanisms, but also facilitate the design of more fascinating quantum control experiments.

Spatially Resolving Electron Spin Resonance of π-Radical in Single-molecule Magnet

The spintronic properties of magnetic molecules have attracted significant scientific attention. Special emphasis has been placed on the qubit for quantum information processing. The single-molecule magnet bis(phthalocyaninato (Pc)) Tb(III) (TbPc2) is one of the best examined cases in which the delocalized π-radical electron spin of the Pc ligand plays the key role in reading and intermediating the localized Tb spin qubits. We utilized the electron spin resonance (ESR) technique implemented on a scanning tunneling microscope (STM) and use it to measure local the ESR of a single TbPc2 molecule decoupled from the Cu(100) substrate by a two-monolayer NaCl film to identify the π-radical spin. We detected the ESR signal at the ligand positions under the resonance condition expected for an S = 1/2 spin. The results reveal that the π-radical electron is delocalized within the ligands and exhibits intramolecular coupling susceptible to the chemical environment.

Hierarchical equations of motion approach for accurate characterization of spin excitations in quantum impurity systems

Recent technological advancement in scanning tunneling microscopes has enabled the measurement of spin-field and spin-spin interactions in single atomic or molecular junctions with an unprecedentedly high resolution. Theoretically, although the fermionic hierarchical equations of motion (HEOM) method has been widely applied to investigate the strongly correlated Kondo states in these junctions, the existence of low-energy spin excitations presents new challenges to numerical simulations. These include the quest for a more accurate and efficient decomposition for the non-Markovian memory of low-temperature environments and a more careful handling of errors caused by the truncation of the hierarchy. In this work, we propose several new algorithms, which significantly enhance the performance of the HEOM method, as exemplified by the calculations on systems involving various types of low-energy spin excitations. Being able to characterize both the Kondo effect and spin excitation accurately, the HEOM method offers a sophisticated and versatile theoretical tool, which is valuable for the understanding and even prediction of the fascinating quantum phenomena explored in cutting-edge experiments.

Unravelling the robustness of magnetic anisotropy of a nickelocene molecule in different environments: a first-principles-based study

Recent scanning tunneling spectroscopy with single metallocene molecule-functionalized tips have proved to be a powerful tool to probe and control individual spins and spin-spin exchange interactions due to the robustness of the magnetic properties of the metallocene molecule in different surroundings. However, accurate prediction of such robustness at a first-principles-based level by the conventional density functional theory (DFT) has remained challenging. In this paper, we have performed a detailed investigation of the evolution of electronic and magnetic properties of a nickelocene molecule (NiCp₂) in different environments, i.e., free-standing, adsorbed on Cu(100) and as a functionalized tip apex. Using an embedding method, which combines DFT and the complete active space self-consistent field (CASSCF) method recently developed, we demonstrate that the nickelocene molecule almost preserves its spin and magnetic anisotropy upon adsorption on Cu(100), and also in the position of the tip apex. In particular, the cyclic π* orbital of the Cp rings could hybridize with the singly occupied d_π orbitals of the Ni center of the molecule, protecting these orbitals from external states. Hence the molecular spin maintains S = 1, the same as in the free-standing case, and its magnetic anisotropy is also robust with energies of 3.56, 3.34, and 3.51 meV in free-standing, adsorbed on Cu(100), and functionalized tip apex states, respectively, in good agreement with previous theoretical and experimental results. This work thus provides a first-principles-based understanding of the relevant experiments. Such agreement between theoretical simulations and experimental measurements highlights the potential usefulness of the method for investigating the local electronic and spin states of organometallic molecule-surface composite systems.

Correlation anisotropy driven Kosterlitz-Thouless-type quantum phase transition in a Kondo simulator

The precise manipulation of the quantum states of individual atoms/molecules adsorbed on metal surfaces is one of the most exciting frontiers in nanophysics, enabling us to realize novel single molecular logic devices and quantum information processing. Herein, by modeling an iron phthalocyanine molecule adsorbed on the Au(111) surface with a two-impurity Anderson model, we demonstrate that the quantum states of such a system could be adjusted by the uniaxial magnetic anisotropy D_z. For negative D_z, the ground state is dominated by a parallel configuration of the z component of local spins, whereas it turns to be an antiparallel one when D_z becomes positive. Interestingly, we found that these two phases are separated by a Kosterlitz-Thouless-type quantum phase transition, which is confirmed by the critical behaviors of the transmission coefficient and the local magnetic moment. Both phases are associated with spin correlation anisotropy, thus move against the Kondo effect. When the external magnetic field is applied, it first plays a role in compensating for the effect of D_z, and then it contributes significantly to the Zeeman effect for positive D_z, accompanied by the reappearance and the splitting of the Kondo peak, respectively. For fixed negative D_z, only the Zeeman behavior is revealed. Our results provide deep insights into the manipulation of the quantum phase within a single molecular junction.

Numerical renormalization group study of the Loschmidt echo in Kondo systems

We study the dynamical properties of the one-channel and two-channel spin-1/2 Kondo models after quenching in Hamiltonian variables. Eigen spectrum of the initial and final Hamiltonians is calculated by using the numerical renormalization group method implemented within the matrix product states formalism. We consider multiple quench protocols in the considered Kondo systems, also in the presence of external magnetic field of different intensities. The main emphasis is put on the analysis of the behavior of the Loschmidt echo L(t), which measures the ability of the system's revival to its initial state after a quench. We show that the decay of the Loschmidt echo strongly depends on the type of quench and the ground state of the system. For the one-channel Kondo model, we show that L(t) decays as, [Formula: see text], where [Formula: see text] is the Kondo temperature, while for the two-channel Kondo model, we demonstrate that the decay is slower and given by [Formula: see text]. In addition, we also determine the dynamical behavior of the impurity's magnetization, which sheds light on identification of the relevant time scales in the system's dynamics.

Trapping integrated molecular devices via a local transport circulation

Interactions between quantum systems and their environments may always result in inevitable decoherence. Isolation of the quantum system from the undesired environment noise brings us a great challenge for an...

Controlling the Entropy of a Single-Molecule Junction

Single molecules are nanoscale thermodynamic systems with few degrees of freedom. Thus, the knowledge of their entropy can reveal the presence of microscopic electron transfer dynamics that are difficult to observe otherwise. Here, we apply thermocurrent spectroscopy to directly measure the entropy of a single free radical molecule in a magnetic field. Our results allow us to uncover the presence of a singlet to triplet transition in one of the redox states of the molecule, not detected by conventional charge transport measurements. This highlights the power of thermoelectric measurements which can be used to determine the difference in configurational entropy between the redox states of a nanoscale system involved in conductance without any prior assumptions about its structure or microscopic dynamics.

Electron spin resonance of single iron phthalocyanine molecules and role of their non-localized spins in magnetic interactions

Electron spin resonance (ESR) spectroscopy is a crucial tool, through spin labelling, in investigations of the chemical structure of materials and of the electronic structure of materials associated with unpaired spins. ESR spectra measured in molecular systems, however, are established on large ensembles of spins and usually require a complicated structural analysis. Recently, the combination of scanning tunnelling microscopy with ESR has proved to be a powerful tool to image and coherently control individual atomic spins on surfaces. Here we extend this technique to single coordination complexes-iron phthalocyanines (FePc)-and investigate the magnetic interactions between their molecular spin with either another molecular spin (in FePc-FePc dimers) or an atomic spin (in FePc-Ti pairs). We show that the molecular spin density of FePc is both localized at the central Fe atom and also distributed to the ligands (Pc), which yields a strongly molecular-geometry-dependent exchange coupling.

Iron phthalocyanine on Au(111) is a "non-Landau" Fermi liquid

The paradigm of Landau’s Fermi liquid theory has been challenged with the finding of a strongly interacting Fermi liquid that cannot be adiabatically connected to a non-interacting system. A spin-1 two-channel Kondo impurity with anisotropy D has a quantum phase transition between two topologically different Fermi liquids with a peak (dip) in the Fermi level for D < D_c (D > D_c). Extending this theory to general multi-orbital problems with finite magnetic field, we reinterpret in a unified and consistent fashion several experimental studies of iron phthalocyanine molecules on Au(111) that were previously described in disconnected and conflicting ways. The differential conductance shows a zero-bias dip that widens when the molecule is lifted from the surface (reducing the Kondo couplings) and is transformed continuously into a peak under an applied magnetic field. We reproduce all features and propose an experiment to induce the topological transition.

Single molecules on metal surfaces are paradigmatic systems for the study of many-body phenomena. Here, the authors show that several spectroscopic experiments on iron phthalocyanine on Au(111) surface can be described in a unified way in terms of a strongly interacting topologically non-trivial (non-Landau) Fermi liquid.

Local Kondo scattering in 4d-electron RuOx nanoclusters on atomically-resolved ultrathin SrRuO3 films

Perovskite SrRuO₃ is a unique 4d transition metal oxide with coexisting spin-orbit coupling (SOC) and electron-electron correlation. However, the intrinsic, non-reconstructed surface structure of SrRuO₃ has not been reported so far. Here we report an atomic imaging of the non-reconstructed, SrO-terminated SrRuO₃ surface by scanning tunneling microscopy/spectroscopy. Moreover, a Kondo resonant behavior is revealed in RuO_x clusters located on top of the nonmagnetic SrO surface layer. The density functional theory calculations confirm that RuO_x clusters possess localized 4d-electron-involved spin moments and hybridize with the conduction electrons in the metal host, resulting in the appearance of the Kondo resonance features around the Fermi level. Our work demonstrates that artificially-engineered transition metal oxides provide new opportunities to explore the Kondo physics in 4d multi-orbital systems.

Theory of Differential Conductance of Co on Cu(111) Including Co s and d Orbitals, and Surface and Bulk Cu States

We revisit the theory of the Kondo effect observed by a scanning-tunneling microscope (STM) for transition-metal atoms (TMAs) on noble-metal surfaces, including d and s orbitals of the TMA, surface and bulk conduction states of the metal, and their hopping to the tip of the STM. Fitting the experimentally observed STM differential conductance for Co on Cu(111) including both the Kondo feature near the Fermi energy and the resonance below the surface band, we conclude that the STM senses mainly the Co s orbital and that the Kondo antiresonance is due to interference between states with electrons in the s orbital and a localized d orbital mediated by the conduction states.

Manipulation of Molecular Spin State on Surfaces Studied by Scanning Tunneling Microscopy

The adsorbed magnetic molecules with tunable spin states have drawn wide attention for their immense potential in the emerging fields of molecular spintronics and quantum computing. One of the key issues toward their application is the efficient controlling of their spin state. This review briefly summarizes the recent progress in the field of molecular spin state manipulation on surfaces. We focus on the molecular spins originated from the unpaired electrons of which the Kondo effect and spin excitation can be detected by scanning tunneling microscopy and spectroscopy (STM and STS). Studies of the molecular spin-carriers in three categories are overviewed, i.e., the ones solely composed of main group elements, the ones comprising 3d-metals, and the ones comprising 4f-metals. Several frequently used strategies for tuning molecular spin state are exemplified, including chemical reactions, reversible atomic/molecular chemisorption, and STM-tip manipulations. The summary of the successful case studies of molecular spin state manipulation may not only facilitate the fundamental understanding of molecular magnetism and spintronics but also inspire the design of the molecule-based spintronic devices and materials.

Collective Spin Manipulation in Antiferroelastic Spin-Crossover Metallo-Supramolecular Chains

Coupled spin-crossover complexes in supramolecular systems feature rich spin phases that can exhibit collective behaviors. Here, we report on a molecular-level exploration of the spin phase and collective spin-crossover dynamics in metallo-supramolecular chains. Using scanning tunneling microscopy, spectroscopy, and density functional theory calculations, we identify an antiferroelastic phase in the metal-organic chains, where the Ni atoms coordinated by deprotonated tetrahydroxybenzene linkers on Au(111) are at a low-spin (S = 0) or a high-spin (S = 1) state alternately along the chains. We demonstrate that the spin phase is stabilized by the combined effects of intrachain interactions and substrate commensurability. The stability of the antiferroelastic structure drives the collective spin-state switching of multiple Ni atoms in the same chain in response to electron/hole tunneling to a Ni atom via a domino-like magnetostructural relaxation process. These results provide insights into the magnetostructural dynamics of the supramolecular structures, offering a route toward their spintronic manipulations.

Exploiting chemistry and molecular systems for quantum information science

The power of chemistry to prepare new molecules and materials has driven the quest for new approaches to solve problems having global societal impact, such as in renewable energy, healthcare and information science. In the latter case, the intrinsic quantum nature of the electronic, nuclear and spin degrees of freedom in molecules offers intriguing new possibilities to advance the emerging field of quantum information science. In this Perspective, which resulted from discussions by the co-authors at a US Department of Energy workshop held in November 2018, we discuss how chemical systems and reactions can impact quantum computing, communication and sensing. Hierarchical molecular design and synthesis, from small molecules to supramolecular assemblies, combined with new spectroscopic probes of quantum coherence and theoretical modelling of complex systems, offer a broad range of possibilities to realize practical quantum information science applications.

Grafting, self-organization and reactivity of double-decker rare-earth phthalocyanine

Unveiling the interplay of semiconducting organic molecules with their environment, such as inorganic materials or atmospheric gas, is the first step to designing hybrid devices with tailored optical, electronic or magnetic properties. The present article focuses on a double-decker lutetium phthalocyanine known as an intrinsic semiconducting molecule, holding a Lu ion in its center, sandwiched between two phthalocyanine rings. Carrying out experimental investigations by means of electron spectroscopies, X-ray diffraction and scanning probe microscopies together with advanced ab initio computations, allows us to unveil how this molecule interacts with weakly or highly reactive surfaces. Our studies reveal that a molecule–surface interaction is evidenced when molecules are deposited on bare silicon or on gold surfaces together with a charge transferred from the substrate to the molecule, affecting to a higher extent the lower ring of the molecule. A new packing of the molecules on gold surfaces is proposed: an eclipse configuration in which molecules are flat and parallel to the surface, even for thick films of several hundreds of nanometers. Surprisingly, a robust tolerance of the double-decker phthalocyanine toward oxygen molecules is demonstrated, leading to weak chemisorption of oxygen below 100 K.

Synchronously voltage-manipulable spin reversing and selecting assisted by exchange coupling in a monomeric dimer with magnetic interface

The use of the molecular spin state as a quantum of next-generation information technology is receiving impressive research attention, within which the fundamental issues include manipulating the phase transition between the spin-up and -down states and generating spin polarized current. The spinterface between ferromagnetic electrodes and a molecular bridge represents one of the most intriguing elements in this context. Herein, by means of the celebrated numerical renormalization group technique, we present an original way to realize spin reversal in a monomeric dimer. Our scheme is based on the exchange interactions between electronic spins on one monomer and those on the other one or on the electrodes, which could be easily controlled through purely electronic technology. Through a careful engineering of the interfacial parameters, one of the monomers is devoted to the spin reversing, whereas the other one contributes to the spin selecting. The charge numbers of spin-up and -down electrons swap their respective occupancies at some particular points, indicating charge sensing between different spins. The competition between the spinterface and the molecular energy level results in charge oscillating in a single spin channel, which is unfavorable to the spin selecting. The observation may provide a prospective example for a multifunctional magnetoelectronics molecular device, which works without any external magnetic field.

Exchange-dependent spin polarized transport and phase transition in a triple monomer molecule

Molecular junctions contribute significantly to the fundamental understanding of the quantum information technologies in molecular spintronics. In this paper, with the aid of the state of the art numerical renormalization group method, we find a triple monomer molecule structure with strong electron-electron interactions could be a potential candidate for a multifunctional spin polarizer when an external magnetic field along the z axis is applied. It is demonstrated that the polarizing scenarios depend closely on the inter-orbital exchange couplings, and results in several kinds of spin polarizers, e.g., the unidirectional, the bidirectional, the dual, and the ternary spin polarizers. We show in detail the related phase diagram, and conclude the Zeeman effect and the charge switching for the bonding, anti-bonding and non-bonding orbitals are responsible for the spin polarizing transport. We stress even when the energy levels are chosen beyond the Kondo regime, the structure still shows a promising platform for molecular spintronics components.

Multi-scale approach to first-principles electron transport beyond 100 nm

Multi-scale computational approaches are important for studies of novel, low-dimensional electronic devices since they are able to capture the different length-scales involved in the device operation, and at the same time describe critical parts such as surfaces, defects, interfaces, gates, and applied bias, on a atomistic, quantum-chemical level. Here we present a multi-scale method which enables calculations of electronic currents in two-dimensional devices larger than 100 nm2, where multiple perturbed regions described by density functional theory (DFT) are embedded into an extended unperturbed region described by a DFT-parametrized tight-binding model. We explain the details of the method, provide examples, and point out the main challenges regarding its practical implementation. Finally we apply it to study current propagation in pristine, defected and nanoporous graphene devices, injected by chemically accurate contacts simulating scanning tunneling microscopy probes.

Tunable Spin-Superconductor Coupling of Spin 1/2 Vanadyl Phthalocyanine Molecules

Atomic-scale magnetic moments in contact with superconductors host rich physics based on the emergence of Yu-Shiba-Rusinov (YSR) magnetic bound states within the superconducting condensate. Here, we focus on a magnetic bound state induced into Pb nanoislands by individual vanadyl phthalocyanine (VOPc) molecules deposited on the Pb surface. The VOPc molecule is characterized by a spin magnitude of 1/2 arising from a well-isolated singly occupied d _xy-orbital and is a promising candidate for a molecular spin qubit with long coherence times. X-ray magnetic circular dichroism (XMCD) measurements show that the molecular spin remains unperturbed even for molecules directly deposited on the Pb surface. Scanning tunneling spectroscopy and density functional theory (DFT) calculations identify two adsorption geometries for this "asymmetric" molecule (i.e., absence of a horizontal symmetry plane): (a) oxygen pointing toward the vacuum with the Pc laying on the Pb, showing negligible spin-superconductor interaction, and (b) oxygen pointing toward the Pb, presenting an efficient interaction with the Pb and promoting a Yu-Shiba-Rusinov bound state. Additionally, we find that in the first case a YSR state can be induced smoothly by exerting mechanical force on the molecules with the scanning tunneling microscope (STM) tip. This allows the interaction strength to be tuned continuously from an isolated molecular spin case, through the quantum critical point (where the bound state energy is zero) and beyond. DFT indicates that a gradual bending of the VO bond relative to the Pc ligand plane promoted by the STM tip can modify the interaction in a continuously tunable manner. The ability to induce a tunable YSR state in the superconductor suggests the possibility of introducing coupled spins on superconductors with switchable interaction.

Visualizing Intramolecular Distortions as the Origin of Transverse Magnetic Anisotropy

The magnetic properties of metal-organic complexes are strongly influenced by conformational changes in the ligand. The flexibility of Fe-tetra-pyridyl-porphyrin molecules leads to different adsorption configurations on a Au(111) surface. By combining low-temperature scanning tunneling spectroscopy and atomic force microscopy, we resolve a correlation of the molecular configuration with different spin states and magnitudes of magnetic anisotropy. When the macrocycle exhibits a laterally undistorted saddle shape, the molecules lie in a S = 1 state with axial anisotropy arising from a square-planar ligand field. If the symmetry in the molecular ligand field is reduced by a lateral distortion of the molecule, we find a finite contribution of transverse anisotropy. Some of the distorted molecules lie in a S = 2 state, again exhibiting substantial transverse anisotropy.

Tuning the Coupling of an Individual Magnetic Impurity to a Superconductor: Quantum Phase Transition and Transport

The exchange scattering at magnetic adsorbates on superconductors gives rise to Yu-Shiba-Rusinov (YSR) bound states. Depending on the strength of the exchange coupling, the magnetic moment perturbs the Cooper pair condensate only weakly, resulting in a free-spin ground state, or binds a quasiparticle in its vicinity, leading to a (partially) screened spin state. Here, we use the flexibility of Fe-porphin (FeP) molecules adsorbed on a Pb(111) surface to reversibly and continuously tune between these distinct ground states. We find that the FeP moment is screened in the pristine adsorption state. Approaching the tip of a scanning tunneling microscope, we exert a sufficiently strong attractive force to tune the molecule through the quantum phase transition into the free-spin state. We ascertain and characterize the transition by investigating the transport processes as function of tip-molecule distance, exciting the YSR states by single-electron tunneling as well as (multiple) Andreev reflections.

The Kondo resonance line shape in scanning tunnelling spectroscopy: instrumental aspects

In the scanning tunnelling microscope, the many-body Kondo effect leads to a zero-bias feature of the differential conductance spectra of magnetic adsorbates on surfaces. The intrinsic line shape of this Kondo resonance and its temperature dependence in principle contain valuable information. We use measurements on a molecular Kondo system, all- trans retinoic acid on Au(1 1 1), and model calculations to discuss the role of instrumental broadening. The modulation voltage used for the lock-in detection, noise on the sample voltage, and the temperature of the microscope tip are considered. These sources of broadening affect the apparent line shapes and render difficult a determination of the intrinsic line width, in particular when variable temperatures are involved.

Two-stage three-channel Kondo physics for an FePc molecule on the Au(1 1 1) surface

We study an impurity Anderson model to describe an iron phthalocyanine (FePc) molecule on Au(1 1 1), motivated by previous results of scanning tunneling spectroscopy (STS) and theoretical studies. The model hybridizes a spin doublet consisting in one hole at the [Formula: see text] orbital of iron and two degenerate doublets corresponding to one hole either in the 3d _xz or in the 3d _yz orbital (called π orbitals) with two degenerate Hund-rule triplets with one hole in the 3d _z orbital and another one in a π orbital. We solve the model using a slave-boson mean-field approximation (SBMFA). For reasonable parameters we can describe very well the observed STS spectrum between sample bias  -60 mV to 20 mV. For these parameters the Kondo effect takes place in two stages, with different energy scales [Formula: see text] corresponding to the Kondo temperatures related with the hopping of the z ² and π orbitals respectively. There is a strong interference between the different channels and the Kondo temperatures, particularly the lowest one is strongly reduced compared with the value in the absence of the competing channel.

Simulation of inelastic spin flip excitations and Kondo effect in STM spectroscopy of magnetic molecules on metal substrates

Single-ion magnetic anisotropy in molecular magnets leads to spin flip excitations that can be measured by inelastic scanning tunneling microscope (STM) spectroscopy. Here I present a semi ab initio scheme to compute the spectral features associated with inelastic spin flip excitations and Kondo effect of single molecular magnets. To this end density functional theory calculations of the molecule on the substrate are combined with more sophisticated many-body techniques for solving the Anderson impurity problem of the spin-carrying orbitals of the magnetic molecule coupled to the rest of the system, containing a phenomenological magnetic anisotropy term. For calculating the STM spectra an exact expression for the [Formula: see text] in the ideal STM limit, when the coupling to the STM tip becomes negligibly small, is derived. In this limit the [Formula: see text] is simply related to the spectral function of the molecule-substrate system. For the case of an Fe porphyrin molecule on the Au(1 1 1) substrate, the calculated STM spectra are in good agreement with recently measured STM spectra, showing the typical step features at finite bias associated with spin flip excitation of a spin-1 quantum magnet. For the case of Kondo effect in Mn porphyrin on Au(1 1 1), the agreement with the experimental spectra is not as good due to the neglect of quantum interference in the tunneling.

Precise Control of Local Spin States in an Adsorbed Magnetic Molecule with an STM Tip: Theoretical Insights from First-Principles-Based Simulation

The precise tuning of local spin states in adsorbed organometallic molecules by a mechanically controlled scanning tunneling microscope (STM) tip has become a focus of recent experiments. However, the underlying mechanisms remain somewhat unclear. We investigate theoretically the STM tip control of local spin states in a single iron(II) porphyrin molecule adsorbed on the Pb(111) substrate. A combined density functional theory and hierarchical equations of motion approach is employed to simulate the tip tuning process in conjunction with the complete active space self-consistent field method for accurate computation of magnetic anisotropy. Our first-principles-based simulation accurately reproduces the tuning of magnetic anisotropy realized in experiment. Moreover, we elucidate the evolution of geometric and electronic structures of the composite junction and disclose the delicate competition between the Kondo resonance and local spin excitation. The understanding and insight provided by the first-principles-based simulation may help to realize more fascinating quantum state manipulations.

Control of Oxidation and Spin State in a Single-Molecule Junction

The oxidation and spin state of a metal-organic molecule determine its chemical reactivity and magnetic properties. Here, we demonstrate the reversible control of the oxidation and spin state in a single Fe porphyrin molecule in the force field of the tip of a scanning tunneling microscope. Within the regimes of half-integer and integer spin state, we can further track the evolution of the magnetocrystalline anisotropy. Our experimental results are corroborated by density functional theory and wave function theory. This combined analysis allows us to draw a complete picture of the molecular states over a large range of intramolecular deformations.

Abrupt Switching of Crystal Fields during Formation of Molecular Contacts

Magnetic molecules have the potential to be used as building blocks for bits in quantum computers. The spin states of the magnetic ion in the molecule can be represented by the effective spin Hamiltonian describing the zero field splitting (ZFS) of the magnetic states. We determined the ZFS of mechanically flexible metal-chelate molecules (Co, Ni, and Cu as metal ions) adsorbed on Cu₂N/Cu(100) by inelastic tunneling spectroscopy at temperatures down to 30 mK. When moving the tip toward the molecule, the tunneling current abruptly jumps to higher values, indicating the sudden deformation of the molecule bridging the tunneling junction. Hand in hand with the formation of the contact, an abrupt change of the ZFS occurs. This work also implies that ZFS expected in mechanical break junctions can drastically deviate from that of adsorbed molecules probed by other techniques.

Spin Control Induced by Molecular Charging in a Transport Junction

The ability of molecules to maintain magnetic multistability in nanoscale-junctions will determine their role in downsizing spintronic devices. While spin-injection from ferromagnetic leads gives rise to magnetoresistance in metallic nanocontacts, nonmagnetic leads probing the magnetic states of the junction itself have been considered as an alternative. Extending this experimental approach to molecular junctions, which are sensitive to chemical parameters, we demonstrate that the electron affinity of a molecule decisively influences its spin transport. We use a scanning tunneling microscope to trap a meso-substituted iron porphyrin, putting the iron center in an environment that provides control of its charge and spin states. A large electron affinity of peripheral ligands is shown to enable switching of the molecular S = 1 ground state found at low electron density to S = ¹/₂ at high density, while lower affinity keeps the molecule inactive to spin-state transition. These results pave the way for spin control using chemical design and electrical means.

Manipulation of spin and magnetic anisotropy in bilayer magnetic molecular junctions

The Kondo effect and magnetic anisotropy in bilayer TMPc/TMPc/Pb(111) junctions can be actively tuned by changing the intermediate decoupling layer.

Tuning the spin-related transport properties of FePc on Au(111) through single-molecule chemistry

Tuning the spin-related transport properties of FePc on Au(111) through single-molecule chemistry.