Spin torque-driven electron paramagnetic resonance of a single spin in a pentacene molecule

Control over quantum systems is typically achieved by time-dependent electric or magnetic fields. Alternatively, electronic spins can be controlled by spin-polarized currents. Here, we demonstrate coherent driving of a single spin by a radiofrequency spin-polarized current injected from the tip of a scanning tunneling microscope into an organic molecule. With the excitation of electron paramagnetic resonance, we established dynamic control of single spins by spin torque using a local electric current. In addition, our work highlights the dissipative action of the spin-transfer torque, in contrast to the nondissipative action of the magnetic field, which allows for the manipulation of individual spins based on controlled decoherence.

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.

Stochastic Syncing in Sinusoidally Driven Atomic Orbital Memory

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

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

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

Valence Orbitals Driving the Spin Dynamics in a Rare-Earth Single-Atom Magnet

We combine spin-polarized scanning tunneling microscopy with quantum master equation analysis to investigate the spin dynamics of the single atom magnet Dy on graphene/Ir(111). By performing reading and writing experiments, we show that the strongly spin polarized 5d6s valence shells, as well as their intra-atomic exchange coupling to the 4f shell, determine the pathways for magnetization relaxation and thus the spin dynamics. The good quantum number that determines which states are stable and which mechanisms for reversal exist in a given crystal field is the atomic total angular momentum J_{z}^{tot} and not the commonly considered J_{z}^{4f} of the 4f shell only.

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

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

Atomic-Scale Photon Mapping Revealing Spin-Current Relaxation

A nanoscopic understanding of spin-current dynamics is crucial for controlling the spin transport in materials. However, gaining access to spin-current dynamics at an atomic scale is challenging. Therefore, we developed spin-polarized scanning tunneling luminescence spectroscopy (SP STLS) to visualize the spin relaxation strength depending on spin injection positions. Atomically resolved SP STLS mapping of gallium arsenide demonstrated a stronger spin relaxation in gallium atomic rows. Hence, SP STLS paves the way for visualizing spin current with single-atom precision.

Gating Orbital Memory with an Atomic Donor

Orbital memory is defined by two stable valencies that can be electrically switched and read out. To explore the influence of an electric field on orbital memory, we studied the distance-dependent influence of an atomic Cu donor on the state favorability of an individual Co atom on black phosphorus. Using low temperature scanning tunneling microscopy and spectroscopy, we characterized the electronic properties of individual Cu donors, corroborating this behavior with ab initio calculations based on density functional theory. We studied the influence of an individual donor on the charging energy and stochastic behavior of an individual Co atom. We found a strong impact on the state favorability in the stochastic limit. These findings provide quantitative information about the influence of local electric fields on atomic orbital memory.

Anomalous excitations of atomically crafted quantum magnets

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

Engineering atomic-scale magnetic fields by dysprosium single atom magnets

Atomic scale engineering of magnetic fields is a key ingredient for miniaturizing quantum devices and precision control of quantum systems. This requires a unique combination of magnetic stability and spin-manipulation capabilities. Surface-supported single atom magnets offer such possibilities, where long temporal and thermal stability of the magnetic states can be achieved by maximizing the magnet/ic anisotropy energy (MAE) and by minimizing quantum tunnelling of the magnetization. Here, we show that dysprosium (Dy) atoms on magnesium oxide (MgO) have a giant MAE of 250 meV, currently the highest among all surface spins. Using a variety of scanning tunnelling microscopy (STM) techniques including single atom electron spin resonance (ESR), we confirm no spontaneous spin-switching in Dy over days at ≈ 1 K under low and even vanishing magnetic field. We utilize these robust Dy single atom magnets to engineer magnetic nanostructures, demonstrating unique control of magnetic fields with atomic scale tunability.

A Molecular Drone for Atomic-Scale Fabrication Working under Ambient Conditions

The direct manipulation of individual atoms has led to the advancement of exciting cutting-edge technologies in sub-nanometric fabrication, information storage and to the exploration of quantum technologies. Atom manipulation is currently performed by scanning probe microscopy (SPM), which enables an extraordinary spatial control, but provides a low throughput, requiring complex critical experimental conditions and advanced instrumentation. Here, a new paradigm is demonstrated for surface atom manipulation that overcomes the limitations of SPM techniques by replacing the SPM probe with a coordination compound that exploits surface atom complexation as a tool for atomic-scale fabrication. The coordination compound works as a "molecular drone": it lands onto a substrate, bonds to a specific atom on the surface, picks it up, and then leaves the surface along with the extracted atom, thus creating an atomic vacancy in a specific position on the surface. Remarkably, the feasibility of the process is demonstrated under electrochemical control and the stability of the fabricated pattern at room temperature, under ambient conditions.

An atomic Boltzmann machine capable of self-adaption

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

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.

Phase-shift control of the exchange coupling between magnetic impurities

The control of magnetic interactions is one of the most relevant topics in spintronics. In this work, we propose to use electric potential barriers for tuning or even suppressing the RKKY exchange coupling between magnetic impurities in a two-dimensional electron gas. Our results show that it is possible to manipulate both the magnitude and sign of the RKKY coupling. Systems with two and three impurities are studied. In the last case, the use of two potential barriers can be employed to decouple one of the impurities to the rest. The possibility to control the interactions between magnetic atoms individually may have applications in neuromorphic and quantum computing.

Probing Magnetism in Artificial Metal-Organic Complexes Using Electronic Spin Relaxometry

Single spins are considered as a versatile candidate for miniaturizing information devices down to the nanoscale. To engineer the spin's properties, metal-organic frameworks provide a promising route which in turn requires thorough understanding of the metal-molecule interaction. Here, we investigate the magnetic robustness of a single iron (Fe) atom in artificially built Fe-tetracyanoethylene (TCNE) complexes by using low-temperature scanning tunneling microscopy (STM). We find that the magnetic anisotropy and spin relaxation dynamics of the Fe atom within the complexes remain unperturbed in comparison to well-isolated Fe atoms. Density functional theory (DFT) calculations support our experimental findings, suggesting that the 3d orbitals of the Fe atom remain largely undisturbed while the 4s and 4p orbitals are rearranged in the process of forming a complex. To precisely determine the location of the spin center within the complex, we utilize STM-based spin relaxometry, mapping out the spatial dependence of spin relaxation with subnanometer resolution. Our work suggests that the magnetic properties of atoms can remain unchanged while being embedded in a weakly bound molecular framework.

Magnetism manipulation of Co n -adsorbed monolayer WS2 through charge injection

The design and manipulation of magnetism in low-dimensional systems are desirable for the development of spin electronic devices. Here, we design two kinds of Co-adsorbed monolayer WS₂ frameworks, i.e. Co₁/WS₂ and Co₂/WS₂, and comprehensively explore the dependences of their magnetic properties on injected charge by using first-principles calculations. The value of magnetic moment can be tuned almost linearly through injecting charge due to the modulated interaction and charge transferring between Co atom and monolayer WS₂. A transition from ferromagnetism to non-ferromagnetism occurs in Co₁/WS₂ system when 1 e/unit cell charge is injected. Furthermore, the magnetic anisotropy can be manipulated by injecting charge as well. The magnetic anisotropy energy (MAE) in Co₁/WS₂ system sharply increases from -4.16 to 2.47 (0.99) meV when injected charge vary from 0.0 to 0.2 (-0.2) e/unit cell, meaning a transition of the magnetic easy axis from in-plane to out-of-plane direction. Similarly, in Co₂/WS₂ system, the magnetic easy axis also can be modified to out-of-plane direction through injecting 0.1 e/unit cell charge. It is found that the changes of Co-3d states are responsible for the tunable magnetic anisotropy. This work provides a theoretical understanding on effective manipulation of magnetism in low-dimensional system.

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.

Piezotronic Tunneling Junction Gated by Mechanical Stimuli

Tunneling junction is used in many devices such as high-frequency oscillators, nonvolatile memories, and magnetic field sensors. In these devices, modulation on the barrier width and/or height is usually realized by electric field or magnetic field. Here, a new piezotronic tunneling junction (PTJ) principle, in which the quantum tunneling is controlled/tuned by externally applied mechanical stimuli, is proposed. In these metal/insulator/piezoelectric semiconductor PTJs, such as Pt/Al₂ O₃ /p-GaN, the height and the width of the tunneling barriers can be mechanically modulated via the piezotronic effect. The tunneling current characteristics of PTJs exhibit critical behavior as a function of external mechanical stimuli, which results in high sensitivity (≈5.59 mV MPa^-1 ), giant switching (>10⁵ ), and fast response (≈4.38 ms). Moreover, the mechanical controlling of tunneling transport in PTJs with various thickness of Al₂ O₃ is systematically investigated. The high performance observed with these metal/insulator/piezoelectric semiconductor PTJs suggest their great potential in electromechanical technology. This study not only demonstrates dynamic mechanical controlling of quantum tunneling, but also paves a way for adaptive interaction between quantum tunneling and mechanical stimuli, with potential applications in the field of ultrasensitive press sensor, human-machine interface, and artificial intelligence.

A radio-frequency spin-polarized scanning tunneling microscope

A scanning tunneling microscope for spin-resolved studies of dynamic systems is presented. The cryogenic setup allows the scanning tunneling microscope to achieve a cutoff frequency beyond 26 GHz at the tunnel junction and to be operable at temperatures of 1.1 K-100 K in a magnetic field of up to 3 T. For this purpose, the microscope and its wiring as well as the associated cryostat system were specially designed and manufactured. For sample preparation, an ultrahigh vacuum system was developed, which is equipped with modular preparation platforms. Measurements showing the characteristics of the scanning tunneling microscope in the time and frequency domain are presented. As a proof of concept, experimental data of the Pd/Fe/Ir(111) sample system at 95 K in a magnetic field of 3 T are presented.

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.

Stabilizing spin systems via symmetrically tailored RKKY interactions

Spins of single atoms adsorbed on substrates are promising building blocks for spintronics and quantum computation schemes. To process spin information and for increased magnetic stability, these spins have to be coupled to arrays. For a single atom, a high symmetry of the environment increases its spin stability. However, little is known about the role of the symmetry of the magnetic couplings in the arrays. Here, we study arrays of atomic spins coupled via Ruderman−Kittel−Kasuya−Yosida interaction, focusing on Dzyaloshinskii−Moriya and symmetric anisotropic exchange. We show that the high spin stability of a trimer can be remotely detected by a nearby atom, and how the Dzyaloshinskii−Moriya interaction leads to its destabilization. Adding more nearby atoms further destabilizes the trimer, due to a non-local effective transverse anisotropy originating in the symmetric anisotropic exchange. This transverse anisotropy can be quenched for highly symmetric structures, where the spin lifetime of the array increases drastically.

Exploration of the atomic spin interactions promises next generation information technologies. Here the authors show the observation and understanding of the Dzyaloshinskii−Moriya and symmetric anisotropic exchange interactions controlled spin dynamics and stability in Fe cluster-adatom complexes on Pt surfaces.

Winding Up Quantum Spin Helices: How Avoided Level Crossings Exile Classical Topological Protection

A magnetic helix can be wound into a classical Heisenberg chain by fixing one end while rotating the other one. We show that in quantum Heisenberg chains of finite length, the magnetization slips back to the trivial state beyond a finite turning angle. Avoided level crossings thus undermine classical topological protection. Yet, for special values of the axial Heisenberg anisotropy, stable spin helices form again, which are nonlocally entangled. Away from these sweet spots, spin helices can be stabilized dynamically or by dissipation. For half-integer spin chains of odd length, a spin slippage state and its Kramers partner define a qubit with a nontrivial Berry connection.

Upgrade of a low-temperature scanning tunneling microscope for electron-spin resonance

Electron spin resonance with a scanning tunneling microscope (ESR-STM) combines the high energy resolution of spin resonance spectroscopy with the atomic scale control and spatial resolution of STM. Here we describe the upgrade of a helium-3 STM with a 2D vector-field magnet (B_z = 8.0 T, B_x = 0.8 T) to an ESR-STM. The system is capable of delivering radio frequency (RF) power to the tunnel junction at frequencies up to 30 GHz. We demonstrate magnetic field-sweep ESR for the model system TiH/MgO/Ag(100) and find a magnetic moment of (1.004 ± 0.001) μ_B. Our upgrade enables to toggle between a DC mode, where the STM is operated with the regular control electronics, and an ultrafast-pulsed mode that uses an arbitrary waveform generator for pump-probe spectroscopy or reading of spin-states. Both modes allow for simultaneous radiofrequency excitation, which we add via a resistive pick-off tee to the bias voltage path. The RF cabling from room temperature to the 350 mK stage has an average attenuation of 18 dB between 5 and 25 GHz. The cable segment between the 350 mK stage and the STM tip presently attenuates an additional 34_-3 ⁺⁵ dB from 10 to 26 GHz and 38_-2 ⁺³ dB between 20 and 30 GHz. We discuss our transmission losses and indicate ways to reduce this attenuation. We finally demonstrate how to synchronize the arrival times of RF and DC pulses coming from different paths to the STM junction, a prerequisite for future pulsed ESR experiments.

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).

Enhanced quantum coherence in exchange coupled spins via singlet-triplet transitions

Manipulation of spin states at the single-atom scale underlies spin-based quantum information processing and spintronic devices. These applications require protection of the spin states against quantum decoherence due to interactions with the environment. While a single spin is easily disrupted, a coupled-spin system can resist decoherence by using a subspace of states that is immune to magnetic field fluctuations. Here, we engineered the magnetic interactions between the electron spins of two spin-1/2 atoms to create a "clock transition" and thus enhance their spin coherence. To construct and electrically access the desired spin structures, we use atom manipulation combined with electron spin resonance (ESR) in a scanning tunneling microscope. We show that a two-level system composed of a singlet state and a triplet state is insensitive to local and global magnetic field noise, resulting in much longer spin coherence times compared with individual atoms. Moreover, the spin decoherence resulting from the interaction with tunneling electrons is markedly reduced by a homodyne readout of ESR. These results demonstrate that atomically precise spin structures can be designed and assembled to yield enhanced quantum coherence.

Assembling fullerene into nanostructures over micrometer scale with atomic precision

Assembling large organic molecules into predesigned structures for nanoscale devices is a long-standing challenge. Here, we present the atom-scale precise repositions of individual fullerene molecules and molecule transportation over the micrometer scale on a Si(111) surface via reproducible and reversible vertical manipulation by a scanning tunneling microscopy tip. A two-rod abacus consisting of ten fullerene molecules was used to perform arithmetic operations with double digits. This opens the door for the use of larger organic molecules displaying intrinsic characteristics as complex molecular devices with novel functions.

An orbitally derived single-atom magnetic memory

A magnetic atom epitomizes the scaling limit for magnetic information storage. Individual atomic spins have recently exhibited magnetic remanence, a requirement for magnetic memory. However, such memory has been only realized on thin insulating surfaces, removing potential tunability via electronic gating or exchange-driven magnetic coupling. Here, we show a previously unobserved mechanism for single-atom magnetic storage based on bistability in the orbital population, or so-called valency, of an individual Co atom on semiconducting black phosphorus (BP). Ab initio calculations reveal that distance-dependent screening from the BP surface stabilizes the two distinct valencies, each with a unique orbital population, total magnetic moment, and spatial charge density. Excellent correspondence between the measured and predicted charge densities reveal that such orbital configurations can be accessed and manipulated without a spin-sensitive readout mechanism. This orbital memory derives stability from the energetic barrier to atomic relaxation, demonstrating the potential for high-temperature single-atom information storage.

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.

Electronically Mediated Magnetic Anisotropy in Vibrating Magnetic Molecules

We address the electronically induced anisotropy field acting on a spin moment in a vibrating magnetic molecule located in the junction between ferromagnetic metals. Under weak coupling between the electrons and molecular vibrations, the nature of the anisotropy can be changed from favoring a high spin (easy-axis) magnetic moment to a low spin (easy plane) by applying a temperature difference or a voltage bias across the junction. For unequal spin polarizations in ferromagnetic metals, it is shown that the character of the anisotropy is essentially determined by the properties of the weaker ferromagnet. By increasing the temperature in this metal or introducing a voltage bias, its influence can be suppressed such that the dominant contribution to the anisotropy is interchanged to the stronger ferromagnet. With increasing coupling strength between the molecular vibrations and the electrons, the nature of the anisotropy is locked into favoring easy-plane magnetism.

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.

Multispeed Prethermalization in Quantum Spin Models with Power-Law Decaying Interactions

The relaxation of uniform quantum systems with finite-range interactions after a quench is generically driven by the ballistic propagation of long-lived quasiparticle excitations triggered by a sufficiently small quench. Here we investigate the case of long-range (1/r^{α}) interactions for a d-dimensional lattice spin model with uniaxial symmetry, and show that, in the regime d<α<d+2, the entanglement and correlation buildup is radically altered by the existence of a nonlinear dispersion relation of quasiparticles, ω∼k^{z<1}, at small wave vectors, leading to a divergence of the quasiparticle group velocity and superballistic propagation. This translates in a superlinear growth of correlation fronts with time and sublinear growth of relaxation times of subsystem observables with size when focusing on k=0 fluctuations. Yet the large dispersion in group velocities leads to an extreme wavelength dependence of relaxation times of finite-k fluctuations, with entanglement being susceptible to all of them. Our predictions are directly relevant to current experiments probing the nonequilibrium dynamics of trapped ions, or ultracold magnetic and Rydberg atoms in optical lattices.

Probing quantum coherence in single-atom electron spin resonance

Spin resonance of individual spin centers allows applications ranging from quantum information technology to atomic-scale magnetometry. To protect the quantum properties of a spin, control over its local environment, including energy relaxation and decoherence processes, is crucial. However, in most existing architectures, the environment remains fixed by the crystal structure and electrical contacts. Recently, spin-polarized scanning tunneling microscopy (STM), in combination with electron spin resonance (ESR), allowed the study of single adatoms and inter-atomic coupling with an unprecedented combination of spatial and energy resolution. We elucidate and control the interplay of an Fe single spin with its atomic-scale environment by precisely tuning the phase coherence time T₂ using the STM tip as a variable electrode. We find that the decoherence rate is the sum of two main contributions. The first scales linearly with tunnel current and shows that, on average, every tunneling electron causes one dephasing event. The second, effective even without current, arises from thermally activated spin-flip processes of tip spins. Understanding these interactions allows us to maximize T₂ and improve the energy resolution. It also allows us to maximize the amplitude of the ESR signal, which supports measurements even at elevated temperatures as high as 4 K. Thus, ESR-STM allows control of quantum coherence in individual, electrically accessible spins.

First-principles study of enhanced magnetic anisotropies in transition-metal atoms doped WS2 monolayer

Considerable progress in contemporary spintronics has been made in recent years for developing nanoscale data memory and quantum information processing. It is, however, still a great challenge to achieve the ultimate limit of storage bit. 2D materials, fortunately, provide an alternative solution for designing materials with the expected miniaturizing scale, chemical stability as well as giant magnetic anisotropy energy. By performing first-principles calculations, we have examined two possible doping sites on a WS₂ monolayer using three kinds of transition metal (TM) atoms (Mn, Fe and Co). It is found that the TM atoms prefer to stay on the W atom site. Additionally, differently from the case of Mn, doping Co and Fe atoms on the W vacancy can achieve perpendicular magnetic anisotropy with a much larger magnitude, which provides a bright prospect for generating atomic-scale magnets of storage devices.

Dynamical Negative Differential Resistance in Antiferromagnetically Coupled Few-Atom Spin Chains

We present the appearance of negative differential resistance (NDR) in spin-dependent electron transport through a few-atom spin chain. A chain of three antiferromagnetically coupled Fe atoms (Fe trimer) was positioned on a Cu_{2}N/Cu(100) surface and contacted with the spin-polarized tip of a scanning tunneling microscope, thus coupling the Fe trimer to one nonmagnetic and one magnetic lead. Pronounced NDR appears at the low bias of 7 mV, where inelastic electron tunneling dynamically locks the atomic spin in a long-lived excited state. This causes a rapid increase of the magnetoresistance between the spin-polarized tip and Fe trimer and quenches elastic tunneling. By varying the coupling strength between the tip and Fe trimer, we find that in this transport regime the dynamic locking of the Fe trimer competes with magnetic exchange interaction, which statically forces the Fe trimer into its high-magnetoresistance state and removes the NDR.

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.

Sensing Noncollinear Magnetism at the Atomic Scale Combining Magnetic Exchange and Spin-Polarized Imaging

Storing and accessing information in atomic-scale magnets requires magnetic imaging techniques with single-atom resolution. Here, we show simultaneous detection of the spin-polarization and exchange force with or without the flow of current with a new method, which combines scanning tunneling microscopy and noncontact atomic force microscopy. To demonstrate the application of this new method, we characterize the prototypical nanoskyrmion lattice formed on a monolayer of Fe/Ir(111). We resolve the square magnetic lattice by employing magnetic exchange force microscopy, demonstrating its applicability to noncollinear magnetic structures for the first time. Utilizing distance-dependent force and current spectroscopy, we quantify the exchange forces in comparison to the spin-polarization. For strongly spin-polarized tips, we distinguish different signs of the exchange force that we suggest arises from a change in exchange mechanisms between the probe and a skyrmion. This new approach may enable both nonperturbative readout combined with writing by current-driven reversal of atomic-scale magnets.

Reading and writing single-atom magnets

The single-atom bit represents the ultimate limit of the classical approach to high-density magnetic storage media. So far, the smallest individually addressable bistable magnetic bits have consisted of 3-12 atoms. Long magnetic relaxation times have been demonstrated for single lanthanide atoms in molecular magnets, for lanthanides diluted in bulk crystals, and recently for ensembles of holmium (Ho) atoms supported on magnesium oxide (MgO). These experiments suggest a path towards data storage at the atomic limit, but the way in which individual magnetic centres are accessed remains unclear. Here we demonstrate the reading and writing of the magnetism of individual Ho atoms on MgO, and show that they independently retain their magnetic information over many hours. We read the Ho states using tunnel magnetoresistance and write the states with current pulses using a scanning tunnelling microscope. The magnetic origin of the long-lived states is confirmed by single-atom electron spin resonance on a nearby iron sensor atom, which also shows that Ho has a large out-of-plane moment of 10.1 ± 0.1 Bohr magnetons on this surface. To demonstrate independent reading and writing, we built an atomic-scale structure with two Ho bits, to which we write the four possible states and which we read out both magnetoresistively and remotely by electron spin resonance. The high magnetic stability combined with electrical reading and writing shows that single-atom magnetic memory is indeed possible.

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.

The geometric phase of Zn- and T-symmetric nanomagnets as a classification toolkit

We derive the general form of the non-trivial geometric phase resulting from the unique combination of point group and time reversal symmetries. This phase arises e.g. when a magnetic adatom is adsorbed on a non-magnetic C_n crystal surface, where n denotes the fold of the principal axis. The energetic ordering and the relevant quantum numbers of the eigenstates are entirely determined by this quantity. Moreover, this phase allows to conveniently predict the protection mechanism of any prepared state, shedding light onto a large number of experiments and allowing a classification scheme. Owing to its robustness this geometric phase also has great relevance for a large number of applications in quantum computing, where topologically protected states bearing long relaxation times are highly desired.

Ferromagnetic coupling in a chloride-bridged erbium single-molecule magnet

We present the first ferromagnetically-coupled Er³⁺ complex with linked, high-anisotropy Er–COT (COT²⁻ = cyclooctatetraene dianion) subunits.

Tomography of a Probe Potential Using Atomic Sensors on Graphene

Our ability to access and explore the quantum world has been greatly advanced by the power of atomic manipulation and local spectroscopy with scanning tunneling and atomic force microscopes, where the key technique is the use of atomically sharp probe tips to interact with an underlying substrate. Here we employ atomic manipulation to modify and quantify the interaction between the probe and the system under study that can strongly affect any measurement in low charge density systems, such as graphene. We transfer Co atoms from a graphene surface onto a probe tip to change and control the probe's physical structure, enabling us to modify the induced potential at a graphene surface. We utilize single Co atoms on a graphene field-effect device as atomic scale sensors to quantitatively map the modified potential exerted by the scanning probe over the whole relevant spatial and energy range.

Magnetic properties of supported metal atoms and clusters

Clusters are small systems ranging from a few atoms up to several thousand atoms. They are of high interest in basic research, but also for applications due to their specific electronic, magnetic or chemical properties depending on size and composition. For small clusters, quantum size effects play an important role and specific material properties might be tailored by choosing a special size or composition of the cluster. Here, we review the magnetic properties of adatoms and supported small mass-selected transition-metal clusters in the few-atom limit investigated by x-ray magnetic circular dichroism spectroscopy in the soft x-ray regime. The influence of cluster size, composition, the cluster-surface and intra-cluster interaction on the spin and orbital magnetic moments will be discussed.

A kilobyte rewritable atomic memory

The advent of devices based on single dopants, such as the single-atom transistor, the single-spin magnetometer and the single-atom memory, has motivated the quest for strategies that permit the control of matter with atomic precision. Manipulation of individual atoms by low-temperature scanning tunnelling microscopy provides ways to store data in atoms, encoded either into their charge state, magnetization state or lattice position. A clear challenge now is the controlled integration of these individual functional atoms into extended, scalable atomic circuits. Here, we present a robust digital atomic-scale memory of up to 1 kilobyte (8,000 bits) using an array of individual surface vacancies in a chlorine-terminated Cu(100) surface. The memory can be read and rewritten automatically by means of atomic-scale markers and offers an areal density of 502 terabits per square inch, outperforming state-of-the-art hard disk drives by three orders of magnitude. Furthermore, the chlorine vacancies are found to be stable at temperatures up to 77 K, offering the potential for expanding large-scale atomic assembly towards ambient conditions.