Proximity superconductivity in atom-by-atom crafted quantum dots.

Gapless materials in electronic contact with superconductors acquire proximity-induced superconductivity in a region near the interface1,2. Numerous proposals build on this addition of electron pairing to originally non-superconducting systems and predict intriguing phases of matter, including topological3-7, odd-frequency8, nodal-point9 or Fulde-Ferrell-Larkin-Ovchinnikov10 superconductivity. Here we investigate the most miniature example of the proximity effect on only a single spin-degenerate quantum level of a surface state confined in a quantum corral11 on a superconducting substrate, built atom by atom by a scanning tunnelling microscope. Whenever an eigenmode of the corral is pitched close to the Fermi energy by adjusting the size of the corral, a pair of particle-hole symmetric states enters the gap of the superconductor. We identify these as spin-degenerate Andreev bound states theoretically predicted 50 years ago by Machida and Shibata12, which had-so far-eluded detection by tunnel spectroscopy but were recently shown to be relevant for transmon qubit devices13,14. We further find that the observed anticrossings of the in-gap states are a measure of proximity-induced pairing in the eigenmodes of the quantum corral. Our results have direct consequences on the interpretation of impurity-induced in-gap states in superconductors, corroborate concepts to induce superconductivity into surface states and further pave the way towards superconducting artificial lattices.

Ultrasensitive Sub-monolayer Palladium Induced Chirality Switching and Topological Evolution of Skyrmions.

Chiral spin textures are fundamentally interesting, with promise for device applications. Stabilizing chirality is conventionally achieved by introducing Dzyaloshinskii-Moriya interaction (DMI) in asymmetric multilayers, where the thickness of each layer is at least a few monolayers. Here we report an ultrasensitive chirality switching in (Ni/Co)n multilayer induced by capping with only 0.22 monolayer of Pd. Using spin-polarized low-energy electron microscopy, we monitor the gradual evolution of domain walls from left-handed to right-handed Néel walls and quantify the DMI induced by the Pd capping layer. We also observe the chiral evolution of a skyrmion during the DMI switching, where no significant topological protection is found as the skyrmion winding number varies. This corresponds to a minimum energy cost of <1 attojoule during the skyrmion chirality switching. Our results demonstrate the detailed chirality evolution within skyrmions during the DMI sign switching, which is relevant to practical applications of skyrmionic devices.

Correlation of Yu-Shiba-Rusinov States and Kondo Resonances in Artificial Spin Arrays on an s-Wave Superconductor.

Mutually interacting magnetic atoms coupled to a superconductor have gained enormous interest due to their potential for the realization of topological superconductivity. Individual magnetic impurities produce states within the superconducting energy gap known as Yu-Shiba-Rusinov (YSR) states. Here, using the tip of a scanning tunneling microscope, we artificially craft spin arrays consisting of an Fe adatom interacting with an assembly of interstitial Fe atoms (IFA) on a superconducting oxygen-reconstructed Ta(100) surface and show that the magnetic interaction between the adatom and the IFA assembly can be tuned by adjusting the number of IFAs in the assembly. The YSR state experiences a characteristic crossover in its energetic position and particle-hole spectral weight asymmetry when the Kondo resonance shows spectral depletion around the Fermi energy. By the help of slave-boson mean-field theory (SBMFT) and numerical renormalization group (NRG) calculations we associate the crossover with the transition from decoupled Kondo singlets to an antiferromagnetic ground state of the Fe adatom spin and the IFA assembly effective spin.

Anomalous Flexural Elasticities of Graphene Membranes Unveiled by Manipulating Topology.

Mechanical behavior of atomically thin membranes is governed by bending rigidity and the Gaussian modulus. However, owing to methodological drawbacks, these two parameters have not been investigated sufficiently. We employed atomic force microscopy to demonstrate that the bending rigidity can be extracted from a quadratic relationship of adhesion energy with monolayer curvatures of rolled and unrolled graphene. The tip-induced topological defects revealed the Gaussian modulus; to the best of our knowledge, this is the first study on these parameters. Our study may hold great significance because existing investigations have been performed only on flat graphene. The configurational (strain) energy was evaluated via changes in the surface geometry, with subatomic resolution, by three-dimensional analyses of attractive interatomic forces. The mechanical parameters, evaluated at the hollow sites of the honeycomb lattice, were consistent with the isotropic elastic attributes. The remarkably large negative Gaussian modulus, observed when a single carbon atom was located at the center of the tip-induced bump, revealed attractive interactions between the topological defects and geometric potentials of the Gaussian curvature. Our approach will aid in developing two-dimensional materials and understanding cell biology.

Spin-Polarized Yu-Shiba-Rusinov States in an Iron-Based Superconductor.

Yu-Shiba-Rusinov (YSR) bound states appear when a magnetic atom interacts with a superconductor. Here, we report on spin-resolved spectroscopic studies of YSR states related with Fe atoms deposited on the surface of the topological superconductor FeTe_{0.55}Se_{0.45} using a spin-polarized scanning tunneling microscope. We clearly identify the spin signature of pairs of YSR bound states at finite energies within the superconducting gap having opposite spin polarization as theoretically predicted. In addition, we also observe zero-energy bound states for some of the adsorbed Fe atoms. In this case, a spin signature is found to be absent indicating the absence of Majorana bound states associated with Fe adatoms on FeTe_{0.55}Se_{0.45}.

Tuning the Properties of Zero-Field Room Temperature Ferromagnetic Skyrmions by Interlayer Exchange Coupling.

Magnetic materials offer an opportunity to overcome the scalability and energy consumption limits affecting the semiconductor industry. New computational device architectures, such as low-power solid state magnetic logic and memory-in-logic devices, have been proposed which rely on the unique properties of magnetic materials. Magnetic skyrmions, topologically protected quasi-particles, are at the core of many of the newly proposed spintronic devices. Many different materials systems have been shown hosting ferromagnetic skyrmions at room temperature. However, a magnetic field is a key ingredient to stabilize skyrmions, and this is not desirable for applications, due to the poor scalability of active components generating magnetic fields. Here we report the observation of ferromagnetic skyrmions at room temperature and zero magnetic field, stabilized through interlayer exchange coupling (IEC) between a reference magnet and a free magnet. Most importantly, by tuning the strength of the IEC, we are able to tune the skyrmion size and areal density. Our findings are relevant to the development of skyrmion-based spintronic devices suitable for general-use applications which go beyond modern nanoelectronics.

Plumbene on a Magnetic Substrate: A Combined Scanning Tunneling Microscopy and Density Functional Theory Study.

As a heavy analog of graphene, plumbene is a two-dimensional material with strong spin-orbit coupling effects. Using scanning tunneling microscopy, we observe that Pb forms a flat honeycomb lattice on an Fe monolayer on Ir(111). In contrast, without the Fe layer, a c(2×4) structure of Pb on Ir(111) is found. We use density-functional theory calculations to rationalize these findings and analyze the impact of the hybridization on the plumbene band structure. In the unoccupied states the splitting of the Dirac cone by spin-orbit interaction is clearly observed, while the occupied Pb states are strongly hybridized with the substrate. In a freestanding plumbene we find a band inversion below the Fermi level that leads to the formation of a topologically nontrivial gap. Exchange splitting as mediated by the strong hybridization with the Fe layer drives a quantum spin Hall to quantum anomalous Hall state transition.

Discovery of Magnetic Single- and Triple-q States in Mn/Re(0001).

We experimentally verify the existence of two model-type magnetic ground states that were previously predicted but so far unobserved. We find them in Mn monolayers on the Re(0001) surface using spin-polarized scanning tunneling microscopy. For fcc stacking of Mn the collinear row-wise antiferromagnetic state occurs, whereas for hcp Mn a three-dimensional spin structure appears, which is a superposition of three row-wise antiferromagnetic states known as the triple-q state. Density-functional theory calculations elucidate the subtle interplay of different magnetic interactions to form these spin structures and provide insight into the role played by relativistic effects.

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.

Vacuum Resonance States as Atomic-Scale Probes of Noncollinear Surface Magnetism.

The reflection of electrons at noncollinear magnetic surfaces is investigated by spin-polarized scanning tunneling microscopy and spectroscopy on unoccupied resonance states located in vacuo. Even for energies up to 20 eV above the Fermi level, the resonance states are found to be spin split, exhibiting the same local spin quantization axis as the underlying spin texture. Mapping the spin-dependent electron phase shift upon reflection at the surface on the atomic scale demonstrates the relevance of all magnetic ground state interactions for the scattering of spin-polarized low-energy electrons.

Electrical Detection of Domain Walls and Skyrmions in Co Films Using Noncollinear Magnetoresistance.

A large noncollinear magnetoresistance (NCMR) is observed for Rh/Co atomic bilayers on Ir(111) using scanning tunneling microscopy and spectroscopy. The effect is 20% at the Fermi energy and large in a broad energy range. The NCMR can be used to electrically detect nanometer-scale domain walls and skyrmions directly in the tunnel current without the need for a differential measurement. The NCMR results from changes in the density of states of noncollinear spin textures with respect to the ferromagnetic state. Density functional theory calculations reveal that they originate from spin mixing between majority d_{xz} and minority p_{z} states.

Long Spin-Relaxation Times in a Transition-Metal Atom in Direct Contact to a Metal Substrate.

Long spin-relaxation times are a prerequisite for the use of spins in data storage or nanospintronics technologies. An atomic-scale solid-state realization of such a system is the spin of a transition-metal atom adsorbed on a suitable substrate. For the case of a metallic substrate, which enables the direct addressing of the spin by conduction electrons, the experimentally measured lifetimes reported to date are on the order of only hundreds of femtoseconds. Here, we show that the spin states of iron atoms adsorbed directly on a conductive platinum substrate have a surprisingly long spin-relaxation time in the nanosecond regime, which is comparable to that of a transition metal atom decoupled from the substrate electrons by a thin decoupling layer. The combination of long spin-relaxation times and strong coupling to conduction electrons implies the possibility to use flexible coupling schemes to process the spin information.

Erratum: Guiding Spin Spirals by Local Uniaxial Strain Relief [Phys. Rev. Lett. 116, 017201 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.116.017201.

Competition of Dzyaloshinskii-Moriya and Higher-Order Exchange Interactions in Rh/Fe Atomic Bilayers on Ir(111).

Using spin-polarized scanning tunneling microscopy and density functional theory we demonstrate the occurrence of a novel type of noncollinear spin structure in Rh/Fe atomic bilayers on Ir(111). We find that higher-order exchange interactions depend sensitively on the stacking sequence. For fcc-Rh/Fe/Ir(111), frustrated exchange interactions are dominant and lead to the formation of a spin spiral ground state with a period of about 1.5 nm. For hcp-Rh/Fe/Ir(111), higher-order exchange interactions favor an up-up-down-down (↑↑↓↓) state. However, the Dzyaloshinskii-Moriya interaction at the Fe/Ir interface leads to a small angle of about 4° between adjacent magnetic moments resulting in a canted ↑↑↓↓ ground state.

Probing the Nano-Skyrmion Lattice on Fe/Ir(111) with Magnetic Exchange Force Microscopy.

We demonstrate that the magnetic nano-Skyrmion lattice on the Fe monolayer on Ir(111) and the positions of the Fe atoms can be resolved simultaneously using magnetic exchange force microscopy. Thus, the relation between magnetic and atomic structure can be determined straightforwardly by evaluating the Fourier transformation of the real space image data. We further show that the magnetic contrast can be mapped on a Heisenberg-like magnetic interaction between tip and sample spins. Since our imaging technique is based on measuring forces, our observation paves the way to study Skyrmions or other complex spin textures on insulating sample systems with atomic resolution.

Temperature-Induced Increase of Spin Spiral Periods.

Spin-polarized scanning tunneling microscopy investigations reveal a significant increase of the magnetic period of spin spirals in three-atomic-layer-thick Fe films on Ir(111), from about 4 nm at 8 K to about 65 nm at room temperature. We attribute this considerable influence of temperature on the magnetic length scale of noncollinear spin states to different exchange interaction coefficients in the different Fe layers. We thus propose a classical spin model that reproduces the experimental observations and in which the crucial feature is the presence of magnetically coupled atomic layers with different interaction strengths. This model might also apply for many other systems, especially magnetic multilayers.

Coupling of Coexisting Noncollinear Spin States in the Fe Monolayer on Re(0001).

Spin-polarized scanning tunneling microscopy is used to investigate the magnetic state of the Fe monolayer on Re(0001). Two coexisting atomic-scale noncollinear spin textures are observed with a sharp transition between them on the order of the atomic lattice spacing. A position correlation between the two spin states is observed both in experiments and in Monte Carlo simulations, demonstrating their coupling behavior.

Toward Tailored All-Spin Molecular Devices.

Molecular based spintronic devices offer great potential for future energy-efficient information technology as they combine ultimately small size, high-speed operation, and low-power consumption. Recent developments in combining atom-by-atom assembly with spin-sensitive imaging and characterization at the atomic level have led to a first prototype of an all-spin atomic-scale logic device, but the very low working temperature limits its application. Here, we show that a more stable spintronic device could be achieved using tailored Co-Salophene based molecular building blocks, combined with in situ electrospray deposition under ultrahigh vacuum conditions as well as control of the surface-confined molecular assembly at the nanometer scale. In particular, we describe the tools to build a molecular, strongly bonded device structure from paramagnetic molecular building blocks including spin-wires, gates, and tails. Such molecular device concepts offer the advantage of inherent parallel fabrication based on molecular self-assembly as well as an order of magnitude higher operation temperatures due to enhanced energy scales of covalent through-bond linkage of basic molecular units compared to substrate-mediated coupling schemes employing indirect exchange coupling between individual adsorbed magnetic atoms on surfaces.

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.

Skyrmions at the Edge: Confinement Effects in Fe/Ir(111).

We have employed spin-polarized scanning tunneling microscopy and Monte Carlo simulations to investigate the effect of lateral confinement onto the nano-Skyrmion lattice in Fe/Ir(111). We find a strong coupling of one diagonal of the square magnetic unit cell to the close-packed edges of Fe nanostructures. In triangular islands this coupling in combination with the mismatching symmetries of the islands and of the square nano-Skyrmion lattice leads to frustration and triple-domain states. In direct vicinity to ferromagnetic NiFe islands, the surrounding Skyrmion lattice forms additional domains. In this case a side of the square magnetic unit cell prefers a parallel orientation to the ferromagnetic edge. These experimental findings can be reproduced and explained by Monte Carlo simulations. Here, the single-domain state of a triangular island is lower in energy, but nevertheless multidomain states occur due to the combined effect of entropy and an intrinsic domain wall pinning arising from the skyrmionic character of the spin texture.