Spin coupling in engineered atomic structures

Anisotropic 2D van der Waals Magnets Hosting 1D Spin Chains

The exploration of 1D magnetism, frequently portrayed as spin chains, constitutes an actively pursued research field that illuminates fundamental principles in many-body problems and applications in magnonics and spintronics. The inherent reduction in dimensionality often leads to robust spin fluctuations, impacting magnetic ordering and resulting in novel magnetic phenomena. Here, structural, magnetic, and optical properties of highly anisotropic 2D van der Waals antiferromagnets that uniquely host spin chains are explored. First-principle calculations reveal that the weakest interaction is interchain, leading to essentially 1D magnetic behavior in each layer. With the additional degree of freedom arising from its anisotropic structure, the structure is engineered by alloying, varying the 1D spin chain lengths using electron beam irradiation, or twisting for localized patterning, and spin textures are calculated, predicting robust stability of the antiferromagnetic ordering. Comparing with other spin chain magnets, these materials are anticipated to bring fresh perspectives on harvesting low-dimensional magnetism.

Unraveling the Nature of Spin Coupling in a Metal-Free Diradical: Theoretical Distinction of Ferromagnetic and Antiferromagnetic Interactions

Metal-free diradicals based on polycyclic aromatic hydrocarbons are promising candidates for organic spintronics due to their stable magnetism and tunable spin coupling. However, distinguishing and elucidating the origins of ferromagnetic and antiferromagnetic interactions in these systems remain challenging. Here, we investigate the 2-OS diradical molecule sandwiched between gold electrodes using a combined density functional theory and hierarchical equations of motion approach. We find that the dihedral angle between the radical moieties controls the nature and strength of the intramolecular spin coupling, transitioning smoothly from antiferromagnetic to ferromagnetic as the angle increases. Distinct features in the inelastic electron tunneling spectra are identified that can discern the two coupling regimes, including spin excitation steps whose energies directly reveal the exchange coupling constant. Mechanical stretching of the junction is predicted to modulate the spectral line shapes by adjusting the hybridization of the molecular radicals with the electrodes. Our work elucidates the electronic origin of tunable spin interactions in 2-OS and provides spectroscopic fingerprints for characterizing magnetism in metal-free diradicals.

Electrostatic potentials of atomic nanostructures at metal surfaces quantified by scanning quantum dot microscopy

The discrete and charge-separated nature of matter - electrons and nuclei - results in local electrostatic fields that are ubiquitous in nanoscale structures and relevant in catalysis, nanoelectronics and quantum nanoscience. Surface-averaging techniques provide only limited experimental access to these potentials, which are determined by the shape, material, and environment of the nanostructure. Here, we image the potential over adatoms, chains, and clusters of Ag and Au atoms assembled on Ag(111) and quantify their surface dipole moments. By focusing on the total charge density, these data establish a benchmark for theory. Our density functional theory calculations show a very good agreement with experiment and allow a deeper analysis of the dipole formation mechanisms, their dependence on fundamental atomic properties and on the shape of the nanostructures. We formulate an intuitive picture of the basic mechanisms behind dipole formation, allowing better design choices for future nanoscale systems such as single-atom catalysts.

Controlling the charge-transfer dynamics of two-level systems around avoided crossings

Two-level quantum systems are fundamental physical models that continue to attract growing interest due to their crucial role as a building block of quantum technologies. The exact analytical solution of the dynamics of these systems is central to control theory and its applications, such as that to quantum computing. In this study, we reconsider the two-state charge transfer problem by extending and using a methodology developed to study (pseudo)spin systems in quantum electrodynamics contexts. This approach allows us to build a time evolution operator for the charge transfer system and to show new opportunities for the coherent control of the system dynamics, with a particular emphasis on the critical dynamic region around the transition state coordinate, where the avoided crossing of the energy levels occurs. We identify and propose possible experimental implementations of a class of rotations of the charge donor (or acceptor) that endow the electronic coupling matrix element with a time-dependent phase that can be employed to realize controllable coherent dynamics of the system across the avoided level crossing. The analogy of these rotations to reference frame rotations in generalized semiclassical Rabi models is discussed. We also show that the physical rotations in the charge-transfer systems can be performed so as to implement quantum gates relevant to quantum computing. From an exquisitely physical-mathematical viewpoint, our approach brings to light situations in which the time-dependent state of the system can be obtained without resorting to the special functions appearing in the Landau-Zener approach.

Stochastic Syncing in Sinusoidally Driven Atomic Orbital Memory

Stochastically fluctuating multiwell systems are a promising route toward physical implementations of energy-based machine learning and neuromorphic hardware. One of the challenges is finding tunable material platforms that exhibit such multiwell behavior and understanding how complex dynamic input signals influence their stochastic response. One such platform is the recently discovered atomic Boltzmann machine, where each stochastic unit is represented by a binary orbital memory state of an individual atom. Here, we investigate the stochastic response of binary orbital memory states to sinusoidal input voltages. Using scanning tunneling microscopy, we investigated orbital memory derived from individual Fe and Co atoms on black phosphorus. We quantify the state residence times as a function of various input parameters such as frequency, amplitude, and offset voltage. The state residence times for both species, when driven by a sinusoidal signal, exhibit synchronization that can be quantitatively modeled by a Poisson process based on the switching rates in the absence of a sinusoidal signal. For individual Fe atoms, we also observe a frequency-dependent response of the state favorability, which can be tuned by the input parameters. In contrast to Fe, there is no significant frequency dependence in the state favorability for individual Co atoms. Based on the Poisson model, the difference in the response of the state favorability can be traced to the difference in the voltage-dependent switching rates of the two different species. This platform provides a tunable way to induce population changes in stochastic systems and provides a foundation toward understanding driven stochastic multiwell systems.

Length-Dependent Magnetic Evolution of Anthenes on Au(111)

Nanographenes with zigzag edges, for example, anthenes, exhibit a unique nonbonding π-electron state, which can be described as a spin-polarized edge state that yields specific magnetic ground state. However, prior researches on the magnetism of anthenes with varying lengths on a surface is lacking. This study systematically fabricated anthenes with inherent zigzag carbon atoms of different lengths ranging from bisanthene to hexanthene. Their magnetic evolution on the Au(111) surface was analyzed through bond-resolved scanning probe techniques and density functional theory calculations. The analyses revealed a transition in magnetic properties associated with the length of the anthenes, arising from the imbalance between hybridization energy and the Coulomb repulsion between valence electrons. With the increasing length of the anthenes, the ground state transforms gradually from a closed-shell to an antiferromagnetic open-shell singlet, exhibiting a weak exchange coupling of 4 meV and a charge transfer-induced doublet. Therefore, this study formulated a chemically tunable platform to explore size-dependent π magnetism at the atomic scale, providing a framework for research in organic spintronics.

Machine-learning prediction of the formation of atomic gold wires by mechanically controlled break junctions

One of the challenging issues in the formation of atomic wires in break-junction experiments is the formation of stable monoatomic chains of reasonable length. To address this issue, in this study, we present a combination of unsupervised and supervised machine learning models trained on the experimentally measured conductance traces, with a goal to develop a microscopic understanding. Applying a machine learning model to two independent data sets from two different samples containing 72 000 and 90 000 conductance-displacement traces of single-atomic junctions, respectively, we first obtain the optimum conditions of bias and the stretching rate for the formation of chains of length > 4 Å. A deep learning method is subsequently applied for the classification of individual breaking traces, leading to the identification of trace features related to long-chain formation. Further investigation by ab initio molecular dynamics simulations provides a molecular-level understanding of the problem.

Exchange Interactions and Intermolecular Hybridization in a Spin-1/2 Nanographene Dimer

Phenalenyl is a radical nanographene with a triangular shape hosting an unpaired electron with spin S = 1/2. The open-shell nature of the phenalenyl is expected to be retained in covalently bonded networks. As a first step, we report synthesis of the phenalenyl dimer by combining in-solution synthesis and on-surface activation and its characterization on Au(111) and on a NaCl decoupling layer by means of inelastic electron tunneling spectroscopy (IETS). IETS shows inelastic steps that are identified as singlet-triplet excitation arising from interphenalenyl exchange. Spin excitation energies with and without the NaCl decoupling layer are 48 and 41 meV, respectively, indicating significant renormalization due to exchange with Au(111) electrons. Furthermore, third-neighbor hopping-induced interphenalenyl hybridization is fundamental to explaining the position-dependent bias asymmetry of the inelastic steps and activation of kinetic interphenalenyl exchange. Our results pave the way for bottom-up synthesis of S = 1/2 spin-lattices with large exchange interactions.

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.

Real-Space Imaging of Triplon Excitations in Engineered Quantum Magnets

Quantum magnets provide a powerful platform to explore complex quantum many-body phenomena. One example is triplon excitations, exotic many-body modes emerging from propagating singlet-triplet transitions. We engineer a minimal quantum magnet from organic molecules and demonstrate the emergence of dispersive triplon modes in one- and two-dimensional assemblies probed with scanning tunneling microscopy and spectroscopy. Our results provide the first demonstration of dispersive triplon excitations from a real-space measurement.

Realization of a Two-Dimensional Checkerboard Lattice in Monolayer Cu2N

Two-dimensional checkerboard lattice, the simplest line-graph lattice, has been intensively studied as a toy model, while material design and synthesis remain elusive. Here, we report theoretical prediction and experimental realization of the checkerboard lattice in monolayer Cu₂N. Experimentally, monolayer Cu₂N can be realized in the well-known N/Cu(100) and N/Cu(111) systems that were previously mistakenly believed to be insulators. Combined angle-resolved photoemission spectroscopy measurements, first-principles calculations, and tight-binding analysis show that both systems host checkerboard-derived hole pockets near the Fermi level. In addition, monolayer Cu₂N has outstanding stability in air and organic solvents, which is crucial for further device applications.

Large Orbital Moment of Two Coupled Spin-Half Co Ions in a Complex on Gold

The magnetic properties of transition-metal ions are generally described by the atomic spins of the ions and their exchange coupling. The orbital moment, usually largely quenched due the ligand field, is then seen as a perturbation. In such a scheme, S = 1/2 ions are predicted to be isotropic. We investigate a Co(II) complex with two antiferromagnetically coupled 1/2 spins on Au(111) using low-temperature scanning tunneling microscopy, X-ray magnetic circular dichroism, and density functional theory. We find that each of the Co ions has an orbital moment comparable to that of the spin, leading to magnetic anisotropy, with the spins preferentially oriented along the Co-Co axis. The orbital moment and the associated magnetic anisotropy is tuned by varying the electronic coupling of the molecule to the substrate and the microscope tip. These findings show the need to consider the orbital moment even in systems with strong ligand fields. As a consequence, the description of S = 1/2 ions becomes strongly modified, which have important consequences for these prototypical systems for quantum operations.

Tuning a Two-Impurity Kondo System by a Moiré Superstructure

Two-impurity Kondo models are paradigmatic for correlated spin-fermion systems. Working with Mn atoms on Au(111) covered by a monolayer of MoS_{2}, we tune the interadatom exchange via the adatom distance and the adatom-substrate exchange via the location relative to a moiré structure of the substrate. Differential-conductance measurements on isolated adatoms exhibit Kondo peaks with heights depending on the adatom location relative to the moiré structure. Mn dimers spaced by a few atomic lattice sites exhibit split Kondo resonances. In contrast, adatoms in closely spaced dimers couple antiferromagnetically, resulting in a molecular-singlet ground state. Exciting the singlet-triplet transition by tunneling electrons, we find that the singlet-triplet splitting is surprisingly sensitive to the moiré structure. We interpret our results theoretically by relating the variations in the singlet-triplet splitting to the heights of the Kondo peaks of single adatoms, finding evidence for coupling of the adatom spin to multiple conduction electron channels.

Atomic scale interfacial magnetism and origin of metal-insulator transition in (LaNiO[Formula: see text])[Formula: see text]/(CaMnO[Formula: see text])[Formula: see text] superlattices: a first principles study

Interfacial magnetism and metal-insulator transition at LaNiO[Formula: see text]-based oxide interfaces have triggered intense research efforts, because of the possible implications in future heterostructure device design and engineering. Experimental observation lack in some points a support from an atomistic view. In an effort to fill such gap, we hereby investigate the structural, electronic, and magnetic properties of (LaNiO[Formula: see text])[Formula: see text]/(CaMnO[Formula: see text])[Formula: see text] superlattices with varying LaNiO[Formula: see text] thickness (n) using density functional theory including a Hubbard-type effective on-site Coulomb term. We successfully capture and explain the metal-insulator transition and interfacial magnetic properties, such as magnetic alignments and induced Ni magnetic moments which were recently observed experimentally in nickelate-based heterostructures. In the superlattices modeled in our study, an insulating state is found for n=1 and a metallic character for n=2, 4, with major contribution from Ni and Mn 3d states. The insulating character originates from the disorder effect induced by sudden environment change for the octahedra at the interface, and associated to localized electronic states; on the other hand, for larger n, less localized interfacial states and increased polarity of the LaNiO[Formula: see text] layers contribute to metallicity. We discuss how the interplay between double and super-exchange interaction via complex structural and charge redistributions results in interfacial magnetism. While (LaNiO[Formula: see text])[Formula: see text]/(CaMnO[Formula: see text])[Formula: see text] superlattices are chosen as prototype and for their experimental feasibility, our approach is generally applicable to understand the intricate roles of interfacial states and exchange mechanism between magnetic ions towards the overall response of a magnetic interface or superlattice.

A spectroscopic-imaging scanning tunneling microscope in vector magnetic field

Cryogenic scanning tunneling microscopy and spectroscopy (STM/STS) performed in a high vector magnetic field provide unique possibilities for imaging surface magnetic structures and anisotropic superconductivity and exploring spin physics in quantum materials with atomic precision. Here, we describe the design, construction, and performance of a low-temperature, ultra-high-vacuum (UHV) spectroscopic-imaging STM equipped with a vector magnet capable of applying a field of up to 3 T in any direction with respect to the sample surface. The STM head is housed in a fully bakeable UHV compatible cryogenic insert and is operational over variable temperatures ranging from ∼300 down to 1.5 K. The insert can be easily upgraded using our home-designed ³He refrigerator. In addition to layered compounds, which can be cleaved at a temperature of either ∼300, ∼77, or ∼4.2 K to expose an atomically flat surface, thin films can also be studied by directly transferring using a UHV suitcase from our oxide thin-film laboratory. Samples can be treated further with a heater and a liquid helium/nitrogen cooling stage on a three-axis manipulator. The STM tips can be treated in vacuo by e-beam bombardment and ion sputtering. We demonstrate the successful operation of the STM with varying the magnetic field direction. Our facility provides a way to study materials in which magnetic anisotropy is a key factor in determining the electronic properties such as in topological semimetals and superconductors.

Geometrical and magnetic properties of small titanium and chromium clusters on monolayer hexagonal boron nitride

Magnetic clusters on an insulating substrate are potential candidates for spin-based quantum devices. Here we investigate the geometric, electronic, and magnetic structures of small Ti and Cr clusters, from dimers to pentamers, adsorbed on a single-layer hexagonal boron nitride (h-BN) sheet within the framework of density functional theory. The stable adsorption configurations of the Ti clusters and Cr clusters composed of the same number of atoms are found to be totally different from each other. The difference in their bonding mechanisms has been revealed by the density of states and the charge density difference of the corresponding adsorption systems. While chemical bonds are formed between the Ti atoms and the supporting sheet, the Cr clusters are found in the physisorption state on the substrate. In addition, it is shown that the h-BN sheet is energetically favorable for building three-dimensional Ti clusters. These findings support the use of h-BN as a suitable decoupling substrate for manipulation of quantum spin states in small transition metal (TM) clusters and fabrication of devices based on them.

Role of the Magnetic Anisotropy in Atomic-Spin Sensing of 1D Molecular Chains

One-dimensional metal-organic chains often possess a complex magnetic structure susceptible to modification by alteration of their chemical composition. The possibility to tune their magnetic properties provides an interesting playground to explore quasi-particle interactions in low-dimensional systems. Despite the great effort invested so far, a detailed understanding of the interactions governing the electronic and magnetic properties of the low-dimensional systems is still incomplete. One of the reasons is the limited ability to characterize their magnetic properties at the atomic scale. Here, we provide a comprehensive study of the magnetic properties of metal-organic one-dimensional (1D) coordination polymers consisting of 2,5-diamino-1,4-benzoquinonediimine ligands coordinated with Co or Cr atoms synthesized under ultrahigh-vacuum conditions on a Au(111) surface. A combination of integral X-ray spectroscopy with local-probe inelastic electron tunneling spectroscopy corroborated by multiplet analysis, density functional theory, and inelastic electron tunneling simulations enables us to obtain essential information about their magnetic structures, including the spin magnitude and orientation at the magnetic atoms, as well as the magnetic anisotropy.

Visualizing the interplay of Dirac mass gap and magnetism at nanoscale in intrinsic magnetic topological insulators

In intrinsic magnetic topological insulators, Dirac surface-state gaps are prerequisites for quantum anomalous Hall and axion insulating states. Unambiguous experimental identification of these gaps has proved to be a challenge, however. Here, we use molecular beam epitaxy to grow intrinsic MnBi₂Te₄ thin films. Using scanning tunneling microscopy/spectroscopy, we directly visualize the Dirac mass gap and its disappearance below and above the magnetic order temperature. We further reveal the interplay of Dirac mass gaps and local magnetic defects. We find that, in high defect regions, the Dirac mass gap collapses. Ab initio and coupled Dirac cone model calculations provide insight into the microscopic origin of the correlation between defect density and spatial gap variations. This work provides unambiguous identification of the Dirac mass gap in MnBi₂Te₄ and, by revealing the microscopic origin of its gap variation, establishes a material design principle for realizing exotic states in intrinsic magnetic topological insulators.

Computational design of magnetic molecules and their environment using quantum chemistry, machine learning and multiscale simulations

Having served as a playground for fundamental studies on the physics of d and f electrons for almost a century, magnetic molecules are now becoming increasingly important for technological applications, such as magnetic resonance, data storage, spintronics and quantum information. All of these applications require the preservation and control of spins in time, an ability hampered by the interaction with the environment, namely with other spins, conduction electrons, molecular vibrations and electromagnetic fields. Thus, the design of a novel magnetic molecule with tailored properties is a formidable task, which does not only concern its electronic structures but also calls for a deep understanding of the interaction among all the degrees of freedom at play. This Review describes how state-of-the-art ab initio computational methods, combined with data-driven approaches to materials modelling, can be integrated into a fully multiscale strategy capable of defining design rules for magnetic molecules.

Interplay of magnetic states and hyperfine fields of iron dimers on MgO(001)

Individual nuclear spin states can have very long lifetimes and could be useful as qubits. Progress in this direction was achieved on MgO/Ag(001) via detection of the hyperfine interaction (HFI) of Fe, Ti and Cu adatoms using scanning tunneling microscopy. Previously, we systematically quantified from first-principles the HFI for the whole series of 3d transition adatoms (Sc-Cu) deposited on various ultra-thin insulators, establishing the trends of the computed HFI with respect to the filling of the magnetic s- and d-orbitals of the adatoms and on the bonding with the substrate. Here we explore the case of dimers by investigating the correlation between the HFI and the magnetic state of free standing Fe dimers, single Fe adatoms and dimers deposited on a bilayer of MgO(001). We find that the magnitude of the HFI can be controlled by switching the magnetic state of the dimers. For short Fe-Fe distances, the antiferromagnetic state enhances the HFI with respect to that of the ferromagnetic state. By increasing the distance between the magnetic atoms, a transition toward the opposite behavior is observed. Furthermore, we demonstrate the ability to substantially modify the HFI by atomic control of the location of the adatoms on the substrate. Our results establish the limits of applicability of the usual hyperfine hamiltonian and we propose an extension based on multiple scattering processes.

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.

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.

Long-lifetime spin excitations near domain walls in 1T-TaS2

SignificanceThere is an intense ongoing search for two-level quantum systems with long lifetimes for applications in quantum communication and computation. Much research has been focused on studying isolated spins in semiconductors or band insulators. Mott insulators provide an interesting alternative platform but have been far less explored. In this work we use a technique capable of resolving individual spins at atomic length scales, to measure the two-level switching of spin states in 1T-TaS₂. We find quasi-1D chains of spin-1/2 electrons embedded in 1T-TaS₂ which have exceptionally long lifetimes. The discovery of long-lived spin states in a tractable van der Waal material opens doors to using Mott systems in future quantum information applications.

The Magnetic Genome of Two-Dimensional van der Waals Materials

Magnetism in two-dimensional (2D) van der Waals (vdW) materials has recently emerged as one of the most promising areas in condensed matter research, with many exciting emerging properties and significant potential for applications ranging from topological magnonics to low-power spintronics, quantum computing, and optical communications. In the brief time after their discovery, 2D magnets have blossomed into a rich area for investigation, where fundamental concepts in magnetism are challenged by the behavior of spins that can develop at the single layer limit. However, much effort is still needed in multiple fronts before 2D magnets can be routinely used for practical implementations. In this comprehensive review, prominent authors with expertise in complementary fields of 2D magnetism (i.e., synthesis, device engineering, magneto-optics, imaging, transport, mechanics, spin excitations, and theory and simulations) have joined together to provide a genome of current knowledge and a guideline for future developments in 2D magnetic materials research.

Anomalous excitations of atomically crafted quantum magnets

High-energy resolution spectroscopic studies of quantum magnets proved extremely valuable in accessing magnetodynamics quantities, such as energy barriers, magnetic interactions, and lifetime of excited states. Here, we investigate a previously unexplored flavor of low-energy spin excitations for quantum spins coupled to an electron bath. In sharp contrast to the usual tunneling signature of two steps symmetrically centered around the Fermi level, we find a single step in the conductance. Combining time-dependent and many-body perturbation theories, magnetic field-dependent tunneling spectra are explained as the result of an interplay between weak magnetic anisotropy energy, magnetic interactions, and Stoner-like electron-hole excitations that are strongly dependent on the magnetic states of the nanostructures. The results are rationalized in terms of a noncollinear magnetic ground state and the dominance of ferro- and antiferromagnetic interactions. The atomically crafted nanomagnets offer an appealing model for the exploration of electrically pumped spin systems.

Harnessing the Quantum Behavior of Spins on Surfaces

The desire to control and measure individual quantum systems such as atoms and ions in a vacuum has led to significant scientific and engineering developments in the past decades that form the basis of today's quantum information science. Single atoms and molecules on surfaces, on the other hand, are heavily investigated by physicists, chemists, and material scientists in search of novel electronic and magnetic functionalities. These two paths crossed in 2015 when it was first clearly demonstrated that individual spins on a surface can be coherently controlled and read out in an all-electrical fashion. The enabling technique is a combination of scanning tunneling microscopy (STM) and electron spin resonance, which offers unprecedented coherent controllability at the Angstrom length scale. This review aims to illustrate the essential ingredients that allow the quantum operations of single spins on surfaces. Three domains of applications of surface spins, namely quantum sensing, quantum control, and quantum simulation, are discussed with physical principles explained and examples presented. Enabled by the atomically-precise fabrication capability of STM, single spins on surfaces might one day lead to the realization of quantum nanodevices and artificial quantum materials at the atomic scale.

Topographic signatures and manipulations of Fe atoms, CO molecules and NaCl islands on superconducting Pb(111)

Topological superconductivity emerging in one- or two-dimensional hybrid materials is predicted as a key ingredient for quantum computing. However, not only the design of complex heterostructures is primordial for future applications but also the characterization of their electronic and structural properties at the atomic scale using the most advanced scanning probe microscopy techniques with functionalized tips. We report on the topographic signatures observed by scanning tunneling microscopy (STM) of carbon monoxide (CO) molecules, iron (Fe) atoms and sodium chloride (NaCl) islands deposited on superconducting Pb(111). For the CO adsorption a comparison with the Pb(110) substrate is demonstrated. We show a general propensity of these adsorbates to diffuse at low temperature under gentle scanning conditions. Our findings provide new insights into high-resolution probe microscopy imaging with terminated tips, decoupling atoms and molecules by NaCl islands or tip-induced lateral manipulation of iron atoms on top of the prototypical Pb(111) superconducting surface.

On-Surface Synthesis and Collective Spin Excitations of a Triangulene-Based Nanostar

Triangulene nanographenes are open‐shell molecules with predicted high spin state due to the frustration of their conjugated network. Their long‐sought synthesis became recently possible over a metal surface. Here, we present a macrocycle formed by six [3]triangulenes, which was obtained by combining the solution synthesis of a dimethylphenyl‐anthracene cyclic hexamer and the on‐surface cyclodehydrogenation of this precursor over a gold substrate. The resulting triangulene nanostar exhibits a collective spin state generated by the interaction of its 12 unpaired π‐electrons along the conjugated lattice, corresponding to the antiferromagnetic ordering of six S=1 sites (one per triangulene unit). Inelastic electron tunneling spectroscopy resolved three spin excitations connecting the singlet ground state with triplet states. The nanostar behaves close to predictions from the Heisenberg model of an S=1 spin ring, representing a unique system to test collective spin modes in cyclic systems.

Observation of fractional edge excitations in nanographene spin chains

Fractionalization is a phenomenon in which strong interactions in a quantum system drive the emergence of excitations with quantum numbers that are absent in the building blocks. Outstanding examples are excitations with charge e/3 in the fractional quantum Hall effect^1,2, solitons in one-dimensional conducting polymers^3,4 and Majorana states in topological superconductors⁵. Fractionalization is also predicted to manifest itself in low-dimensional quantum magnets, such as one-dimensional antiferromagnetic S = 1 chains. The fundamental features of this system are gapped excitations in the bulk⁶ and, remarkably, S = 1/2 edge states at the chain termini^7-9, leading to a four-fold degenerate ground state that reflects the underlying symmetry-protected topological order^10,11. Here, we use on-surface synthesis¹² to fabricate one-dimensional spin chains that contain the S = 1 polycyclic aromatic hydrocarbon triangulene as the building block. Using scanning tunnelling microscopy and spectroscopy at 4.5 K, we probe length-dependent magnetic excitations at the atomic scale in both open-ended and cyclic spin chains, and directly observe gapped spin excitations and fractional edge states therein. Exact diagonalization calculations provide conclusive evidence that the spin chains are described by the S = 1 bilinear-biquadratic Hamiltonian in the Haldane symmetry-protected topological phase. Our results open a bottom-up approach to study strongly correlated phases in purely organic materials, with the potential for the realization of measurement-based quantum computation¹³.

First-principles study of Mn3 adsorbed on Au(111) and Cu(111) surfaces

A theoretical study of the Mn trimer adsorbed on the noble metal surfaces Au(111) and Cu(111) is reported. The calculations were performed using first-principles methods within the density functional theory and the generalized gradient approximation in the collinear and non-collinear magnetic phases. The system was modeled by considering a surface unit cell of 25 atoms to improve the trimer's isolation on the surface. We evaluated the trimer as a linear chain and forming triangular structures. The triangular trimer can be adsorbed in two possible configurations, above an empty surface triangle site (Δ) or on a triangle with a surface atom at the center in a hexagonal structure (H). The difference is the coordination of the Mn with surface atoms. We studied the antiferromagnetic (AF), ferromagnetic (FM), and non-collinear (NC) magnetic cases. As a result, the lowest energy configuration on both metals is the AFΔ configuration, which has an isosceles triangle shape. In comparison, the NC and the FM configurations adopt an equilateral geometry. The same trend was observed for the H configurations, but they are less bonded. The results are supported by calculating the spin-polarized electronic structure and the electronic charge transfer. Finally, we computed the energy barriers that inhibit the transformation of the linear chain to a delta Mn trimer on both substrates.

On-Surface Synthesis and Characterization of Super-nonazethrene

Beginning with the early work of Clar et al. in 1955, zethrenes and their laterally extended homologues, super-zethrenes, have been intensively studied in the solution phase and widely investigated as optical and charge transport materials. Superzethrenes are also considered to exhibit an open-shell ground state and may thus serve as model compounds to investigate nanoscale π-magnetism. However, their synthesis is extremely challenging due to their high reactivity. We report here the on-surface synthesis of the hitherto largest zethrene homologue-super-nonazethrene-on Au(111). Using single-molecule scanning tunneling microscopy and spectroscopy, we show that super-nonazethrene exhibits an open-shell singlet ground state featuring a large spin polarization-driven electronic gap of 1 eV. Consistent with the emergence of an open-shell ground state, high-resolution tunneling spectroscopy reveals singlet-triplet spin excitations in super-nonazethrene, characterized by a strong intramolecular magnetic exchange coupling of 51 meV. Given the paucity of zethrene chemistry on surfaces, our results therefore provide unprecedented access to large, open-shell zethrene compounds amenable to scanning probe measurements, with potential application in molecular spintronics.

Solution/Ammonolysis Syntheses of Unsupported and Silica-Supported Copper(I) Nitride Nanostructures from Oxidic Precursors

Herein we describe an alternative strategy to achieve the preparation of nanoscale Cu3N. Copper(II) oxide/hydroxide nanopowder precursors were successfully fabricated by solution methods. Ammonolysis of the oxidic precursors can be achieved essentially pseudomorphically to produce either unsupported or supported nanoparticles of the nitride. Hence, Cu3N particles with diverse morphologies were synthesized from oxygen-containing precursors in two-step processes combining solvothermal and solid-gas ammonolysis stages. The single-phase hydroxochloride precursor, Cu2(OH)3Cl was prepared by solution-state synthesis from CuCl2·2H2O and urea, crystallising with the atacamite structure. Alternative precursors, CuO and Cu(OH)2, were obtained after subsequent treatment of Cu2(OH)3Cl with NaOH solution. Cu3N, in the form of micro- and nanorods, was the sole product formed from ammonolysis using either CuO or Cu(OH)2. Conversely, the ammonolysis of dicopper trihydroxide chloride resulted in two-phase mixtures of Cu3N and the monoamine, Cu(NH3)Cl under similar experimental conditions. Importantly, this pathway is applicable to afford composite materials by incorporating substrates or matrices that are resistant to ammoniation at relatively low temperatures (ca. 300 °C). We present preliminary evidence that Cu3N/SiO2 nanocomposites (up to ca. 5 wt.% Cu3N supported on SiO2) could be prepared from CuCl2·2H2O and urea starting materials following similar reaction steps. Evidence suggests that in this case Cu3N nanoparticles are confined within the porous SiO2 matrix.

Eigenmodes of a disordered FeCo magnonic crystal at finite temperatures

In this report we present a systematic study of the magnonic modes in the disordered Fe_0.5Co_0.5alloy based on the Heisenberg Hamiltonian using two complementary approaches. In order to account for substitutional disorder, on the one hand we directly average the transverse magnetic susceptibility in real space over different disorder configurations and on the other hand we use the coherent potential approximation (CPA). While the method of direct averaging is numerically exact, it is computationally expensive and limited by the maximal size of the supercell which can be simulated on a computer. On the contrary the CPA does not suffer from this drawback and yields a cheap numerical scheme. Therefore, we additionally compare the results of these two approaches and show that the CPA gives very good results for most of the magnetic properties considered in this report, including the magnon energies and the spatial shape of the eigenmodes. However, it turns out that while reproducing the general trend, the CPA systematically underestimates the disorder induced damping of the magnons. This provides evidence that the physics of impurity scattering in this system is governed by non-local effects missing in the CPA. Finally, we study the real space eigenmodes of the system, including their spatial shapes, and analyze their temperature dependence within the random phase approximation.

Free coherent evolution of a coupled atomic spin system initialized by electron scattering

Full insight into the dynamics of a coupled quantum system depends on the ability to follow the effect of a local excitation in real-time. Here, we trace the free coherent evolution of a pair of coupled atomic spins by means of scanning tunneling microscopy. Rather than using microwave pulses, we use a direct-current pump-probe scheme to detect the local magnetization after a current-induced excitation performed on one of the spins. By making use of magnetic interaction with the probe tip, we are able to tune the relative precession of the spins. We show that only if their Larmor frequencies match, the two spins can entangle, causing angular momentum to be swapped back and forth. These results provide insight into the locality of electron spin scattering and set the stage for controlled migration of a quantum state through an extended spin lattice.

Large magnetic exchange coupling in rhombus-shaped nanographenes with zigzag periphery

Nanographenes with zigzag edges are predicted to manifest non-trivial π-magnetism resulting from the interplay of concurrent electronic effects, such as hybridization of localized frontier states and Coulomb repulsion between valence electrons. This provides a chemically tunable platform to explore quantum magnetism at the nanoscale and opens avenues towards organic spintronics. The magnetic stability in nanographenes is thus far greatly limited by the weak magnetic exchange coupling, which remains below the room-temperature thermal energy. Here, we report the synthesis of large rhombus-shaped nanographenes with zigzag peripheries on gold and copper surfaces. Single-molecule scanning probe measurements show an emergent magnetic spin singlet ground state with increasing nanographene size. The magnetic exchange coupling in the largest nanographene (C₇₀H₂₂, containing five benzenoid rings along each edge), determined by inelastic electron tunnelling spectroscopy, exceeds 100 meV or 1,160 K, which outclasses most inorganic nanomaterials and survives on a metal electrode.

In-Situ Manipulation of the Magnetic Anisotropy of Single Mn Atom via Molecular Ligands

Magnetic anisotropy is essential for permanent magnets to maintain their magnetization along specific directions. Understanding and controlling the magnetic anisotropy on a single-molecule scale are challenging but of fundamental importance for the future's spintronic technology. Here, by using scanning tunneling microscopy (STM), we demonstrated the ability to control the magnetic anisotropy by tuning the ligand field at the single-molecule level. We constructed a molecular magnetic complex with a single Mn atom and an organic molecule (4,4'-biphenyldicarbonitrile) as a ligand via atomic manipulation. Inelastic tunneling spectra (IETS) show that the Mn complex has much larger axial magnetic anisotropy than individual Mn atoms, and the anisotropy energy can be tuned by the coupling strength of the ligand. With density functional theory calculations, we revealed that the enhanced magnetic anisotropy of Mn arising from the carbonitrile ligand provides a prototype for the engineering of the magnetism of quantum devices.

Highly Degenerate Ground States in a Frustrated Antiferromagnetic Kagome Lattice in a Two-Dimensional Metal-Organic Framework

Realization of the Kagome antiferromagnetic (KAF) lattice is of high interest because the geometric frustration in the Kagome lattice is expected to give rise to highly degenerated ground states that may host exotic phases such as quantum spin liquid. Here we demonstrate the design and synthesis of a single-layer two-dimensional metal-organic framework (2D-MOF) containing a Kagome lattice of Fe(II) ions assembled on a Au(111) surface. First-principles calculations reveal that the Fe(II) ions are at a high spin state of S = 2 and are coupled antiferromagnetically with nearest-neighboring exchange J₁ = 5.8 meV. The ground state comprises various degenerated spin configurations including the well-known q = 0 and q = √3 × √3 phases. Remarkably, we observe a spin excitation at 6 meV using tunneling spectroscopy. This work points out a feasible route toward realizing spin ¹/₂ KAF, a candidate quantum spin liquid system, by replacing Fe(II) by Cu(II) in the same structure.

Magnetic and vibrational properties of small chromium clusters on the Cu(111) surface

The structure and magnetic properties of small Cr clusters, Cr₃ and Cr₄, adsorbed on the Cu(111) surface have been investigated using density functional theory (DFT) calculations and their vibrational properties have been studied within calculations based on tight-binding second moment approximation interatomic interaction potentials (TBSMA). It has been shown that the magnetic ordering in the Cr clusters significantly affects their crystal structure and symmetry, which influences the vibrational modes of the clusters and nearest neighbor copper atoms. In turn, these modes select potentially possible structures of Cr₃ and Cr₄, prohibiting the lowest total energy cluster structure as dynamically unstable.

Tuning interactions between spins in a superconductor

Novel many-body and topological electronic phases can be created in assemblies of interacting spins coupled to a superconductor, such as one-dimensional topological superconductors with Majorana zero modes (MZMs) at their ends. Understanding and controlling interactions between spins and the emergent band structure of the in-gap Yu-Shiba-Rusinov (YSR) states they induce in a superconductor are fundamental for engineering such phases. Here, by precisely positioning magnetic adatoms with a scanning tunneling microscope (STM), we demonstrate both the tunability of exchange interaction between spins and precise control of the hybridization of YSR states they induce on the surface of a bismuth (Bi) thin film that is made superconducting with the proximity effect. In this platform, depending on the separation of spins, the interplay among Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, spin-orbit coupling, and surface magnetic anisotropy stabilizes different types of spin alignments. Using high-resolution STM spectroscopy at millikelvin temperatures, we probe these spin alignments through monitoring the spin-induced YSR states and their energy splitting. Such measurements also reveal a quantum phase transition between the ground states with different electron number parity for a pair of spins in a superconductor tuned by their separation. Experiments on larger assemblies show that spin-spin interactions can be mediated in a superconductor over long distances. Our results show that controlling hybridization of the YSR states in this platform provides the possibility of engineering the band structure of such states for creating topological phases.

An atomic Boltzmann machine capable of self-adaption

The quest to implement machine learning algorithms in hardware has focused on combining various materials, each mimicking a computational primitive, to create device functionality. Ultimately, these piecewise approaches limit functionality and efficiency, while complicating scaling and on-chip learning, necessitating new approaches linking physical phenomena to machine learning models. Here, we create an atomic spin system that emulates a Boltzmann machine directly in the orbital dynamics of one well-defined material system. Utilizing the concept of orbital memory based on individual cobalt atoms on black phosphorus, we fabricate the prerequisite tuneable multi-well energy landscape by gating patterned atomic ensembles using scanning tunnelling microscopy. Exploiting the anisotropic behaviour of black phosphorus, we realize plasticity with multi-valued and interlinking synapses that lead to tuneable probability distributions. Furthermore, we observe an autonomous reorganization of the synaptic weights in response to external electrical stimuli, which evolves at a different time scale compared to neural dynamics. This self-adaptive architecture paves the way for autonomous learning directly in atomic-scale machine learning hardware.

Extended iron phthalocyanine islands self-assembled on a Ge(001):H surface

Self-assembly of iron(II) phthalocyanine (FePc) molecules on a Ge(001):H surface results in monolayer islands extending over hundreds of nanometers and comprising upright-oriented entities. Scanning tunneling spectroscopy reveals a transport gap of 2.70 eV in agreement with other reports regarding isolated FePc molecules. Detailed analysis of single FePc molecules trapped at surface defects indicates that the molecules stay intact upon adsorption and can be manipulated away from surface defects onto a perfectly hydrogenated surface. This allows for their isolation from the germanium surface.

Stable single atomic silver wires assembling into a circuitry-connectable nanoarray

Atomic metal wires have great promise for practical applications in devices due to their unique electronic properties. Unfortunately, such atomic wires are extremely unstable. Here we fabricate stable atomic silver wires (ASWs) with appreciably unoccupied states inside the parallel tunnels of α-MnO₂ nanorods. These unoccupied Ag 4d orbitals strengthen the Ag–Ag bonds, greatly enhancing the stability of ASWs while the presence of delocalized 5s electrons makes the ASWs conducting. These stable ASWs form a coherently oriented three-dimensional wire array of over 10 nm in width and up to 1 μm in length allowing us to connect it to nano-electrodes. Current-voltage characteristics of ASWs show a temperature-dependent insulator-to-metal transition, suggesting that the atomic wires could be used as thermal electrical devices.

One-dimensional atomic metal wires can exhibit useful properties distinct from their bulk equivalents; however they typically suffer from limited stability. Here, Chen et al create atomic silver wires which are stable and exhibit a temperature dependent metal to insulator transition.

Probing resonating valence bond states in artificial quantum magnets

Designing and characterizing the many-body behaviors of quantum materials represents a prominent challenge for understanding strongly correlated physics and quantum information processing. We constructed artificial quantum magnets on a surface by using spin-1/2 atoms in a scanning tunneling microscope (STM). These coupled spins feature strong quantum fluctuations due to antiferromagnetic exchange interactions between neighboring atoms. To characterize the resulting collective magnetic states and their energy levels, we performed electron spin resonance on individual atoms within each quantum magnet. This gives atomic-scale access to properties of the exotic quantum many-body states, such as a finite-size realization of a resonating valence bond state. The tunable atomic-scale magnetic field from the STM tip allows us to further characterize and engineer the quantum states. These results open a new avenue to designing and exploring quantum magnets at the atomic scale for applications in spintronics and quantum simulations.

The resonating valence bond state is a spin-liquid state where spins continuously alter their singlet partners. Here Yang et al. use spin-1/2 atoms precision-placed by a scanning tunnelling microscope to create artificial quantum magnets exhibiting the resonating valence bond state.

Imprinting Tunable π-Magnetism in Graphene Nanoribbons via Edge Extensions

Magnetic carbon nanostructures are currently under scrutiny for a wide spectrum of applications. Here, we theoretically investigate armchair graphene nanoribbons patterned with asymmetric edge extensions consisting of laterally fused naphtho groups, as recently fabricated via on-surface synthesis. We show that an individual edge extension acts as a spin-12 center and develops a sizable spin-polarization of the conductance around the band edges. The Heisenberg exchange coupling between a pair of edge extensions is dictated by the position of the second naphtho group in the carbon backbone, thus enabling ferromagnetic, antiferromagnetic, or nonmagnetic states. The periodic arrangement of edge extensions yields full spin-polarization at the band extrema, and the accompanying ferromagnetic ground state can be driven into nonmagnetic or antiferromagnetic phases through external stimuli. Overall, our work reveals a precise tunability of the π-magnetism in graphene nanoribbons induced by naphtho groups, thereby establishing these one-dimensional architectures as suitable platforms for logic spintronics.

On-surface synthesis of graphene nanostructures with π-magnetism

Graphene nanostructures (GNs) including graphene nanoribbons and nanoflakes have attracted tremendous interest in the field of chemistry and materials science due to their fascinating electronic, optical and magnetic properties. Among them, zigzag-edged GNs (ZGNs) with precisely-tunable π-magnetism hold great potential for applications in spintronics and quantum devices. To improve the stability and processability of ZGNs, substitutional groups are often introduced to protect the reactive edges in organic synthesis, which renders the study of their intrinsic properties difficult. In contrast to the conventional wet-chemistry method, on-surface bottom-up synthesis presents a promising approach for the fabrication of both unsubstituted ZGNs and functionalized ZGNs with atomic precision via surface-catalyzed transformation of rationally-designed precursors. The structural and spin-polarized electronic properties of these ZGNs can then be characterized with sub-molecular resolution by means of scanning probe microscopy techniques. This review aims to highlight recent advances in the on-surface synthesis and characterization of a diversity of ZGNs with π-magnetism. We also discuss the important role of precursor design and reaction stimuli in the on-surface synthesis of ZGNs and their π-magnetism origin. Finally, we will highlight the existing challenges and future perspective surrounding the synthesis of novel open-shell ZGNs towards next-generation quantum technology.

Unravelling the Open-Shell Character of Peripentacene on Au(111)

Polycyclic aromatic hydrocarbons (PAHs) are a family of organic compounds comprising two or more fused aromatic rings which feature manifold applications in modern technology. Among these species, those presenting an open-shell magnetic ground state are of particular interest for organic electronic, spintronic, and non-linear optics and energy storage devices. Within PAHs, special attention has been devoted in recent years to the synthesis and study of the acene and fused acene (periacene) families, steered by their decreasing HOMO-LUMO gap with length and predicted open-shell character above some size. However, an experimental fingerprint of such magnetic ground state has remained elusive. Here, we report on the in-depth electronic characterization of isolated peripentacene molecules on a Au(111) surface. Scanning tunnelling spectroscopy, complemented by computational investigations, reveals an antiferromagnetic singlet ground state, characterized by singlet-triplet inelastic excitations with an experimental effective exchange coupling (J_eff) of 40.5 meV. Our results deepen the fundamental understanding of organic compounds with magnetic ground states, featuring perspectives in carbon-based spintronic devices.

Image of Dynamic Local Exchange Interactions in the dc Magnetoresistance of Spin-Polarized Current through a Dopant

We predict strong, dynamical effects in the dc magnetoresistance of current flowing from a spin-polarized electrical contact through a magnetic dopant in a nonmagnetic host. Using the stochastic Liouville formalism we calculate clearly defined resonances in the dc magnetoresistance when the applied magnetic field matches the exchange interaction with a nearby spin. At these resonances spin precession in the applied magnetic field is canceled by spin evolution in the exchange field, preserving a dynamic bottleneck for spin transport through the dopant. Similar features emerge when the dopant spin is coupled to nearby nuclei through the hyperfine interaction. These features provide a precise means of measuring exchange or hyperfine couplings between localized spins near a surface using spin-polarized scanning tunneling microscopy, without any ac electric or magnetic fields, even when the exchange or hyperfine energy is orders of magnitude smaller than the thermal energy.

A new view on the origin of zero-bias anomalies of Co atoms atop noble metal surfaces

Many-body phenomena are paramount in physics. In condensed matter, their hallmark is considerable on a wide range of material characteristics spanning electronic, magnetic, thermodynamic and transport properties. They potentially imprint non-trivial signatures in spectroscopic measurements, such as those assigned to Kondo, excitonic and polaronic features, whose emergence depends on the involved degrees of freedom. Here, we address systematically zero-bias anomalies detected by scanning tunneling spectroscopy on Co atoms deposited on Cu, Ag and Au(111) substrates, which remarkably are almost identical to those obtained from first-principles. These features originate from gaped spin-excitations induced by a finite magnetic anisotropy energy, in contrast to the usual widespread interpretation relating them to Kondo resonances. Resting on relativistic time-dependent density functional and many-body perturbation theories, we furthermore unveil a new many-body feature, the spinaron, resulting from the interaction of electrons and spin-excitations localizing electronic states in a well defined energy.