Spin polarization of the split Kondo state

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.

Manipulating the Spin Orientation of Co Atoms Using Monatomic Cu Chains

Harnessing the spin of single atoms is at the heart of quantum information nanotechnology based on magnetic concepts. By attaching single Co atoms to monatomic Cu chains, we demonstrate the ability to control the spin orientation by the atomic environment. Due to spin-orbit coupling (SOC), the spin is tilted by ≈58° from the surface normal toward the chain as evidenced by inelastic tunneling spectroscopy. These findings are reproduced by density functional theory calculations and have implications for Co atoms on pristine Cu(111), which are believed to be Kondo systems. Our quantum Monte Carlo calculations suggest that SOC suppresses the Kondo effect of Co atoms at chains and on the flat surface. Our work impacts the fundamental understanding of low-energy excitations in nanostructures on surfaces and demonstrates the ability to manipulate atomic-scale magnetic moments, which can have tremendous implications for quantum devices.

Controlling the Spin States of FeTBrPP on Au(111)

Spin-flip excitations of iron porphyrin molecules on Au(111) are investigated with a low-temperature scanning tunneling microscope. The molecules adopt two distinct adsorption configurations on the surface that exhibit different magnetic anisotropy energies. Density functional theory calculations show that the different structures and excitation energies reflect unlike occupations of the Fe 3d levels. We demonstrate that the magnetic anisotropy energy can be controlled by changing the adsorption site, the orientation, or the tip-molecule distance.

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.

Observation of Biradical Spin Coupling through Hydrogen Bonds

Investigation of intermolecular electron spin interaction is of fundamental importance in both science and technology. Here, radical pairs of all-trans retinoic acid molecules on Au(111) are created using an ultralow temperature scanning tunneling microscope. Antiferromagnetic coupling between two radicals is identified by magnetic-field-dependent spectroscopy. The measured exchange energies are from 0.1 to 1.0 meV. The biradical spin coupling is mediated through O─H⋯O hydrogen bonds, as elucidated from analysis combining density functional theory calculation and a modern version of valence bond theory.

Manipulating the Electronic and Magnetic Properties of Coordinated Nickel Atoms in Metal-Organic Frameworks by Hydrogenation

In the pursuit of manipulating the properties of single atoms, the surface-supported metal-organic frameworks (MOFs) provide us opportunities to individually address the electronic and magnetic properties of coordinated metal atoms by scanning tunneling microscopy. Recently, we have synthesized Ni-TPyP (TPyP = 5,10,15,20-tetra-(4-pyridyl) porphyrin) networks with dinuclear Ni centers on a Au(111) surface, in which the top-Ni atoms are sitting above the molecular plane. Here, we investigate the top-Ni atoms and their hydrogenated derivatives by low-temperature scanning tunneling microscopy and spectroscopy, and show that the electronic and magnetic states of top-Ni atoms can be manipulated by hydrogen adsorption. Specifically, by fitting the spin-flip spectra in vertical magnetic field, we find the spin state of top-Ni atoms is tuned from S = 1/2 to S = 1 by attaching one H atom and S = 3/2 by attaching two H atoms. Our work demonstrates atomic-scale control over the electronic and magnetic properties of coordinated metal atoms in a surface-supported MOF.

Indirect Spin-Readout of Rare-Earth-Based Single-Molecule Magnet with Scanning Tunneling Microscopy

Rare-earth based single-molecule magnets are promising candidates for magnetic information storage including qubits as their large magnetic moments are carried by localized 4f electrons. This shielding from the environment in turn hampers a direct electronic access to the magnetic moment. Here, we present the indirect readout of the Dy moment in Bis(phthalocyaninato)dysprosium (DyPc_{2}) molecules on Au(111) using milli-Kelvin scanning tunneling microscopy. Because of an unpaired electron on the exposed Pc ligand, the molecules show a Kondo resonance that is, however, split by the ferromagnetic exchange interaction between the unpaired electron and the Dy angular momentum. Using spin-polarized scanning tunneling spectroscopy, we read out the Dy magnetic moment as a function of the applied magnetic field, exploiting the spin polarization of the exchange-split Kondo state.

Resolving Ambiguity of the Kondo Temperature Determination in Mechanically Tunable Single-Molecule Kondo Systems

Determination of the molecular Kondo temperature (T_K) poses a challenge in most cases when the experimental temperature cannot be tuned to a sufficient extent. We show how this ambiguity can be resolved if additional control parameters are present, such as magnetic field and mechanical gating. We record the evolution of the differential conductance by lifting an individual molecule from the metal surface with the tip of a scanning tunneling microscope. By fitting the measured conductance spectra with the single impurity Anderson model we are able to demonstrate that the lifting tunes the junction continuously from the strongly correlated Kondo-singlet to the free spin-1/2 ground state. In the crossover regime, where T_K is similar to the temperature of experiment, the fitting yields ambiguous estimates of T_K varying by an order of magnitude. We show that analysis of the conductance measured in two distinct external magnetic fields can be used to resolve this problem.

The Kondo Effect of a Molecular Tip As a Magnetic Sensor

A single molecule offers to tailor and control the probing capability of a scanning tunneling microscope when placed on the tip. With the help of first-principles calculations, we show that on-tip spin sensitivity is possible through the Kondo ground state of a spin S = 1/2 cobaltocene molecule. When attached to the tip apex, we observe a reproducible Kondo resonance, which splits apart upon tuning the exchange coupling of cobaltocene to an iron atom on the surface. The spin-split Kondo resonance provides quantitative information on the exchange field and on the spin polarization of the iron atom. We also demonstrate that molecular vibrations cause the emergence of Kondo side peaks, which, unlike the Kondo resonance, are sensitive to cobaltocene adsorption.

Sensing the Spin of an Individual Ce Adatom

The magnetic moment of rare earth elements originates from electrons in the partially filled 4f orbitals. Accessing this moment electrically by scanning tunneling spectroscopy is hampered by shielding of outerlying orbitals. Here, we show that we can detect the magnetic moment of an individual Ce atom adsorbed on a Cu_{2}N ultrathin film on Cu(100) by using a sensor tip that has its apex functionalized with a Kondo screened spin system. We calibrate the sensor tip by deliberately coupling it to a well characterized Fe atom. Subsequently, we use the splitting of the tip's Kondo resonance when approaching a spectroscopically dark Ce atom to sense its magnetic moment.

Manipulation of the two-site Kondo effect in linear CoCu n CoCu m clusters

Artificially assembled linear atomic clusters, CoCu _n CoCu _m , are used to explore variations of the Kondo effect at the two Co sites. For all investigated Cu _n chain lengths ([Formula: see text]) the addition of a single Cu atom to one edge Co atom of the chain ([Formula: see text]) strongly reduces the amplitude of the Abrikosov-Suhl-Kondo resonance of that Co atom. Concomitantly, the resonance line width is more than halved. On the contrary, the Kondo effect of the opposite edge Co atom remains unaffected. Hybridization together with the linear geometry of the cluster are likely to drive the effect.

Exploring the Kondo Effect of an Extended Impurity with Chains of Co Adatoms in a Magnetic Field

Motivated by recent STM experiments, we explore the magnetic field induced Kondo effect that takes place at symmetry protected level crossings in finite Co adatom chains. We argue that the effective two-level system realized at a level crossing acts as an extended impurity coupled to the conduction electrons of the substrate by a distribution of Kondo couplings at the sites of the chain. Using auxiliary-field quantum Monte Carlo simulations, which quantitatively reproduce the field dependence of the zero-bias signal, we show that a proper Kondo resonance is present at the sites where the effective Kondo coupling dominates. Our modeling and numerical simulations provide a theoretical basis for the interpretation of the STM spectrum in terms of level crossings of the Co adatom chains.

Jahn-Teller Splitting in Single Adsorbed Molecules Revealed by Isospin-Flip Excitations

Scanning tunneling spectroscopy measurements of Mn phthalocyanine (MnPc) molecules adsorbed on (sqrt[3]×sqrt[3]) surface alloys show single inelastic steps at exclusively positive or negative bias strongly depending on the tip position. This is in contrast to conventional molecular excitation thresholds, which are independent of the current direction and therefore always occur at both positive and negative bias. This polarity selectivity is found to coincide with the spatial distribution of occupied and empty orbitals. Because of the interaction with the substrate, charge transfer into the doubly degenerate d_{π} orbitals of MnPc takes place. The resulting Jahn-Teller effect lifts the degeneracy and leads to an isospin- or pseudospin-flip excitation, the inelastic analogue of an orbital Kondo resonance.

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.

Spin-fluctuation and spin-relaxation effects of single adatoms from first principles

Single adatoms offer an exceptional playground for studying magnetism and its associated dynamics at the atomic scale. Here we review recent results on single adatoms deposited on metallic substrates, based on time-dependent density functional theory. First we analyze quantum zero-point spin-fluctuations (ZPSF) as calculated from the fluctuation-dissipation theorem, and show how they affect the magnetic stability by modifying the magnetic anisotropy energy. We also assess the impact of ZPSF in the limit of small hybridization to the substrate characteristic of semi-insulating substrates, connecting to recent experimental investigations where magnetic stability of a single adatom was achieved for the first time. Secondly, we inspect further the dynamics of single adatoms by considering the longitudinal and transverse spin-relaxation processes, whose time-scales are analyzed and related to the underlying electronic structure of both the adatom and the substrate. Thirdly, we analyze spin-fluctuation modes of paramagnetic adatoms, i.e. adatoms where the Stoner criterion for magnetism is almost fulfilled. Interestingly, such modes can develop well-defined peaks in the meV range, their main characteristics being determined by two fundamental electronic properties, namely the Stoner parameter and the density of states at the Fermi level. Furthermore, simulated inelastic scanning tunneling spectroscopy curves reveal that these spin-fluctuation modes can be triggered by tunneling electrons, opening up potential applications also for paramagnetic adatoms. Lastly, an overview of the outstanding issues and future directions is given.

An Iron-Porphyrin Complex with Large Easy-Axis Magnetic Anisotropy on Metal Substrate

Easy-axis magnetic anisotropy separates two magnetic states with opposite magnetic moments, and single magnetic atoms and molecules with large easy-axis magnetic anisotropy are highly desired for future applications in high-density data storage and quantum computation. By tuning the metalation reaction between tetra-pyridyl-porphyrin molecules and Fe atoms, we have stabilized the so-called initial complex, an intermediate state of the reaction, on Au(111) substrate, and investigated the magnetic property of this complex at a single-molecule level by low-temperature scanning tunneling microscopy and spectroscopy. As revealed by inelastic electron tunneling spectroscopy in magnetic field, this Fe-porphyrin complex has magnetic anisotropy energy of more than 15 meV with its easy-axis perpendicular to the molecular plane. Two magnetic states with opposite spin directions are discriminated by the dependence of spin-flip excitation energy on magnetic field and are found to have long spin lifetimes. Our density functional theory calculations reveal that the Fe atom in this complex, decoupled from Au substrate by a weak ligand field with elongated Fe-N bonds, has a high-spin state S = 2 and a large orbital angular momentum L = 2, which give rise to easy-axis anisotropy perpendicular to the molecular plane and large magnetic anisotropy energy by spin-orbit coupling. Since the Fe atom is protected by the molecular ligand, the complex can be processed at room or even higher temperatures. The reported system may have potential applications in nonvolatile data storage, and our work demonstrates on-surface metalation reactions can be utilized to synthesize organometallic complexes with large magnetic anisotropy.

Building Complex Kondo Impurities by Manipulating Entangled Spin Chains

The creation of molecule-like structures in which magnetic atoms interact controllably is full of potential for the study of complex or strongly correlated systems. Here, we create spin chains in which a strongly correlated Kondo state emerges from magnetic coupling of transition-metal atoms. We build chains up to ten atoms in length by placing Fe and Mn atoms on a Cu₂N surface with a scanning tunneling microscope. The atoms couple antiferromagnetically via superexchange interaction through the nitrogen atom network of the surface. The emergent Kondo resonance is spatially distributed along the chain. Its strength can be controlled by mixing atoms of different transition metal elements and manipulating their spatial distribution. We show that the Kondo screening of the full chain by the electrons of the nonmagnetic substrate depends on the interatomic entanglement of the spins in the chain, demonstrating the prerequisites to build and probe spatially extended strongly correlated nanostructures.

Tuning Paramagnetic Spin Excitations of Single Adatoms

We predict the existence of paramagnetic spin excitations (PSE) in nonmagnetic single adatoms. Our calculations demonstrate that PSE develop a well-defined structure in the meV region when the adatom's Stoner criterion for magnetism is close to the critical point. We further reveal a subtle tunability and enhancement of PSE by external magnetic fields. Finally, we show how PSE can be detected as moving steps in the dI/dV signal of inelastic scanning tunneling spectroscopy, opening a potential route for experimentally accessing electronic properties of nonmagnetic adatoms, such as the Stoner parameter.

Correlation-driven transport asymmetries through coupled spins in a tunnel junction

Spin-spin correlations can be the driving force that favours certain ground states and are key in numerous models that describe the behaviour of strongly correlated materials. While the sum of collective correlations usually lead to a macroscopically measurable change in properties, a direct quantification of correlations in atomic scale systems is difficult. Here we determine the correlations between a strongly hybridized spin impurity on the tip of a scanning tunnelling microscope and its electron bath by varying the coupling to a second spin impurity weakly hybridized to the sample surface. Electronic transport through these coupled spins reveals an asymmetry in the differential conductance reminiscent of spin-polarized transport in a magnetic field. We show that at zero field, this asymmetry can be controlled by the coupling strength and is related to either ferromagnetic or antiferromagnetic spin-spin correlations in the tip.

Kondo Resonance of a Co Atom Exchange Coupled to a Ferromagnetic Tip

The Kondo effect of a Co atom on Cu(100) was investigated with a low-temperature scanning tunneling microscope using a monoatomically sharp nickel tip. Upon a tip-Co contact, the differential conductance spectra exhibit a spin-split asymmetric Kondo resonance. The computed ab initio value of the exchange coupling is too small to suppress the Kondo effect, but sufficiently large to produce the splitting observed. A quantitative analysis of the line shape using the numerical renormalization group technique indicates that the junction spin polarization is weak.

Spin Manipulation by Creation of Single-Molecule Radical Cations

All-trans-retinoic acid (ReA), a closed-shell organic molecule comprising only C, H, and O atoms, is investigated on a Au(111) substrate using scanning tunneling microscopy and spectroscopy. In dense arrays single ReA molecules are switched to a number of states, three of which carry a localized spin as evidenced by conductance spectroscopy in high magnetic fields. The spin of a single molecule may be reversibly switched on and off without affecting its neighbors. We suggest that ReA on Au is readily converted to a radical by the abstraction of an electron.

Exploring the phase diagram of the two-impurity Kondo problem

A system of two exchange-coupled Kondo impurities in a magnetic field gives rise to a rich phase space hosting a multitude of correlated phenomena. Magnetic atoms on surfaces probed through scanning tunnelling microscopy provide an excellent platform to investigate coupled impurities, but typical high Kondo temperatures prevent field-dependent studies from being performed, rendering large parts of the phase space inaccessible. We present a study of pairs of Co atoms on insulating Cu₂N/Cu(100), which each have a Kondo temperature of only 2.6 K. The pairs are designed to have interaction strengths similar to the Kondo temperature. By applying a sufficiently strong magnetic field, we are able to access a new phase in which the two coupled impurities are simultaneously screened. Comparison of differential conductance spectra taken on the atoms to simulated curves, calculated using a third-order transport model, allows us to independently determine the degree of Kondo screening in each phase.

Magnetic atoms on a surface possess diverse correlated phases under an applied magnetic field due to a balance of exchange interaction and carrier-mediated coupling. Here, the authors use scanning tunnel microscopy to explore the phase diagram of coupled Co atom pairs on the surface of Cu₂N/Cu(100).