Tuning the Exchange Bias on a Single Atom from 1 mT to 10 T

A quantum sensor for atomic-scale electric and magnetic fields

The detection of faint magnetic fields from single-electron and nuclear spins at the atomic scale is a long-standing challenge in physics. While current mobile quantum sensors achieve single-electron spin sensitivity, atomic spatial resolution remains elusive for existing techniques. Here we fabricate a single-molecule quantum sensor at the apex of the metallic tip of a scanning tunnelling microscope by attaching Fe atoms and a PTCDA (3,4,9,10-perylenetetracarboxylic-dianhydride) molecule to the tip apex. We address the molecular spin by electron spin resonance and achieve ~100 neV resolution in energy. In a proof-of-principle experiment, we measure the magnetic and electric dipole fields emanating from a single Fe atom and an Ag dimer on an Ag(111) surface with sub-angstrom spatial resolution. Our method enables atomic-scale quantum sensing experiments of electric and magnetic fields on conducting surfaces and may find applications in the sensing of spin-labelled biomolecules and of spin textures in quantum materials.

Coherent spin dynamics between electron and nucleus within a single atom

The nuclear spin, being much more isolated from the environment than its electronic counterpart, presents opportunities for quantum experiments with prolonged coherence times. Electron spin resonance (ESR) combined with scanning tunnelling microscopy (STM) provides a bottom-up platform to study the fundamental properties of nuclear spins of single atoms on a surface. However, access to the time evolution of nuclear spins remained a challenge. Here, we present an experiment resolving the nanosecond coherent dynamics of a hyperfine-driven flip-flop interaction between the spin of an individual nucleus and that of an orbiting electron. We use the unique local controllability of the magnetic field emanating from the STM probe tip to bring the electron and nuclear spins in tune, as evidenced by a set of avoided level crossings in ESR-STM. Subsequently, we polarize both spins through scattering of tunnelling electrons and measure the resulting free evolution of the coupled spin system using a DC pump-probe scheme. The latter reveals a complex pattern of multiple interfering coherent oscillations, providing unique insight into hyperfine physics on a single atom level.

An Atomic-Scale Vector Network Analyzer

Electronic devices have been ever-shrinking toward atomic dimensions and have reached operation frequencies in the GHz range, thereby outperforming most conventional test equipment, such as vector network analyzers (VNA). Here the capabilities of a VNA on the atomic scale in a scanning tunneling microscope are implemented. Nonlinearities present in the voltage-current characteristic of atoms and nanostructures for phase-resolved microwave spectroscopy with unprecedented spatial resolution at GHz frequencies are exploited. The amplitude and phase response up to 9.3 GHz is determined, which permits accurate de-embedding of the transmission line and application of distortion-corrected waveforms in the tunnel junction itself. This enables quantitative characterization of the complex-valued admittance of individual magnetic iron atoms which show a lowpass response with a magnetic-field-tunable cutoff frequency.

Construction of topological quantum magnets from atomic spins on surfaces

Artificial quantum systems have emerged as platforms to realize topological matter in a well-controlled manner. So far, experiments have mostly explored non-interacting topological states, and the realization of many-body topological phases in solid-state platforms with atomic resolution has remained challenging. Here we construct topological quantum Heisenberg spin lattices by assembling spin chains and two-dimensional spin arrays from spin-1/2 Ti atoms on an insulating MgO film in a scanning tunnelling microscope. We engineer both topological and trivial phases of the quantum spin model and thereby realize first- and second-order topological quantum magnets. We probe the many-body excitations of the quantum magnets by single-atom electron spin resonance with an energy resolution better than 100 neV. Making use of the atomically localized magnetic field of the scanning tunnelling microscope tip, we visualize various many-body topological bound modes including topological edge states, topological defects and higher-order corner modes. Our results provide a bottom-up approach for the simulation of exotic quantum many-body phases of interacting spins.

An atomic-scale multi-qubit platform

Individual electron spins in solids are promising candidates for quantum science and technology, where bottom-up assembly of a quantum device with atomically precise couplings has long been envisioned. Here, we realized atom-by-atom construction, coherent operations, and readout of coupled electron-spin qubits using a scanning tunneling microscope. To enable the coherent control of "remote" qubits that are outside of the tunnel junction, we complemented each electron spin with a local magnetic field gradient from a nearby single-atom magnet. Readout was achieved by using a sensor qubit in the tunnel junction and implementing pulsed double electron spin resonance. Fast single-, two-, and three-qubit operations were thereby demonstrated in an all-electrical fashion. Our angstrom-scale qubit platform may enable quantum functionalities using electron spin arrays built atom by atom on a surface.

On-Surface Synthesis of Graphene Nanoribbons with Atomically Precise Structural Heterogeneities and On-Site Characterizations

Graphene nanoribbons (GNRs) are strips of graphene, with widths of a few nanometers, that are promising candidates for future applications in nanodevices and quantum information processing due to their highly tunable structure-dependent electronic, spintronic, topological, and optical properties. Implantation of periodic structural heterogeneities, such as heteroatoms, nanopores, and non-hexagonal rings, has become a powerful manner for tailoring the designer properties of GNRs. The bottom-up synthesis approach, by combining on-surface chemical reactions based on rationally designed molecular precursors and in situ tip-based microscopic and spectroscopic techniques, promotes the construction of atomically precise GNRs with periodic structural modulations. However, there are still obstacles and challenges lying on the way toward the understanding of the intrinsic structure-property relations, such as the strong screening and Fermi level pinning effect of the normally used transition metal substrates and the lack of collective tip-based techniques that can cover multi-internal degrees of freedom of the GNRs. In this Perspective, we briefly review the recent progress in the on-surface synthesis of GNRs with diverse structural heterogeneities and highlight the structure-property relations as characterized by the noncontact atomic force microscopy and scanning tunneling microscopy/spectroscopy. We furthermore motivate to deliver the need for developing strategies to achieve quasi-freestanding GNRs and for exploiting multifunctional tip-based techniques to collectively probe the intrinsic properties.

Influence of the Magnetic Tip on Heterodimers in Electron Spin Resonance Combined with Scanning Tunneling Microscopy

Investigating the quantum properties of individual spins adsorbed on surfaces by electron spin resonance combined with scanning tunneling microscopy (ESR-STM) has shown great potential for the development of quantum information technology on the atomic scale. A magnetic tip exhibiting high spin polarization is critical for performing an ESR-STM experiment. While the tip has been conventionally treated as providing a static magnetic field in ESR-STM, it was found that the tip can exhibit bistability, influencing ESR spectra. Ideally, the ESR splitting caused by the magnetic interaction between two spins on a surface should be independent of the tip. However, we found that the measured ESR splitting of a metal atom-molecule heterodimer can be tip-dependent. Detailed theoretical analysis reveals that this tip-dependent ESR splitting is caused by a different interaction energy between the tip and each spin of the heterodimer. Our work provides a comprehensive reference for characterizing tip features in ESR-STM experiments and highlights the importance of employing a proper physical model when describing the ESR tip, in particular, for heterospin systems.

Electric-Field-Driven Spin Resonance by On-Surface Exchange Coupling to a Single-Atom Magnet

Coherent control of individual atomic and molecular spins on surfaces has recently been demonstrated by using electron spin resonance (ESR) in a scanning tunneling microscope (STM). Here, a combined experimental and modeling study of the ESR of a single hydrogenated Ti atom that is exchange-coupled to a Fe adatom positioned 0.6-0.8 nm away by means of atom manipulation is presented. Continuous wave and pulsed ESR of the Ti spin show a Rabi rate with two contributions, one from the tip and the other from the Fe, whose spin interactions with Ti are modulated by the radio-frequency electric field. The Fe contribution is comparable to the tip, as revealed by its dominance when the tip is retracted, and tunable using a vector magnetic field. The new ESR scheme allows on-surface individual spins to be addressed and coherently controlled without the need for magnetic interaction with a tip. This study establishes a feasible implementation of spin-based multi-qubit systems on surfaces.

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.

Double-Resonance Spectroscopy of Coupled Electron Spins on a Surface

Scanning-tunneling microscopy (STM) combined with electron spin resonance (ESR) has enabled single-spin spectroscopy with nanoelectronvolt energy resolution and angstrom-scale spatial resolution, which allows quantum sensing and magnetic resonance imaging at the atomic scale. Extending this spectroscopic tool to a study of multiple spins, however, is nontrivial due to the extreme locality of the STM tunnel junction. Here we demonstrate double electron-electron spin resonance spectroscopy in an STM for two coupled atomic spins by simultaneously and independently driving them using two continuous-wave radio frequency voltages. We show the ability to drive and detect the resonance of a spin that is remote from the tunnel junction while read-out is achieved via the spin in the tunnel junction. Open quantum system simulations for two coupled spins reproduce all double-resonance spectra and further reveal a relaxation time of the remote spin that is longer by an order of magnitude than that of the local spin in the tunnel junction. Our technique can be applied to quantum-coherent multi-spin sensing, simulation, and manipulation in engineered spin structures on surfaces.

Single-Molecule Continuous-Wave Terahertz Rectification Spectroscopy and Microscopy

We report rectification spectroscopy (RS) for single molecules performed with continuous-wave terahertz (CW THz) radiation at the tunneling junction of a scanning tunneling microscope (STM) at 8 K. CW THz-RS serves as a new technique in single-molecule vibrational and magnetic excitation spectroscopy besides inelastic electron tunneling spectroscopy (IETS). By quantitatively studying IETS and THz RS, we show that CW THz induces a sinusoidal bias modulation with amplitude linearly dependent on the THz far-field amplitude. Such THz-induced bias modulation amplitude appears to be sensitive to the THz beam alignment but insensitive to variation in the tunneling gap far smaller than the THz wavelength.

ESR-STM on diamagnetic molecule: C60 on graphene

Electron Spin Resonance-Scanning Tunneling Microscopy (ESR-STM) of C₆₀ radical ion on graphene is a first demonstration of ESR-STM on diamagnetic molecules. ESR-STM signal at g_average=2.0±0.1 was measured in accordance with macroscopic ESR of C₆₀ radical ion. The ESR-STM signal was bias voltage dependent, as it reflects the charge state of the molecule. The signal appears in the bias voltage which enables the ionization of the lowest unoccupied molecular orbital (LUMO) - creation of radical anion, and the highest occupied molecular orbital (HOMO) - creation of a radical cation of the C₆₀ molecule when it deposited on graphene. In parallel, ESR-STM signal at g_average=1.7±0.1 was ascribed to Tungsten oxide (WO₃) at the tip apex. In several experiments, triplet spectrum was observed, and we ascribed their origin to zero-field splitting of doubly ionized C₁₂₀O^-2 dimer, as argued in previous ESR experiments of C₆₀ samples. Second possibility is hyperfine coupling with two ¹³C nuclei. In addition, we further validate the interference mechanism previously suggested for ESR-STM noise spectroscopy. The ability of ESR-STM to observe ESR of diamagnetic molecules in parallel with observing their electronic structure, provides a general single molecule identification technique.

Development of a scanning tunneling microscope for variable temperature electron spin resonance

Recent advances in improving the spectroscopic energy resolution in scanning tunneling microscopy (STM) have been achieved by integrating electron spin resonance (ESR) with STM. Here, we demonstrate the design and performance of a homebuilt STM capable of ESR at temperatures ranging from 1 to 10 K. The STM is incorporated with a homebuilt Joule-Thomson refrigerator and a two-axis vector magnet. Our STM design allows for the deposition of atoms and molecules directly into the cold STM, eliminating the need to extract the sample for deposition. In addition, we adopt two methods to apply radio-frequency (RF) voltages to the tunnel junction: the early design of wiring to the STM tip directly and a more recent idea to use an RF antenna. Direct comparisons of ESR results measured using the two methods and simulations of electric field distribution around the tunnel junction show that, despite their different designs and capacitive coupling to the tunnel junction, there is no discernible difference in the driving and detection of ESR. Furthermore, at a magnetic field of ∼1.6 T, we observe ESR signals (near 40 GHz) sustained up to 10 K, which is the highest temperature for ESR-STM measurement reported to date, to the best of our knowledge. Although the ESR intensity exponentially decreases with increasing temperature, our ESR-STM system with low noise at the tunnel junction allows us to measure weak ESR signals with intensities of a few fA. Our new design of an ESR-STM system, which is operational in a large frequency and temperature range, can broaden the use of ESR spectroscopy in STM and enable the simple modification of existing STM systems, which will hopefully accelerate a generalized use of ESR-STM.

Engineering the Crack Structure and Fracture Behavior in Monolayer MoS2 By Selective Creation of Point Defects

Monolayer transition-metal dichalcogenides, e.g., MoS₂ , typically have high intrinsic strength and Young's modulus, but low fracture toughness. Under high stress, brittle fracture occurs followed by cleavage along a preferential lattice direction, leading to catastrophic failure. Defects have been reported to modulate the fracture behavior, but pertinent atomic mechanism still remains elusive. Here, sulfur (S) and MoS_n point defects are selectively created in monolayer MoS₂ using helium- and gallium-ion-beam lithography, both of which reduce the stiffness of the monolayer, but enhance its fracture toughness. By monitoring the atomic structure of the cracks before and after the loading fracture, distinct atomic structures of the cracks and fracture behaviors are found in the two types of defect-containing monolayer MoS₂ . Combined with molecular dynamics simulations, the key role of individual S and MoS_n point defects is identified in the fracture process and the origin of the enhanced fracture toughness is elucidated. It is a synergistic effect of defect-induced deflection and bifurcation of cracks that enhance the energy release rate, and the formation of widen crack tip when fusing with point defects that prevents the crack propagation. The findings of this study provide insights into defect engineering and flexible device applications of monolayer MoS₂ .

Origin of Asymmetric Splitting of Kondo Peak in Spin-Polarized Scanning Tunneling Spectroscopy: Insights from First-Principles-Based Simulations

The spin-polarized scanning tunneling microscope (SP-STM) has served as a versatile tool for probing and manipulating the spintronic properties of atomic and molecular devices with high precision. The interplay between the local spin state and its surrounding magnetic environment significantly affects the transport behavior of the device. Particularly, in the contact regime, the strong hybridization between the SP-STM tip and the magnetic atom or molecule could give rise to unconventional Kondo resonance signatures in the differential conductance (dI/dV) spectra. This poses challenges for the simulation of a realistic tip control process. By combining the density functional theory and the hierarchical equations of motion methods, we achieve first-principles-based simulation of the control of a Ni-tip/Co/Cu(100) junction in both the tunneling and contact regimes. The calculated dI/dV spectra reproduce faithfully the experimental data. A cotunneling mechanism is proposed to elucidate the physical origin of the observed unconventional Kondo signatures.

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.

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.

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.

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.

Longitudinal and transverse electron paramagnetic resonance in a scanning tunneling microscope

Electron paramagnetic resonance (EPR) spectroscopy is widely used to characterize paramagnetic complexes. Recently, EPR combined with scanning tunneling microscopy (STM) achieved single-spin sensitivity with sub-angstrom spatial resolution. The excitation mechanism of EPR in STM, however, is broadly debated, raising concerns about widespread application of this technique. We present an extensive experimental study and modeling of EPR-STM of Fe and hydrogenated Ti atoms on a MgO surface. Our results support a piezoelectric coupling mechanism, in which the EPR species oscillate adiabatically in the inhomogeneous magnetic field of the STM tip. An analysis based on Bloch equations combined with atomic-multiplet calculations identifies different EPR driving forces. Specifically, transverse magnetic field gradients drive the spin-1/2 hydrogenated Ti, whereas longitudinal magnetic field gradients drive the spin-2 Fe. Also, our results highlight the potential of piezoelectric coupling to induce electric dipole moments, thereby broadening the scope of EPR-STM to nonpolar species and nonlinear excitation schemes.

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.

Exact Nonequilibrium Steady State of Open XXZ/XYZ Spin-1/2 Chain with Dirichlet Boundary Conditions

We investigate a dissipatively driven XYZ spin-1/2 chain in the Zeno limit of strong dissipation, described by the Lindblad master equation. The nonequilibrium steady state is expressed in terms of a matrix product ansatz using novel site-dependent Lax operators. The components of Lax operators satisfy a simple set of linear recurrence equations that generalize the defining algebraic relations of the quantum group U_{q}(sl_{2}). We reveal connection between the nonequilibrium steady state of the nonunitary dynamics and the respective integrable model with edge magnetic fields, described by coherent unitary dynamics.

Quantifying exchange forces of a spin spiral on the atomic scale

The large interest in chiral magnetic structures for realization of nanoscale magnetic storage or logic devices has necessitated methods which can quantify magnetic interactions at the atomic scale. To overcome the limitations of the typically used current-based sensing of atomic-scale exchange interactions, a force-based detection scheme is highly advantageous. Here, we quantify the atomic-scale exchange force field between a ferromagnetic tip and a cycloidal spin spiral using our developed combination of current and exchange force detection. Compared to the surprisingly weak spin polarization, the exchange force field is more sensitive to atomic-scale variations in the magnetization. First-principles calculations reveal that the measured atomic-scale variations in the exchange force originate from different contributions of direct and indirect (Zener type) exchange mechanisms, depending on the chemical tip termination. Our work opens the perspective of quantifying different exchange mechanisms of chiral magnetic structures with atomic-scale precision using 3D magnetic exchange force field measurements.

Tuning Single-Atom Electron Spin Resonance in a Vector Magnetic Field

Spin resonance of single spin centers bears great potential for chemical structure analysis, quantum sensing, and quantum coherent manipulation. Essential for these experiments is the presence of a two-level spin system whose energy splitting can be chosen by applying a magnetic field. In recent years, a combination of electron spin resonance (ESR) and scanning tunneling microscopy (STM) has been demonstrated as a technique to detect magnetic properties of single atoms on surfaces and to achieve sub-microelectronvolts energy resolution. Nevertheless, up to now the role of the required magnetic fields has not been elucidated. Here, we perform single-atom ESR on individual Fe atoms adsorbed on magnesium oxide (MgO) using a two-dimensional vector magnetic field as well as the local field of the magnetic STM tip in a commercially available STM. We show how the ESR amplitude can be greatly improved by optimizing the magnetic fields, revealing in particular an enhanced signal at large in-plane magnetic fields. Moreover, we demonstrate that the stray field from the magnetic STM tip is a versatile tool. We use it here to drive the electron spin more efficiently and to perform ESR measurements at constant frequency by employing tip-field sweeps. Lastly, we show that it is possible to perform ESR using only the tip field, under zero external magnetic field, which promises to make this technique available in many existing STM systems.