Quantifying the quantum nature of high-spin YSR excitations in transverse magnetic field

Excitations of individual and coupled spins on superconductors provide a platform to study quantum spin impurity models as well as a pathway toward realizing topological quantum computing. Here, we characterize, using ultralow temperature scanning tunneling microscopy/spectroscopy, the Yu-Shiba-Rusinov (YSR) states of individual manganese phthalocyanine molecules with high spin on an ultrathin lead film in variable transverse magnetic field. We observe two types of YSR excitations, depending on the adsorption geometry. Using a zero-bandwidth model, we detail the role of the magnetic anisotropy, spin-spin exchange, and Kondo exchange. We illustrate that one molecular type can be treated as an individual spin, whereas the other type is best described by a coupled spin system. Using the field dependence of the YSR excitations combined with modeling, we describe the quantum phase of each excitation type. These results provide an insight into the quantum nature of YSR excitations in magnetic field and a platform to study spin impurity models on superconductors in magnetic field.

Geometric Amplitude Accompanying Local Responses: Spinor Phase Information from the Amplitudes of Spin-Polarized STM Measurements

Solving the Hamiltonian of a system yields the energy dispersion and eigenstates. The geometric phase of the eigenstates generates many novel effects and potential applications. However, the geometric properties of the energy dispersion go unheeded. Here, we provide geometric insight into energy dispersion and introduce a geometric amplitude, namely, the geometric density of states (GDOS) determined by the Riemann curvature of the constant-energy contour. The geometric amplitude should accompany various local responses, which are generally formulated by the real-space Green's function. Under the stationary phase approximation, the GDOS simplifies the Green's function into its ultimate form. In particular, the amplitude factor embodies the spinor phase information of the eigenstates, favoring the extraction of the spin texture for topological surface states under an in-plane magnetic field through spin-polarized STM measurements. This work opens a new avenue for exploring the geometric properties of electronic structures and excavates the unexplored potential of spin-polarized STM measurements to probe the spinor phase information of eigenstates from their amplitudes.

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.

Ferromagnetism on an atom-thick & extended 2D metal-organic coordination network

Ferromagnetism is the collective alignment of atomic spins that retain a net magnetic moment below the Curie temperature, even in the absence of external magnetic fields. Reducing this fundamental property into strictly two-dimensions was proposed in metal-organic coordination networks, but thus far has eluded experimental realization. In this work, we demonstrate that extended, cooperative ferromagnetism is feasible in an atomically thin two-dimensional metal-organic coordination network, despite only ≈ 5% of the monolayer being composed of Fe atoms. The resulting ferromagnetic state exhibits an out-of-plane easy-axis square-like hysteresis loop with large coercive fields over 2 Tesla, significant magnetic anisotropy, and persists up to TC ≈ 35 K. These properties are driven by exchange interactions mainly mediated by the molecular linkers. Our findings resolve a two decade search for ferromagnetism in two-dimensional metal-organic coordination networks.

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.

A Non-Perturbative, Low-Noise Surface Coating for Sensitive Force-Gradient Detection of Electron Spin Resonance in Thin Films

The sensitivity of magnetic resonance force microscopy (MRFM) is limited by surface noise. Coating a thin-film polymer sample with metal has been shown to decrease, by orders of magnitude, sample-related force noise and frequency noise in MRFM experiments. Using both MRFM and inductively detected measurements of electron-spin resonance, we show that thermally evaporating a 12 nm gold layer on a 40 nm nitroxide-doped polystyrene film inactivates the nitroxide spin labels to a depth of 20 nm, making single-spin measurements difficult or impossible. We introduce a "laminated sample" protocol in which the gold layer is first evaporated on a sacrificial polymer. The sample is deposited on the room-temperature gold layer, removed using solvent lift-off, and placed manually on a coplanar waveguide. Electron spin resonance (ESR) of such a laminated sample was detected via MRFM at cryogenic temperatures using a high-compliance cantilever with an integrated 100-nm-scale cobalt tip. A 20-fold increase of spin signal was observed relative to a thin-film sample prepared instead with an evaporated metal coating. The observed signal is still somewhat smaller than expected, and we discuss possible remaining sources of signal loss.

Magnetic ground state of supported monatomic Fe chains from first principles

A new computational scheme is presented based on a combination of the conjugate gradient and the Newton-Raphson method to self-consistently minimize the energy within local spin-density functional theory, thus to identify the ground state magnetic order of a finite cluster of atoms. The applicability of the newab initiooptimization method is demonstrated for Fe chains deposited on different metallic substrates. The optimized magnetic ground states of the Fe chains on Rh(111) are analyzed in details and a good comparison is found with those obtained from an extended Heisenberg model containing first principles based interaction parameters. Moreover, the effect of the different bilinear spin-spin interactions in the formation of the magnetic ground states is monitored. In case of Fe chains on Nb(110) spin-spiral configurations with opposite rotational sense are found as compared to previous spin-model results which hints on the importance of higher order chiral interactions. The wavelength of the spin-spiral states of Fe chains on Re(0001) was obtained in good agreement with scanning tunneling microscopy experiments.

Slow Magnetic Relaxation of Dy Adatoms with In-Plane Magnetic Anisotropy on a Two-Dimensional Electron Gas

We report on the magnetic properties of Dy atoms adsorbed on the (001) surface of SrTiO3. X-ray magnetic circular dichroism reveals slow relaxation of the Dy magnetization on a time scale of about 800 s at 2.5 K, unusually associated with an easy-plane magnetic anisotropy. We attribute these properties to Dy atoms occupying hollow adsorption sites on the TiO2-terminated surface. Conversely, Ho atoms adsorbed on the same surface show paramagnetic behavior down to 2.5 K. With the help of atomic multiplet simulations and first-principles calculations, we establish that Dy populates also the top-O and bridge sites on the coexisting SrO-terminated surface. A simple magnetization relaxation model predicts these two sites to have an even longer magnetization lifetime than the hollow site. Moreover, the adsorption of Dy on the insulating SrTiO3 crystal leads, regardless of the surface termination, to the formation of a spin-polarized two-dimensional electron gas of Ti 3dxy character, together with an antiferromagnetic Dy-Ti coupling. Our findings support the feasibility of tuning the magnetic properties of the rare-earth atoms by acting on the substrate electronic gas with electric fields.

On-surface synthesis of Mn-phthalocyanines with optically active ligands

The synthesis of novel organic prototypes combining different functionalities is key to achieve operational elements for applications in organic electronics. Here we set the stage towards individually addressable magneto-optical transducers by the on-surface synthesis of optically active manganese-phthalocyanine derivatives (MnPc) obtained directly on a metallic substrate. We created these 2D nanostructures under ultra-high vacuum conditions with atomic precision starting from a simple phthalonitrile precursor with reversible photo-induced reactivity in solution. These precursors maintain their integrity after powder sublimation and coordinate with the Mn ions into tetrameric complexes and then transform into MnPcs on Ag(111) after a cyclotetramerization reaction. Using scanning tunnelling microscopy and spectroscopy together with DFT calculations, we identify the isomeric configuration of two bi-stable structures and show that it is possible to switch them reversibly by mechanical manipulation. Moreover, the robust magnetic moment brought by the central Mn ion provides a feasible pathway towards magneto-optical transducer fabrication. This work should trigger further research confirming such magneto-optical effects in MnPcs both on surfaces and in liquid environments.

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.

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.

A scanning tunneling microscope capable of electron spin resonance and pump-probe spectroscopy at mK temperature and in vector magnetic field

In the last decade, detecting spin dynamics at the atomic scale has been enabled by combining techniques such as electron spin resonance (ESR) or pump-probe spectroscopy with scanning tunneling microscopy (STM). Here, we demonstrate an ultra-high vacuum STM operational at milliKelvin (mK) temperatures and in a vector magnetic field capable of both ESR and pump-probe spectroscopy. By implementing GHz compatible cabling, we achieve appreciable RF amplitudes at the junction while maintaining the mK base temperature and high energy resolution. We demonstrate the successful operation of our setup by utilizing two experimental ESR modes (frequency sweep and magnetic field sweep) on an individual TiH molecule on MgO/Ag(100) and extract the effective g-factor. We trace the ESR transitions down to MHz into an unprecedented low frequency band enabled by the mK base temperature. We also implement an all-electrical pump-probe scheme based on waveform sequencing suited for studying dynamics down to the nanoseconds range. We benchmark our system by detecting the spin relaxation time T₁ of individual Fe atoms on MgO/Ag(100) and note a field strength and orientation dependent relaxation time.

Valence electrons in lanthanide-based single-atom magnets: a paradigm shift in 4f-magnetism modeling and design

Impact of valence electrons on the magnetic properties of lanthanide-based monatomic magnetic systems on surfaces and in molecules. And FV-magnetism - as a crucial bit in the further understanding and design of a new generation of atomic magnets.

Atomic-scale spin-polarization maps using functionalized superconducting probes

A scanning tunneling microscope (STM) with a magnetic tip that has a sufficiently strong spin polarization can be used to map the sample's spin structure down to the atomic scale but usually lacks the possibility to absolutely determine the value of the sample's spin polarization. Magnetic impurities in superconducting materials give rise to pairs of perfectly, i.e., 100%, spin-polarized subgap resonances. In this work, we functionalize the apex of a superconducting Nb STM tip with such impurity states by attaching Fe atoms to probe the spin polarization of atom-manipulated Mn nanomagnets on a Nb(110) surface. By comparison with spin-polarized STM measurements of the same nanomagnets using Cr bulk tips, we demonstrate an extraordinary spin sensitivity and the possibility to measure the sample's spin-polarization values close to the Fermi level quantitatively with our new functionalized probes.

Long-range focusing of magnetic bound states in superconducting lanthanum

Quantum mechanical systems with long-range interactions between quasiparticles provide a promising platform for coherent quantum information technology. Superconductors are a natural choice for solid-state based quantum devices, while magnetic impurities inside superconductors give rise to quasiparticle excitations of broken Cooper pairs that provide characteristic information about the host superconductor. Here, we reveal that magnetic impurities embedded below a superconducting La(0001) surface interact via quasiparticles extending to very large distances, up to several tens of nanometers. Using low-temperature scanning probe techniques, we observe the corresponding anisotropic and giant oscillations in the LDOS. Theoretical calculations indicate that the quasi-two-dimensional surface states with their strongly anisotropic Fermi surface play a crucial role for the focusing and long-range extension of the magnetic bound states. The quasiparticle focusing mechanism should facilitate the design of versatile magnetic structures with tunable and directed magnetic interactions over large distances, thereby paving the way toward the design of low-dimensional magnet-superconductor hybrid systems exhibiting topologically non-trivial quantum states as possible elements of quantum computation schemes based on Majorana quasiparticles.

Spin-orbit quantum impurity in a topological magnet

Quantum states induced by single-atomic impurities are at the frontier of physics and material science. While such states have been reported in high-temperature superconductors and dilute magnetic semiconductors, they are unexplored in topological magnets which can feature spin-orbit tunability. Here we use spin-polarized scanning tunneling microscopy/spectroscopy (STM/S) to study the engineered quantum impurity in a topological magnet Co3Sn2S2. We find that each substituted In impurity introduces a striking localized bound state. Our systematic magnetization-polarized probe reveals that this bound state is spin-down polarized, in lock with a negative orbital magnetization. Moreover, the magnetic bound states of neighboring impurities interact to form quantized orbitals, exhibiting an intriguing spin-orbit splitting, analogous to the splitting of the topological fermion line. Our work collectively demonstrates the strong spin-orbit effect of the single-atomic impurity at the quantum level, suggesting that a nonmagnetic impurity can introduce spin-orbit coupled magnetic resonance in topological magnets.

Minimally invasive spin sensing with scanning tunneling microscopy

Minimizing the invasiveness of scanning tunneling measurements is paramount for observation of the magnetic properties of unperturbed atomic-scale objects. We show that the invasiveness of STM inspection on few-atom spin systems can be drastically reduced by means of a remote detection scheme, which makes use of a sensor spin weakly coupled to the sensed object. By comparing direct and remote measurements we identify the relevant perturbations caused by the local probe. For direct inspection we find that tunneling electrons strongly perturb the investigated object even for currents as low as 3 pA. Electrons injected into the sensor spin induce perturbations with much reduced probability. The sensing scheme uses standard differential conductance measurements, and is decoupled both by its non-local nature, and by dynamic decoupling due to the significantly different time scales at which the sensor and sensed object evolve. The latter makes it possible to effectively remove static interactions between the sensed object and the spin sensor while still allowing the spin sensing. In this way we achieve measurements with a reduction in perturbative effects of up to 100 times relative to direct scanning tunneling measurements, which enables minimally invasive measurements of a few-atom magnet's fragile spin states with STM.

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.

Probing Weakly Hybridized Magnetic Molecules by Single-Atom Magnetometry

Advances in molecular spintronics rely on the in-depth characterization of the molecular building blocks in terms of their electronic and, more importantly, magnetic properties. For this purpose, inert substrates that interact only weakly with adsorbed molecules are required in order to preserve their electronic states. Here, we investigate the magnetic-field response of a single paramagnetic 5,5'-dibromosalophenatocobalt(II) (CoSal) molecule adsorbed on a weakly interacting magnetic substrate, namely, Fe-intercalated graphene (GR/Fe) grown on Ir(111), by using spin-polarized scanning tunneling microscopy and spectroscopy. We have obtained local magnetization curves, spin-dependent tunneling spectra, and spatial maps of magnetic asymmetry for a single CoSal molecule, revealing its magnetic properties and coupling to the local environment. The distinct magnetic behavior of the Co metal center is found to rely strictly on its position relative to the GR/Fe moiré structure, which determines the level of hybridization between the GR/Fe surface π-system and the molecular orbitals.

Observation of a Majorana zero mode in a topologically protected edge channel

Superconducting proximity pairing in helical edge modes, such as those of topological insulators, is predicted to provide a unique platform for realizing Majorana zero modes (MZMs). We used scanning tunneling microscopy measurements to probe the influence of proximity-induced superconductivity and magnetism on the helical hinge states of bismuth(111) films grown on a superconducting niobium substrate and decorated with magnetic iron clusters. Consistent with model calculations, our measurements revealed the emergence of a localized MZM at the interface between the superconducting helical edge channel and the iron clusters, with a strong magnetization component along the edge. Our experiments also resolve the MZM’s spin signature, which distinguishes it from trivial in-gap states that may accidentally occur at zero energy in a superconductor.

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

Shrinking spintronic devices to the nanoscale ultimately requires localized control of individual atomic magnetic moments. At these length scales, the exchange interaction plays important roles, such as in the stabilization of spin-quantization axes, the production of spin frustration, and creation of magnetic ordering. Here, we demonstrate the precise control of the exchange bias experienced by a single atom on a surface, covering an energy range of 4 orders of magnitude. The exchange interaction is continuously tunable from milli-eV to micro-eV by adjusting the separation between a spin-1/2 atom on a surface and the magnetic tip of a scanning tunneling microscope. We seamlessly combine inelastic electron tunneling spectroscopy and electron spin resonance to map out the different energy scales. This control of exchange bias over a wide span of energies provides versatile control of spin states, with applications ranging from precise tuning of quantum state properties, to strong exchange bias for local spin doping. In addition, we show that a time-varying exchange interaction generates a localized ac magnetic field that resonantly drives the surface spin. The static and dynamic control of the exchange interaction at the atomic scale provides a new tool to tune the quantum states of coupled-spin systems.

Antiferromagnetic MnNi tips for spin-polarized scanning probe microscopy

Spin-polarized scanning tunneling microscopy (SP-STM) measures magnetoresistance with atomic resolution. While various methods for achieving SP probes have been developed, each is limited with respect to fabrication, performance, and operating conditions. In this study, we present the fabrication and use of SP-STM tips made from commercially available antiferromagnetic Mn₈₈Ni₁₂ foils. The tips are intrinsically SP, which is attractive for exploring magnetic phenomena in the zero field limit. The tip material is relatively ductile, is straightforward to etch, and has a Néel temperature exceeding 300 K. We benchmark the topographic and spectroscopic performance of our tips and demonstrate their spin sensitivity by measuring the two-state switching of holmium single atom magnets on MgO/Ag(100).

Engineering of entanglement and spin state transfer via quantum chains of atomic spins at large separations

Several recent experiments have shown that long-range exchange interactions can determine collective magnetic ground states of nanostructures in bulk and on surfaces. The ability to generate and control entanglement in a system with long-range interaction will be of great importance for future quantum technology. An important step forward to reach this goal is the creation of entangled states for spins of distant magnetic atoms. Herein, the generation of long-distance entanglement between remote spins at large separations in bulk and on surface is studied theoretically, based on a quantum spin Hamiltonian and time-dependent Schrödinger equation for experimentally realized conditions. We demonstrate that long-distance entanglement can be generated between remote spins by using an appropriate quantum spin chain (a quantum mediator), composed by sets of antiferromagnetically coupled spin dimers. Ground state properties and quantum spin dynamics of entangled atoms are studied. We demonstrate that one can increase or suppress entanglement by adding a single spin in the mediator. The obtained result is explained by monogamy property of entanglement distribution inside a quantum spin system. We present a novel approach for non-local sensing of remote magnetic adatoms via spin entanglement.

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

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

Non-collinear spin states in bottom-up fabricated atomic chains

Non-collinear spin states with unique rotational sense, such as chiral spin-spirals, are recently heavily investigated because of advantages for future applications in spintronics and information technology and as potential hosts for Majorana Fermions when coupled to a superconductor. Tuning the properties of such spin states, e.g., the rotational period and sense, is a highly desirable yet difficult task. Here, we experimentally demonstrate the bottom-up assembly of a spin-spiral derived from a chain of iron atoms on a platinum substrate using the magnetic tip of a scanning tunneling microscope as a tool. We show that the spin-spiral is induced by the interplay of the Heisenberg and Dzyaloshinskii-Moriya components of the Ruderman-Kittel-Kasuya-Yosida interaction between the iron atoms. The relative strengths and signs of these two components can be adjusted by the interatomic iron distance, which enables tailoring of the rotational period and sense of the spin-spiral.

A chemist's overview of surface electron spins

This review summarizes recent research progress in the measurement and tuning of the electron spins of alien atoms and molecules adsorbed on well-defined substrates. After a brief introduction to the main experimental techniques employed to study surface electron spins, some well-explored systems consisting of atomic and molecular spin-carriers at surfaces are overviewed from a chemist's viewpoint, focusing on the experimental measurements and chemical modifications of the electron spin states of the alien entities at the surfaces on the atomic/molecular level. Finally, personal perspectives have been provided, aiming at describing some of the remaining issues that need to be addressed in the future and proposing potential applications in surface chemistry.

Design and performance of an ultra-high vacuum spin-polarized scanning tunneling microscope operating at 30 mK and in a vector magnetic field

We describe the design and performance of a scanning tunneling microscope (STM) that operates at a base temperature of 30 mK in a vector magnetic field. The cryogenics is based on an ultra-high vacuum (UHV) top-loading wet dilution refrigerator that contains a vector magnet allowing for fields up to 9 T perpendicular and 4 T parallel to the sample. The STM is placed in a multi-chamber UHV system, which allows in situ preparation and exchange of samples and tips. The entire system rests on a 150-ton concrete block suspended by pneumatic isolators, which is housed in an acoustically isolated and electromagnetically shielded laboratory optimized for extremely low noise scanning probe measurements. We demonstrate the overall performance by illustrating atomic resolution and quasiparticle interference imaging and detail the vibrational noise of both the laboratory and microscope. We also determine the electron temperature via measurement of the superconducting gap of Re(0001) and illustrate magnetic field-dependent measurements of the spin excitations of individual Fe atoms on Pt(111). Finally, we demonstrate spin resolution by imaging the magnetic structure of the Fe double layer on W(110).

Engineering the Eigenstates of Coupled Spin-1/2 Atoms on a Surface

Quantum spin networks having engineered geometries and interactions are eagerly pursued for quantum simulation and access to emergent quantum phenomena such as spin liquids. Spin-1/2 centers are particularly desirable, because they readily manifest coherent quantum fluctuations. Here we introduce a controllable spin-1/2 architecture consisting of titanium atoms on a magnesium oxide surface. We tailor the spin interactions by atomic-precision positioning using a scanning tunneling microscope (STM) and subsequently perform electron spin resonance on individual atoms to drive transitions into and out of quantum eigenstates of the coupled-spin system. Interactions between the atoms are mapped over a range of distances extending from highly anisotropic dipole coupling to strong exchange coupling. The local magnetic field of the magnetic STM tip serves to precisely tune the superposition states of a pair of spins. The precise control of the spin-spin interactions and ability to probe the states of the coupled-spin network by addressing individual spins will enable the exploration of quantum many-body systems based on networks of spin-1/2 atoms on surfaces.

Spin-Resolved Spectroscopy of the Yu-Shiba-Rusinov States of Individual Atoms

A magnetic atom in a superconducting host induces so-called Yu-Shiba-Rusinov (YSR) bound states inside the superconducting energy gap. By combining spin-resolved scanning tunneling spectroscopy with simulations we demonstrate that the pair of peaks associated with the YSR states of an individual Fe atom coupled to an oxygen-reconstructed Ta surface gets spin polarized in an external magnetic field. As theoretically predicted, the electron and hole parts of the YSR states have opposite signs of spin polarizations which keep their spin character when crossing the Fermi level through the quantum phase transition. The simulation of a YSR state right at the Fermi level reveals zero spin polarization which can be used to distinguish such states from Majorana zero modes in chains of YSR atoms.

Optically and Electrically Controllable Adatom Spin-orbital Dynamics in Transition Metal Dichalcogenides

We analyze the interplay of spin-valley coupling, orbital physics, and magnetic anisotropy taking place at single magnetic atoms adsorbed on semiconducting transition metal dichalcogenides, MX₂ (M = Mo, W; X = S, Se). Orbital selection rules turn out to govern the kinetic exchange coupling between the adatom and charge carriers in the MX₂ and lead to highly orbitally dependent spin-flip scattering rates, as we illustrate for the example of transition metal adatoms with d⁹ configuration. Our ab initio calculations suggest that d⁹ configurations are realizable by single Co, Rh, or Ir adatoms on MoS₂, which additionally exhibit a sizable magnetic anisotropy. We find that the interaction of the adatom with carriers in the MX₂ allows to tune its behavior from a quantum regime with full Kondo screening to a regime of "Ising spintronics" where its spin-orbital moment acts as classical bit, which can be erased and written electronically and optically.

A gateway towards non-collinear spin processing using three-atom magnets with strong substrate coupling

A cluster of a few magnetic atoms on the surface of a nonmagnetic substrate is one suitable realization of a bit for spin-based information technology. The prevalent approach to achieve magnetic stability is decoupling the cluster spin from substrate conduction electrons in order to suppress destabilizing spin-flips. However, this route entails less flexibility in tailoring the coupling between the bits needed for spin-processing. Here, we use a spin-resolved scanning tunneling microscope to write, read, and store spin information for hours in clusters of three atoms strongly coupled to a substrate featuring a cloud of non-collinearly polarized host atoms, a so-called non-collinear giant moment cluster. The giant moment cluster can be driven into a Kondo screened state by simply moving one of its atoms to a different site. Using the exceptional atomic tunability of the non-collinear substrate mediated Dzyaloshinskii–Moriya interaction, we propose a logical scheme for a four-state memory.

Information technology based on few atom magnets requires both long spin-energy relaxation times and flexible inter-bit coupling. Here, the authors show routes to manipulate information in three-atom clusters strongly coupled to substrate electrons by exploiting Dzyaloshinskii–Moriya interactions.

Recent trends in high spin sensitivity magnetic resonance

Magnetic resonance is a very powerful methodology that has been employed successfully in many applications for about 70years now, resulting in a wealth of scientific, technological, and diagnostic data. Despite its many advantages, one major drawback of magnetic resonance is its relatively poor sensitivity and, as a consequence, its bad spatial resolution when examining heterogeneous samples. Contemporary science and technology often make use of very small amounts of material and examine heterogeneity on a very small length scale, both of which are well beyond the current capabilities of conventional magnetic resonance. It is therefore very important to significantly improve both the sensitivity and the spatial resolution of magnetic resonance techniques. The quest for higher sensitivity led in recent years to the development of many alternative detection techniques that seem to rival and challenge the conventional "old-fashioned" induction-detection approach. The aim of this manuscript is to briefly review recent advances in the field, and to provide a quantitative as well as qualitative comparison between various detection methods with an eye to future potential advances and developments. We first offer a common definition of sensitivity in magnetic resonance to enable proper quantitative comparisons between various detection methods. Following that, up-to-date information about the sensitivity capabilities of the leading recently-developed detection approaches in magnetic resonance is provided, accompanied by a critical comparison between them and induction detection. Our conclusion from this comparison is that induction detection is still indispensable, and as such, it is very important to look for ways to significantly improve it. To do so, we provide expressions for the sensitivity of induction-detection, derived from both classical and quantum mechanics, that identify its main limiting factors. Examples from current literature, as well as a description of new ideas, show how these limiting factors can be mitigated to significantly improve the sensitivity of induction detection. Finally, we outline some directions for the possible applications of high-sensitivity induction detection in the field of electron spin resonance.

Nonlocally sensing the magnetic states of nanoscale antiferromagnets with an atomic spin sensor

The ability to sense the magnetic state of individual magnetic nano-objects is a key capability for powerful applications ranging from readout of ultradense magnetic memory to the measurement of spins in complex structures with nanometer precision. Magnetic nano-objects require extremely sensitive sensors and detection methods. We create an atomic spin sensor consisting of three Fe atoms and show that it can detect nanoscale antiferromagnets through minute, surface-mediated magnetic interaction. Coupling, even to an object with no net spin and having vanishing dipolar stray field, modifies the transition matrix element between two spin states of the Fe atom-based spin sensor that changes the sensor's spin relaxation time. The sensor can detect nanoscale antiferromagnets at up to a 3-nm distance and achieves an energy resolution of 10 μeV, surpassing the thermal limit of conventional scanning probe spectroscopy. This scheme permits simultaneous sensing of multiple antiferromagnets with a single-spin sensor integrated onto the surface.

Superlattice of Single Atom Magnets on Graphene

Regular arrays of single atoms with stable magnetization represent the ultimate limit of ultrahigh density storage media. Here we report a self-assembled superlattice of individual and noninteracting Dy atoms on graphene grown on Ir(111), with magnetic hysteresis up to 5.6 T and spin lifetime of 1000 s at 2.5 K. The observed magnetic stability is a consequence of the intrinsic low electron and phonon densities of graphene and the 6-fold symmetry of the adsorption site. Our array of single atom magnets has a density of 115 Tbit/inch², defined by the periodicity of the graphene moiré pattern.

Size-Dependent Ligand Quenching of Ferromagnetism in Co3(benzene)n+ Clusters Studied with X-ray Magnetic Circular Dichroism Spectroscopy

Cobalt-benzene cluster ions of the form Co₃(bz)_n⁺ (n = 0-3) were produced in the gas phase, mass-selected, and cooled in a cryogenic ion trap held at 3-4 K. To explore ligand effects on cluster magnetic moments, these species were investigated with X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) spectroscopy. XMCD spectra yield both the spin and orbital angular momenta of these clusters. Co₃⁺ has a spin magnetic moment of μ_S = 6 μ_B and an orbital magnetic moment of μ_L = 3 μ_B. Co₃(bz)⁺ and Co₃(bz)₂⁺ complexes were found to have spin and orbital magnetic moments identical to the values for ligand-free Co₃⁺. However, coordination of the third benzene to form Co₃(bz)₃⁺ completely quenches the high spin state of the system. Density functional theory calculations elucidate the spin states of the Co₃(bz)_n⁺ species as a function of the number of attached benzene ligands, explaining the transition from septet to singlet for n = 0 → 3.

Zero-Point Spin-Fluctuations of Single Adatoms

Stabilizing the magnetic signal of single adatoms is a crucial step toward their successful usage in widespread technological applications such as high-density magnetic data storage devices. The quantum mechanical nature of these tiny objects, however, introduces intrinsic zero-point spin-fluctuations that tend to destabilize the local magnetic moment of interest by dwindling the magnetic anisotropy potential barrier even at absolute zero temperature. Here, we elucidate the origins and quantify the effect of the fundamental ingredients determining the magnitude of the fluctuations, namely, the (i) local magnetic moment, (ii) spin-orbit coupling, and (iii) electron-hole Stoner excitations. Based on a systematic first-principles study of 3d and 4d adatoms, we demonstrate that the transverse contribution of the fluctuations is comparable in size to the magnetic moment itself, leading to a remarkable ≳50% reduction of the magnetic anisotropy energy. Our analysis gives rise to a comprehensible diagram relating the fluctuation magnitude to characteristic features of adatoms, providing practical guidelines for designing magnetically stable nanomagnets with minimal quantum fluctuations.

Magnetic remanence in single atoms

A permanent magnet retains a substantial fraction of its saturation magnetization in the absence of an external magnetic field. Realizing magnetic remanence in a single atom allows for storing and processing information in the smallest unit of matter. We show that individual holmium (Ho) atoms adsorbed on ultrathin MgO(100) layers on Ag(100) exhibit magnetic remanence up to a temperature of 30 kelvin and a relaxation time of 1500 seconds at 10 kelvin. This extraordinary stability is achieved by the realization of a symmetry-protected magnetic ground state and by decoupling the Ho spin from the underlying metal by a tunnel barrier.

Guiding Spin Spirals by Local Uniaxial Strain Relief

We report on the influence of uniaxial strain relief on the spin spiral state in the Fe double layer grown on Ir(111). Scanning tunneling microscopy (STM) measurements reveal areas with reconstruction lines resulting from uniaxial strain relief due to the lattice mismatch of Fe and Ir atoms, as well as pseudomorphic strained areas. Magnetic field-dependent spin-polarized STM measurements of the reconstructed Fe double layer reveal cycloidal spin spirals with a period on the nm scale. Globally, the spin spiral wave fronts are guided along symmetry-equivalent [112̅] crystallographic directions of the fcc(111) substrate. On an atomic scale the spin spiral propagation direction is linked to the [001] direction of the bcc(110)-like Fe, leading to a zigzag shaped wave front. The isotropically strained pseudomorphic areas also exhibit a preferred magnetic periodicity on the nm scale but no long-range order. We find that already for local strain relief with a single set of reconstruction lines a strict guiding of the spin spiral is realized.

Charging single Co atoms on ultrathin NaCl films

Single Co adatoms adsorbed on a double-layer NaCl film were negatively charged after applying a positive voltage pulse by STM.

Antiferromagnetic coupling between surface and bulk magnetization and anomalous magnetic transport in electro-deposited cobalt film

Correlation of morphology and structure and magnetization depth profiles of Co films grown by two different techniques, e.g. electrodeposition (S1) and sputtering (S2).

Sub-monolayer film growth of a volatile lanthanide complex on metallic surfaces

We deposited a volatile lanthanide complex, tris(2,2,6,6-tetramethyl-3,5-heptanedionato)terbium(III), onto metal surfaces of Cu(111), Ag(111) and Au(111) in vacuum and observed well-ordered sub-monolayer films with low temperature (5 K) scanning tunneling microscopy. The films show a distorted three-fold symmetry with a commensurate structure. Scanning tunneling spectroscopy reveals molecular orbitals delocalized on the ligands of the molecule. Our results imply that this complex can be transferred onto the metal substrates without molecular decomposition or contamination of the surface. This new rare-earth-based class of molecules broadens the choice of molecular magnets to study with scanning tunneling microscopy.

Origin of Perpendicular Magnetic Anisotropy and Large Orbital Moment in Fe Atoms on MgO

We report on the magnetic properties of individual Fe atoms deposited on MgO(100) thin films probed by x-ray magnetic circular dichroism and scanning tunneling spectroscopy. We show that the Fe atoms have strong perpendicular magnetic anisotropy with a zero-field splitting of 14.0±0.3  meV/atom. This is a factor of 10 larger than the interface anisotropy of epitaxial Fe layers on MgO and the largest value reported for Fe atoms adsorbed on surfaces. The interplay between the ligand field at the O adsorption sites and spin-orbit coupling is analyzed by density functional theory and multiplet calculations, providing a comprehensive model of the magnetic properties of Fe atoms in a low-symmetry bonding environment.

Tuning an Atomic Switch on a Surface with Electric and Magnetic Fields

Controllable switching an adatom position and its magnetization could lead to a single-atom memory. Our theoretical studies show that switching adatom between different surface sites by the quantum tunneling, discovered in several experiments, can be controlled by an external electric field. Switching a single spin by magnetic fields is found to be strongly site-dependent on a surface. This could enable to control a spin-dynamics of adatom.

Antiferromagnetic Spin Coupling between Rare Earth Adatoms and Iron Islands Probed by Spin-Polarized Tunneling

High-density magnetic storage or quantum computing could be achieved using small magnets with large magnetic anisotropy, a requirement that rare-earth iron alloys fulfill in bulk. This compelling property demands a thorough investigation of the magnetism in low dimensional rare-earth iron structures. Here, we report on the magnetic coupling between 4f single atoms and a 3d magnetic nanoisland. Thulium and lutetium adatoms deposited on iron monolayer islands pseudomorphically grown on W(110) have been investigated at low temperature with scanning tunneling microscopy and spectroscopy. The spin-polarized current indicates that both kind of adatoms have in-plane magnetic moments, which couple antiferromagnetically with their underlying iron islands. Our first-principles calculations explain the observed behavior, predicting an antiparallel coupling of the induced 5d electrons magnetic moment of the lanthanides with the 3d magnetic moment of iron, as well as their in-plane orientation, and pointing to a non-contribution of 4f electrons to the spin-polarized tunneling processes in rare earths.