Harnessing the Quantum Behavior of Spins on Surfaces

Probing Magnetism in Self-Assembled Organometallic Complexes Using Kondo Spectroscopy

Control of individual spins at the atomic level holds great promise for miniaturized spintronics, quantum sensing, and quantum information processing. Both single atomic and molecular spin centers are prime candidates for these applications and are often individually addressed and manipulated using scanning tunneling microscopy (STM). In this work, we present a hybrid approach and demonstrate a robust method for self-assembly of magnetic organometallic complexes consisting of individual iron (Fe) atoms and molecules on a silver substrate using STM. We employ two types of molecules, bis(dibenzoylmethane) copper(II) [Cu(dbm)2] and iron phthalocyanine (FePc). We show that in both cases, the Fe atoms preferentially attach underneath the benzene ring ligand of the molecules, effectively forming an organometallic half-sandwich arene complex, Fe(C6H6), which is akin to the properties of metallocenes. In both situations, a molecule can be combined with up to two Fe atoms. In addition, we observe a change in the magnetic properties of the attached Fe atoms in scanning tunneling spectroscopy, revealing a distinct Kondo signature at the Fe sites. We explain the latter using density functional theory calculations and find that the bond formation between the Fe 3d-orbitals and the benzene π-molecular orbitals creates a favorable situation for Kondo screening of the dxz- and dyz-like orbitals. Thus, this work establishes a reliable design principle for forming hybrid organometallic complexes and simultaneous tuning of their atomic spin states.

Structural Manipulation of Spin Excitations in a Molecular Junction

Single metallocene molecules act as sensitive spin detectors when decorating the probe of a scanning tunneling microscope (STM). However, the impact of the atomic-scale electrode details on the molecular spin state has remained elusive to date. Here, a nickelocene (Nc) STM junction is manipulated in an atomwise manner showing clearly the dependence of the spin excitation spectrum on the anchoring of Nc to Cu(111), a Cu monomer, and trimer. Moreover, while the spin state of the same Nc tip is a triplet with tunable spin excitation energies upon contacting the surface, it transitions to a Kondo-screened doublet on a Cu atom. Notably, the nontrivial magnetic exchange interaction of the molecular spin with the electron continuum of the substrate determines the spectral line shape of the spin excitations.

Theory of Electron Spin Resonance Spectroscopy in Scanning Tunneling Microscopy

The integration of scanning tunneling microscopy (STM) and electron spin resonance (ESR) spectroscopy has emerged as a powerful and innovative tool for discerning spin excitations and spin-spin interactions within atoms and molecules adsorbed on surfaces. However, the origin of the STM-ESR signal and the underlying mechanisms that govern the essential features of the measured spectra have remained elusive, thereby significantly impeding the future development of the STM-ESR approach. Here, we construct a model to carry out precise numerical simulations of STM-ESR spectra for a single hydrogenated Ti adatom and a hydrogenated Ti dimer, achieving excellent agreement with experimental observations. We further develop an analytic theory that elucidates the fundamental origin of the signal as well as the essential features in the measured spectra. These new theoretical developments establish a solid foundation for the on-demand detection and manipulation of atomic-scale spin states, with promising implications for cutting-edge applications in spin sensing, quantum information, and quantum computing.

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.

Roadmap on nanoscale magnetic resonance imaging

The field of nanoscale magnetic resonance imaging (NanoMRI) was started 30 years ago. It was motivated by the desire to image single molecules and molecular assemblies, such as proteins and virus particles, with near-atomic spatial resolution and on a length scale of 100 nm. Over the years, the NanoMRI field has also expanded to include the goal of useful high-resolution nuclear magnetic resonance (NMR) spectroscopy of molecules under ambient conditions, including samples up to the micron-scale. The realization of these goals requires the development of spin detection techniques that are many orders of magnitude more sensitive than conventional NMR and MRI, capable of detecting and controlling nanoscale ensembles of spins. Over the years, a number of different technical approaches to NanoMRI have emerged, each possessing a distinct set of capabilities for basic and applied areas of science. The goal of this roadmap article is to report the current state of the art in NanoMRI technologies, outline the areas where they are poised to have impact, identify the challenges that lie ahead, and propose methods to meet these challenges. This roadmap also shows how developments in NanoMRI techniques can lead to breakthroughs in emerging quantum science and technology applications.

Spin-Lattice Relaxation and Spin-Phonon Coupling of ns1 Metal Ions at the Surface

To use transition metal ions for spin-based applications, it is essential to understand fundamental contributions to electron spin relaxation in different ligand environments. For example, to serve as building blocks for a device, transition metal ion-based molecular qubits must be organized on surfaces and preserve long electron spin relaxation times, up to room temperature. Here we propose monovalent group 12 ions (Zn+ and Cd+) as potential electronic metal qubits with an ns1 ground state. The relaxation properties of Zn+ and Cd+, stabilized at the interface of porous aluminosilicates, are investigated and benchmarked against vanadium (3d1) and copper (3d9) ions. The spin-phonon coupling has been evaluated through DFT modeling and found to be negligible for the ns1 states, explaining the long coherence time, up to 2 μs, at room temperature. These so far unexplored metal qubits may represent viable candidates for room temperature quantum operations and sensing.

Electrically driven spin resonance of 4f electrons in a single atom on a surface

A pivotal challenge in quantum technologies lies in reconciling long coherence times with efficient manipulation of the quantum states of a system. Lanthanide atoms, with their well-localized 4f electrons, emerge as a promising solution to this dilemma if provided with a rational design for manipulation and detection. Here we construct tailored spin structures to perform electron spin resonance on a single lanthanide atom using a scanning tunneling microscope. A magnetically coupled structure made of an erbium and a titanium atom enables us to both drive the erbium's 4f electron spins and indirectly probe them through the titanium's 3d electrons. The erbium spin states exhibit an extended spin relaxation time and a higher driving efficiency compared to 3d atoms with spin ½ in similarly coupled structures. Our work provides a new approach to accessing highly protected spin states, enabling their coherent control in an all-electric fashion.

A continuous-wave and pulsed X-band electron spin resonance spectrometer operating in ultra-high vacuum for the study of low dimensional spin ensembles

We report the development of a continuous-wave and pulsed X-band electron spin resonance (ESR) spectrometer for the study of spins on ordered surfaces down to cryogenic temperatures. The spectrometer operates in ultra-high vacuum and utilizes a half-wavelength microstrip line resonator realized using epitaxially grown copper films on single crystal Al2O3 substrates. The one-dimensional microstrip line resonator exhibits a quality factor of more than 200 at room temperature, close to the upper limit determined by radiation losses. The surface characterizations of the copper strip of the resonator by atomic force microscopy, low-energy electron diffraction, and scanning tunneling microscopy show that the surface is atomically clean, flat, and single crystalline. Measuring the ESR spectrum at 15 K from a few nm thick molecular film of YPc2, we find a continuous-wave ESR sensitivity of 2.6 × 1011 spins/G · Hz1/2, indicating that a signal-to-noise ratio of 3.9 G · Hz1/2 is expected from a monolayer of YPc2 molecules. Advanced pulsed ESR experimental capabilities, including dynamical decoupling and electron-nuclear double resonance, are demonstrated using free radicals diluted in a glassy matrix.

Challenges for exploiting nanomagnet properties on surfaces

Molecular complexes with single-molecule magnet (SMM) or qubit properties, commonly called molecular nanomagnets, are great candidates for information storage or quantum information processing technologies. However, the implementation of molecular nanomagnets in devices for the above-mentioned applications requires controlled surface deposition and addressing the nanomagnets' properties on the surface. This Perspectives paper gives a brief overview of molecular properties on a surface relevant for magnetic molecules and how they are affected when the molecules interact with a surface; then, we focus on systems of increasing complexity, where the relevant SMMs and qubit properties have been observed for the molecules deposited on surfaces; finally, future perspectives, including possible ways of overcoming the problems encountered so far are discussed.

Nanoscale Magnets Embedded in a Microstrip

Nanoscale magnetic resonance imaging (NanoMRI) is an active area of applied research with potential applications in structural biology and quantum engineering. The success of this technological vision hinges on improving the instrument's sensitivity and functionality. A particular challenge is the optimization of the magnetic field gradient required for spatial encoding and of the radio frequency field used for spin control, in analogy to the components used in clinical MRI. In this work, we present the fabrication and characterization of a magnet-in-microstrip device that yields a compact form factor for both elements. We find that our design leads to a number of advantages, among them a 4-fold increase of the magnetic field gradient compared to those achieved with traditional fabrication methods. Our results can be useful for boosting the efficiency of a variety of different experimental arrangements and detection principles in the field of NanoMRI.

Single-molecule electron spin resonance by means of atomic force microscopy

Understanding and controlling decoherence in open quantum systems is of fundamental interest in science, whereas achieving long coherence times is critical for quantum information processing1. Although great progress was made for individual systems, and electron spin resonance (ESR) of single spins with nanoscale resolution has been demonstrated2-4, the understanding of decoherence in many complex solid-state quantum systems requires ultimately controlling the environment down to atomic scales, as potentially enabled by scanning probe microscopy with its atomic and molecular characterization and manipulation capabilities. Consequently, the recent implementation of ESR in scanning tunnelling microscopy5-8 represents a milestone towards this goal and was quickly followed by the demonstration of coherent oscillations9,10 and access to nuclear spins11 with real-space atomic resolution. Atomic manipulation even fuelled the ambition to realize the first artificial atomic-scale quantum devices12. However, the current-based sensing inherent to this method limits coherence times12,13. Here we demonstrate pump-probe ESR atomic force microscopy (AFM) detection of electron spin transitions between non-equilibrium triplet states of individual pentacene molecules. Spectra of these transitions exhibit sub-nanoelectronvolt spectral resolution, allowing local discrimination of molecules that only differ in their isotopic configuration. Furthermore, the electron spins can be coherently manipulated over tens of microseconds. We anticipate that single-molecule ESR-AFM can be combined with atomic manipulation and characterization and thereby paves the way to learn about the atomistic origins of decoherence in atomically well-defined quantum elements and for fundamental quantum-sensing experiments.

Electric control of spin transitions at the atomic scale

Electric control of spins has been a longstanding goal in the field of solid state physics due to the potential for increased efficiency in information processing. This efficiency can be optimized by transferring spintronics to the atomic scale. We present electric control of spin resonance transitions in single TiH molecules by employing electron spin resonance scanning tunneling microscopy (ESR-STM). We find strong bias voltage dependent shifts in the ESR signal of about ten times its line width. We attribute this to the electric field in the tunnel junction, which induces a displacement of the spin system changing the g-factor and the effective magnetic field of the tip. We demonstrate direct electric control of the spin transitions in coupled TiH dimers. Our findings open up new avenues for fast coherent control of coupled spin systems and expands on the understanding of spin electric coupling.

Entanglement Degradation in Two Interacting Qubits Coupled to Dephasing Environments

One of the main obstacles toward building efficient quantum computing systems is decoherence, where the inevitable interaction between the qubits and the surrounding environment leads to a vanishing entanglement. We consider a system of two interacting asymmetric two-level atoms (qubits) in the presence of pure and correlated dephasing environments. We study the dynamics of entanglement while varying the interaction strength between the two qubits, their relative frequencies, and their coupling strength to the environment starting from different initial states of practical interest. The impact of the asymmetry of the two qubits, reflected in their different frequencies and coupling strengths to the environment, varies significantly depending on the initial state of the system and its degree of anisotropy. For an initial disentangled, or a Werner, state, as the difference between the frequencies increases, the entanglement decay rate increases, with more persistence at the higher degrees of anisotropy in the former state. However, for an initial anti-correlated Bell state, the entanglement decays more rapidly in the symmetric case compared with the asymmetric one. The difference in the coupling strengths of the two qubits to the pure (uncorrelated) dephasing environment leads to higher entanglement decay in the different initial state cases, though the rate varies depending on the degree of anisotropy and the initial state. Interestingly, the correlated dephasing environment, within a certain range, was found to enhance the entanglement dynamics starting from certain initial states, such as the disentangled, anti-correlated Bell, and Werner, whereas it exhibits a decaying effect in other cases such as the initial correlated Bell state.

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.

Anisotropic Hyperfine Interaction of Surface-Adsorbed Single Atoms

Hyperfine interactions have been widely used in material science, organic chemistry, and structural biology as a sensitive probe to local chemical environments. However, traditional ensemble measurements of hyperfine interactions average over a macroscopic number of spins with different geometrical locations and nuclear isotopes. Here, we use a scanning tunneling microscope (STM) combined with electron spin resonance (ESR) to measure hyperfine spectra of hydrogenated-Ti on MgO/Ag(100) at low-symmetry binding sites and thereby determine the isotropic and anisotropic hyperfine interactions at the single-atom level. Combining vector-field ESR spectroscopy with STM-based atom manipulation, we characterize the full hyperfine tensors of ⁴⁷Ti and ⁴⁹Ti and identify significant spatial anisotropy of the hyperfine interactions for both isotopes. Density functional theory calculations reveal that the large hyperfine anisotropy arises from highly anisotropic distributions of the ground-state electron spin density. Our work highlights the power of ESR-STM-enabled single-atom hyperfine spectroscopy in revealing electronic ground states and atomic-scale chemical environments.

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.