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Considering the growing interest in magnetic materials for unconventional computing, data storage, and sensor applications, there is active research not only on material synthesis but also characterisation of their properties. In addition to structural and integral magnetic characterisations, imaging of magnetisation patterns, current distributions and magnetic fields at nano- and microscale is of major importance to understand the material responses and qualify them for specific applications. In this roadmap, we aim to cover a broad portfolio of techniques to perform nano- and microscale magnetic imaging using superconducting quantum interference devices, spin centre and Hall effect magnetometries, scanning probe microscopies, x-ray- and electron-based methods as well as magnetooptics and nanoscale magnetic resonance imaging. The roadmap is aimed as a single access point of information for experts in the field as well as the young generation of students outlining prospects of the development of magnetic imaging technologies for the upcoming decade with a focus on physics, materials science, and chemistry of planar, three-dimensional and geometrically curved objects of different material classes including two-dimensional materials, complex oxides, semi-metals, multiferroics, skyrmions, antiferromagnets, frustrated magnets, magnetic molecules/nanoparticles, ionic conductors, superconductors, spintronic and spinorbitronic materials.

The reduced dimensionality of thin transition metal dihalide films on single-crystal surfaces unlocks a diverse range of magnetic and electronic properties. However, achieving stoichiometric monolayer islands requires precise control over the growth conditions. In this study, we employ scanning probe microscopy to investigate the growth of MnI 2 on Ag(111) via single-crucible evaporation. The catalytic properties of the Ag(111) surface facilitate MnI 2 dehalogenation, leading to the formation of a reconstructed iodine adlayer that acts as a buffer layer for the growth of truncated hexagonal MnI 2 islands. These islands exhibit alternating edge lengths and distinct Kelvin potentials, as revealed by Kelvin probe force microscopy. Density functional theory (DFT) calculations support the experimentally observed island heights and lattice parameters and provide insights into the formation energies of both pristine and reconstructed edges. The asymmetry in edge lengths is attributed to differences in edge formation energies, driven by the position (up or down) of edge iodine atoms, as confirmed by DFT. This structural difference accounts for the observed variation in the Kelvin potential between the two types of island edge terminations.

Cantilever-based atomic force microscopy (AFM) performed under ambient conditions has become an important tool to characterize new material systems as well as devices. Current instruments permit robust scanning over large areas, atomic-scale lateral resolution, and the characterization of various sample properties using multifrequency and multimodal AFM operation modes. Research of new quantum materials and devices, however, often requires low temperatures and ultrahigh vacuum (UHV) conditions and, more specifically, AFM instrumentation providing atomic resolution. For this, AFM instrumentation based on a tuning fork force sensor became increasingly popular. In comparison to microfabricated cantilevers, the more macroscopic tuning forks, however, lack sensitivity, which limits the measurement bandwidth. Moreover, multimodal and multifrequency techniques, such as those available in cantilever-based AFM carried out under ambient conditions, are challenging to implement. In this article, we describe a cantilever-based low-temperature UHV AFM setup that allows one to transfer the versatile AFM techniques developed for ambient conditions to UHV and low-temperature conditions. We demonstrate that such a cantilever-based AFM offers experimental flexibility by permitting multimodal or multifrequency operations with superior force derivative sensitivities and bandwidths. Our instrument has a sub-picometer gap stability and can simultaneously map not only vertical and lateral forces with atomic-scale resolution, but also perform rapid overview scans with the tip kept at larger tip-sample distances for robust imaging., (Copyright © 2022, Liu et al.)

The development of skyrmionic devices requires a suitable tuning of material parameters to stabilize skyrmions and control their density. It has been demonstrated recently that different skyrmion types can be simultaneously stabilized at room temperature in heterostructures involving ferromagnets, ferrimagnets, and heavy metals, offering a new platform of coding binary information in the type of skyrmion instead of the presence/absence of skyrmions. Here, we tune the energy landscape of the two skyrmion types in such heterostructures by engineering the geometrical and material parameters of the individual layers. We find that a fine adjustment of the ferromagnetic layer thickness, and thus its magnetic anisotropy, allows the trilayer system to support either one of the skyrmion types or the coexistence of both and with varying densities.

Machine learning is changing how we design and interpret experiments in materials science. In this work, we show how unsupervised learning, combined with ab initio random structure searching, improves our understanding of structural metastability in multicomponent alloys. We focus on the case of Al-O-N alloys where the formation of aluminum vacancies in wurtzite AlN upon the incorporation of substitutional oxygen can be seen as a general mechanism of solids where crystal symmetry is reduced to stabilize defects. The ideal AlN wurtzite crystal structure occupation cannot be matched due to the presence of an aliovalent hetero-element into the structure. The traditional interpretation of the c -lattice shrinkage in sputter-deposited Al-O-N films from X-ray diffraction (XRD) experiments suggests the existence of a solubility limit at 8 at % oxygen content. Here, we show that such naive interpretation is misleading. We support XRD data with accurate ab initio modeling and dimensionality reduction on advanced structural descriptors to map structure-property relationships. No signs of a possible solubility limit are found. Instead, the presence of a wide range of non-equilibrium oxygen-rich defective structures emerging at increasing oxygen contents suggests that the formation of grain boundaries is the most plausible mechanism responsible for the lattice shrinkage measured in Al-O-N sputtered films. We further confirm our hypothesis using positron annihilation lifetime spectroscopy.

Materials hosting magnetic skyrmions at room temperature could enable compact and energetically-efficient storage such as racetrack memories, where information is coded by the presence/absence of skyrmions forming a moving chain through the device. The skyrmion Hall effect leading to their annihilation at the racetrack edges can be suppressed, for example, by antiferromagnetically-coupled skyrmions. However, avoiding modifications of the inter-skyrmion distances remains challenging. As a solution, a chain of bits could also be encoded by two different solitons, such as a skyrmion and a chiral bobber, with the limitation that it has solely been realized in B20-type materials at low temperatures. Here, we demonstrate that a hybrid ferro/ferri/ferromagnetic multilayer system can host two distinct skyrmion phases at room temperature, namely tubular and partial skyrmions. Furthermore, the tubular skyrmion can be converted into a partial skyrmion. Such systems may serve as a platform for designing memory applications using distinct skyrmion types.

Giant exchange bias shifts of several Tesla have been reported in ferrimagnetic/ferromagnetic bilayer systems, which could be highly beneficial for contemporary high energy density permanent magnets and spintronic devices. However, the lack of microscopic studies of the reversal owing to the difficulty of measuring few nanometer-wide magnetic structures in high fields precludes the assessment of the lateral size of the inhomogeneity in relation to the intended application. In this study, the magnetic reversal process of nanoscale exchange-coupled bilayer systems, consisting of a ferrimagnetic TbFeCo alloy layer and a ferromagnetic [Co/Ni/Pt] N multilayer, was investigated. In particular, minor loop measurements, probing solely on the reversal characteristics of the softer ferromagnetic layer, reveal two distinct reversal mechanisms, which depend critically on the thickness of the ferromagnetic layer. For thick layers, irreversible switching of the macroscopic minor loop is observed. The underlying microscopic origin of this reversal process was studied in detail by high-resolution magnetic force microscopy, showing that the reversal is triggered by in-plane domain walls propagating through the ferromagnetic layer. In contrast, thin ferromagnetic layers show a hysteresis-free reversal, which is nucleation-dominated due to grain-to-grain variations in magnetic anisotropy of the Co/Ni/Pt multilayer and an inhomogeneous exchange coupling with the magnetically hard TbFeCo layer, as confirmed by micromagnetic simulations., Competing Interests: The authors declare no competing financial interest., (Copyright © 2020 American Chemical Society.)

Research in new quantum materials requires multi-mode measurements spanning length scales, correlations of atomic-scale variables with a macroscopic function, and spectroscopic energy resolution obtainable only at millikelvin temperatures, typically in a dilution refrigerator. In this article, we describe a multi-mode instrument achieving a μeV tunneling resolution with in-operando measurement capabilities of scanning tunneling microscopy, atomic force microscopy, and magnetotransport inside a dilution refrigerator operating at 10 mK. We describe the system in detail including a new scanning probe microscope module design and sample and tip transport systems, along with wiring, radio-frequency filtering, and electronics. Extensive benchmarking measurements were performed using superconductor-insulator-superconductor tunnel junctions, with Josephson tunneling as a noise metering detector. After extensive testing and optimization, we have achieved less than 8 μeV instrument resolving capability for tunneling spectroscopy, which is 5-10 times better than previous instrument reports and comparable to the quantum and thermal limits set by the operating temperature at 10 mK.

Optically transparent, colorless Al-O-N and Al-Si-O-N coatings with discretely varied O and Si contents were fabricated by reactive direct current magnetron sputtering (R-DCMS) from elemental Al and Si targets and O 2 and N 2 reactive gases. The Si/Al content was adjusted through the electrical power on the Si and Al targets, while the O/N content was controlled through the O 2 flow piped to the substrate in addition to the N 2 flow at the targets. The structure and morphology of the coatings were studied by X-ray diffraction (XRD) and transmission electron microscopy (TEM), while the elemental composition was obtained from Rutherford backscattering spectrometry (RBS) and heavy ion elastic recoil detection analysis (ERDA). The chemical states of the elements in the coatings were analyzed by X-ray photoelectron spectroscopy (XPS). Based on analytical results, a model describing the microstructural evolution of the Al-O-N and also previously studied Al-Si-N [1, 2, 3, 4] coatings with O and Si content, respectively, is established. The universality of the microstructural evolution of these coatings with the concentration of the added element is attributed to the extra valence electron (e - ) that must be incorporated into the AlN wurtzite host lattice. In the case of Al-O-N, this additional valence charge arises from the e - acceptor O replacing N in the AlN wurtzite lattice, while the e - donor Si substituting Al fulfills that role in the Al-Si-N system. In view of future applications of ternary Al-O-N and quaternary Al-Si-O-N transparent protective coatings, their mechanical properties such as residual stress ( σ ), hardness (HD) and Young's modulus (E) were obtained from the curvature of films deposited onto thin substrates and by nanoindentation, respectively. Moderate compressive stress levels between -0.2 and -0.5 GPa, which suppress crack formation and film-substrate delamination, could be obtained together with HD values around 25 GPa., (© 2019 The Author(s). Published by National Institute for Materials Science in partnership with Taylor & Francis Group.)

Skyrmion imaging and electrical detection via topological Hall (TH) effect are two primary techniques for probing magnetic skyrmions, which hold promise for next-generation magnetic storage. However, these two kinds of complementary techniques have rarely been employed to investigate the same samples. We report the observation of nanoscale skyrmions in SrIrO 3 /SrRuO 3 (SIO/SRO) bilayers in a wide temperature range from 10 to 100 K. The SIO/SRO bilayers exhibit a remarkable TH effect, which is up to 200% larger than the anomalous Hall (AH) effect at 5 K, and zero-field TH effect at 90 K. Using variable-temperature, high-field magnetic force microscopy (MFM), we imaged skyrmions as small as 10 nm, which emerge in the same field ranges as the TH effect. These results reveal a rich space for skyrmion exploration and tunability in oxide heterostructures.

The current-driven motion of skyrmions in MnSi and FeGe thinned single crystals could be initiated at current densities of the order of 10 6 A/m 2 , five orders of magnitude smaller than for magnetic domain walls. The technologically crucial step of replicating these results in thin films has not been successful to-date, but the reasons are not clear. Elucidating them requires analyzing system characteristics at scales of few nm where the key Dzyaloshinskii-Moriya (DM) interactions vary, and doing so in near-application conditions, i.e. in systems at room temperature, capped with additional layers for oxidation protection. In this work's magnetic force microscopy (MFM) studies of magnetron-sputtered Ir/Co/Pt-multilayers we show skyrmions that are smaller than previously observed, are not circularly symmetric, and are pinned to 50-nm wide areas where the DM interaction is higher than average. This finding matches our measurement of inhomogeneity of the magnetic moment areal density, which amounts to a standard deviation of the Co layer thickness of 0.3 monolayers in our 0.6 nm thick Co layers. This likely originates in small Co layer thickness variation and alloying. These film characteristics must be controlled with greater precision to preclude skyrmion pinning.

The redistribution of ions in light-emitting electrochemical cells (LECs) plays a key role in their functionality. The direct quantitative mapping of ion density distributions in operating realistic sandwich-type devices, however, has not been experimentally achieved. Here we operate high-performing [Super Yellow/trimethylolpropane ethoxylate/lithium trifluoromethanesulfonate (Li + CF 3 SO 3 - )] LEC devices inside a time-of-flight secondary ion mass spectrometer and cool the devices after different operation times to liquid nitrogen temperatures before depth profiling is performed. The results reveal the dependence of the elemental and molecular distributions across the device layer on operation conditions. We find that the ion displacements lead to a substantial shift of the local chemical equilibria governing the free ion concentration.

Mallinson's idea that some spin textures in planar magnetic structures could produce an enhancement of the magnetic flux on one side of the plane at the expense of the other gave rise to permanent magnet configurations known as Halbach magnet arrays. Applications range from wiggler magnets in particle accelerators and free electron lasers to motors and magnetic levitation trains, but exploiting Halbach arrays in micro- or nanoscale spintronics devices requires solving the problem of fabrication and field metrology below a 100 μm size. In this work, we show that a Halbach configuration of moments can be obtained over areas as small as 1 μm × 1 μm in sputtered thin films with Néel-type domain walls of unique domain wall chirality, and we measure their stray field at a controlled probe-sample distance of 12.0 ± 0.5 nm. Because here chirality is determined by the interfacial Dyzaloshinkii-Moriya interaction, the field attenuation and amplification is an intrinsic property of this film, allowing for flexibility of design based on an appropriate definition of magnetic domains. Skyrmions (<100 nm wide) illustrate the smallest kind of such structures, for which our measurement of stray magnetic fields and mapping of the spin structure shows they funnel the field toward one specific side of the film given by the sign of the Dyzaloshinkii-Moriya interaction parameter D.

Configuration transitions of individual molecules and atoms on surfaces are traditionally described using an Arrhenius equation with energy barrier and pre-exponential factor (attempt rate) parameters. Characteristic parameters can vary even for identical systems, and pre-exponential factors sometimes differ by orders of magnitude. Using low-temperature scanning tunnelling microscopy (STM) to measure an individual dibutyl sulfide molecule on Au(111), we show that the differences arise when the relative position of tip apex and molecule changes by a fraction of the molecule size. Altering the tip position on that scale modifies the transition's barrier and attempt rate in a highly correlated fashion, which results in a single-molecular enthalpy-entropy compensation. Conversely, appropriately positioning the STM tip allows selecting the operating point on the compensation line and modifying the transition rates. The results highlight the need to consider entropy in transition rates of single molecules, even at low temperatures.

The combination of complementary measurement techniques has become a frequent approach to improve scientific knowledge. Pairing of the high lateral resolution scanning force microscopy (SFM) with the spectroscopic information accessible through scanning transmission soft x-ray microscopy (STXM) permits assessing physical and chemical material properties with high spatial resolution. We present progress from the NanoXAS instrument towards using an SFM probe as an x-ray detector for STXM measurements. Just by the variation of one parameter, the SFM probe can be utilised to detect either sample photo-emitted electrons or transmitted photons. This allows the use of a single probe to detect electrons, photons and physical forces of interest. We also show recent progress and demonstrate the current limitations of using a high aspect ratio coaxial SFM probe to detect photo-emitted electrons with very high lateral resolution. Novel probe designs are proposed to further progress in using an SFM probe as a STXM detector.

Models of exchange-bias in thin films have been able to describe various aspects of this technologically relevant effect. Through appropriate choices of free parameters the modelled hysteresis loops adequately match experiment, and typical domain structures can be simulated. However, the use of these parameters, notably the coupling strength between the systems' ferromagnetic (F) and antiferromagnetic (AF) layers, obscures conclusions about their influence on the magnetization reversal processes. Here we develop a 2D phase-field model of the magnetization process in exchange-biased CoO/(Co/Pt)×n that incorporates the 10 nm-resolved measured local biasing characteristics of the antiferromagnet. Just three interrelated parameters set to measured physical quantities of the ferromagnet and the measured density of uncompensated spins thus suffice to match the experiment in microscopic and macroscopic detail. We use the model to study changes in bias and coercivity caused by different distributions of pinned uncompensated spins of the antiferromagnet, in application-relevant situations where domain wall motion dominates the ferromagnetic reversal. We show the excess coercivity can arise solely from inhomogeneity in the density of biasing- and anti-biasing pinned uncompensated spins in the antiferromagnet. Counter to conventional wisdom, irreversible processes in the latter are not essential.

A combined x-ray transmission and scanning force microscope setup (NanoXAS) recently installed at a dedicated beamline of the Swiss Light Source combines complementary experimental techniques to access chemical and physical sample properties with nanometer scale resolution. While scanning force microscopy probes physical properties such as sample topography, local mechanical properties, adhesion, electric and magnetic properties on lateral scales even down to atomic resolution, scanning transmission x-ray microscopy offers direct access to the local chemical composition, electronic structure and magnetization. Here we present three studies which underline the advantages of complementary access to nanoscale properties in prototype thin film samples.

A single propene molecule, located in the junction between the tip of a scanning tunneling microscope (STM) and a Cu(211) surface can be dehydrogenated by inelastic electron tunneling. This reaction requires excitation of the asymmetric C-H stretching vibration of the ═CH(2) group. The product is then identified by inelastic electron tunneling action spectroscopy (IETAS).

For a fixed 2 μm×2 μm area of a Co/Pt-CoO perpendicular exchange bias system we image the ferromagnetic (FM) domains for various applied fields with 10-nm resolution by magnetic force microscopy (MFM). Using quantitative MFM we measure the local areal density of pinned uncompensated spins (pinUCS) in the antiferromagnetic (AFM) CoO layer and correlate the FM domain structure with the UCS density. Larger applied fields drive the receding domains to areas of proportionally higher pinUCS aligned antiparallel to FM moments. The data confirm that the evolution of the FM domains is determined by the pinUCS in the AFM layer, and also present examples of frustration in the system.

We studied atomic contact potential variations of Si(111)-7 x 7 by Kelvin probe force microscopy with the amplitude modulation technique at the second resonance of a silicon cantilever. Enhanced sensitivity due to the high mechanical quality factor in ultra-high vacuum enabled local contact potential difference (LCPD) measurements of individual adatoms. The contrast of the measured LCPD map became stronger by reducing the tip-sample distance, and the averaged LCPD value shifted to more negative. The short-range interaction, arising from the covalent bonding interactions, strongly affects the LCPD measurement. Theoretical calculations indicate that the amplitude modulation method has a higher sensitivity than the frequency modulation method in practical cases. The tip-sample distance dependence of LCPD was investigated by numerical calculations.

Pumped up: Propene molecules form chiral complexes when adsorbed on a copper surface. Inelastically scattered tunneling electrons from the tip of a scanning tunneling microscope induce rotation or diffusion of the adsorbate on the surface. Higher tunneling currents can lead to conversion of the adsorbate into the opposite enantiomer.

We have developed an optical cantilever deflection detector with a spot size <3 µm and fm Hz(-1/2) sensitivity over a>10 MHz bandwidth. In this work, we demonstrate its potential for detecting small-amplitude oscillations of various flexural and torsional oscillation modes of cantilevers. The high deflection sensitivity of the interferometer is particularly useful for detecting cantilever oscillations in aqueous solutions, enabling us to reach the thermal noise limit in scanning or atomic force microscopy experiments with stiff cantilevers. This has resulted in atomic-resolution images of solid-liquid interfaces and submolecular-resolution images of native membranes.

Atomistic simulations considering larger tip structures than hitherto assumed reveal novel dissipation mechanisms in noncontact atomic force microscopy. The potential energy surfaces of realistic silicon tips exhibit many energetically close local minima that correspond to different structures. Most of them easily deform, thus causing dissipation arising from hysteresis in force versus distance characteristics. Furthermore, saddle points which connect local minima can suddenly switch to connect different minima. Configurations driven into metastability by the tip motion can thus suddenly access lower energy structures when thermal activation becomes allowed within the time required to detect the resulting average dissipation.

The resonance frequency and the excitation amplitude of a silicon cantilever have been measured as a function of distance to a cleaved KBr(001) surface with a low-temperature scanning force microscope (SFM) in ultrahigh vacuum. We identify two regimes of tip-sample distances. Above a site-dependent critical tip-sample distance reproducible data with low noise and no interaction-induced energy dissipation are measured. In this regime reproducible SFM images can be recorded. At closer tip-sample distances, above two distinct atomic sites, the frequency values jump between two limiting curves on a timescale of tens of milliseconds. Furthermore, additional energy dissipation occurs wherever jumps are observed. We attribute both phenomena to rarely occurring changes in the tip apex configuration which are affected by short-range interactions with the sample. Their respective magnitudes are related to each other. A specific candidate two-level system is also proposed.

Atomic Force Microscopy (AFM) was used to investigate the ultrastructural appearance of transverse wood cell wall surfaces in embedded and polished Norway spruce wood blocks. The prepared surfaces showed only little height differences, suitable for high resolution AFM phase contrast imaging. Our results revealed randomly arranged wood cell wall components in the thick secondary 2 (S2) layers of the tracheid cell walls. It is concluded that the observed distribution pattern of the cellulose fibril/matrix structure is close to the original cell wall structure. In this context, the plasticity of wood cell wall components to re-arrange and adjust to different conditions resulting in diverse structural pattern is discussed.

200-nm-thick Ni films in an epitaxial Cu/Ni/Cu/Si(001) structure are expected to have an in-plane effective magnetic anisotropy. However, the in-plane remanence is only 42%, and magnetic force microscopy domain images suggest perpendicular magnetization. Quantitative magnetic force microscopy analysis can resolve the inconsistencies and show that (i) the films have perpendicular domains capped by closure domains with magnetization canted at 51 degrees from the film normal, (ii) the magnetization in the Bloch domain walls between the perpendicular domains accounts for the low in-plane remanence, and (iii) the perpendicular magnetization process requires a short-range domain wall motion prior to wall-magnetization rotation and is nonhysteretic, whereas the in-plane magnetization requires long-range motion before domain-magnetization rotation and is hysteretic.

Recent advances in dynamic force microscopy show that it is possible to measure the forces between atomically sharp tips and particular atomic positions on surfaces as a function of distance. However, on most ionic surfaces, the positive and negative ions can so far not be distinguished. In this paper, we use the CaF2(111) surface, where atomic resolution force microscopy has allowed identification of the positions of the Ca2+ and F- ions in the obtained images, to demonstrate that short-range interaction forces can be measured selectively above chemically identified surface sites. Combining experimental and theoretical results allows a quantification of the strength and distance dependence of the interaction of a tip-terminating cluster with particular surface ions and reveals details of cluster and surface relaxation. Further development of this approach will provide new insight into mechanisms of chemical bond formation between clusters, cluster deposition at surfaces, processes in adhesion and tribology, and single atom manipulation with the force microscope.

We propose and apply to the KBr(001) surface a new procedure for species recognition in scanning force microscopy (SFM) of ionic crystal surfaces which show a high symmetry of the charge arrangement. The method is based on a comparison between atomistic simulations and site-specific frequency versus distance measurements. First, by taking the difference of force-distance curves extracted at a few judiciously chosen surface sites we eliminate site-independent long-range forces. The obtained short-range force differences are then compared with calculated ones assuming plausible tip apex models. This procedure allows for the first time identification of the tip apex polarity and of the positive and negative sublattices in SFM images of the (001) cleavage surface of an ionic crystal with the rock salt structure.

Magnetic force microscopy (MFM) measurements were performed on an exchange-biased CoO/(CoPt) multilayer sample at 7.5 K. Applying an external magnetic field of up to 7 T saturates the ferromagnetic layer and the remaining uncompensated antiferromagnetic spins at the antiferromagnet-ferromagnet interfaces are imaged with high lateral resolution. The coupling between the uncompensated spins and the spins in the ferromagnet are found to be antiferromagnetic. Quantitative analysis of the MFM images revealed that 7% of the spins at the interface are uncompensated and contribute to the exchange biasing.

We report direct force measurements of the formation of a chemical bond. The experiments were performed using a low-temperature atomic force microscope, a silicon tip, and a silicon (111) 7x7 surface. The measured site-dependent attractive short-range force, which attains a maximum value of 2.1 nanonewtons, is in good agreement with first-principles calculations of an incipient covalent bond in an analogous model system. The resolution was sufficient to distinguish differences in the interaction potential between inequivalent adatoms, demonstrating the ability of atomic force microscopy to provide quantitative, atomic-scale information on surface chemical reactivity.

A low temperature scanning force microscope (SFM) operating in a dynamic mode in ultrahigh vacuum was used to study the Si(111)- (7x7) surface at 7.2 K. Not only the twelve adatoms but also the six rest atoms of the unit cell are clearly resolved for the first time with SFM. In addition, the first measurements of the short range chemical bonding forces above specific atomic sites are presented. The data are in good agreement with first principles computations and indicate that the nearest atoms in the tip and sample relax significantly when the tip is within a few A of the surface.