problem is that we have neglected the spin on the intervening oxygen. The third is that Eq. 1 describes the ground state for a single FM bond, implying that neutron scattering should be elastic, not inelastic as seen experimentally.The first difficulty has a simple resolution. At finite hole densities, the polarization clouds overlap and the isolated impurity model is inadequate. A crude model, which considers the overlaps, simply truncates the polarization clouds at neighboring impurity sites. Because FM impurity bonds are randomly distributed, the inversion symmetry characterizing isolated impurities is broken, thus allowing intensity at q ϭ . Because we know the impurity density, x, from neutron activation analysis, the only parameters in such a description are the extent of the polarization cloud, Ϫ1, which we adjusted to optimize the fit to our data. As shown by the red lines in Fig. 4, the model provides a good account of the data with Ϫ1 ϭ 8.1 Ϯ 0.2, 7.3 Ϯ 0.2, and 7.2 Ϯ 0.5 for x ϭ 0.04, 0.095, and 0.14 respectively. These values are close to the exponential decay length of 6.03 calculated for the AFM spin polarization at the end of an S ϭ 1 chain (25).The modeling described so far does not include the spins of the holes responsible for the effective FM couplings between Ni 2ϩ ions. The holes reside in oxygen orbitals of Y 2Ϫx Ca x BaNiO 5 (5) but are almost certainly not confined to single, isolated oxygens. We consequently generalized Eq. 1 to take into account the hole spins, with-for the sake of definiteness-the same net amplitude as either of the Ni 2ϩ spins next to the FM bond and distributed (with exponential decay) over ᐉ lattice sites centered on the FM bond. As long as ᐉ exceeds the modest value of 2, comparable to the localization length deduced from transport data (5), the pronounced asymmetry about that occurs when ᐉ ϭ 0 is relieved sufficiently to produce fits indistinguishable from those in Fig. 4.How do we account for the inelasticity of the incommensurate signal? One approach is to view the chain as consisting not of the original S ϭ 1 degrees of freedom but of the composite spin degrees of freedom induced around holes. The latter interact through overlapping AFM polarization clouds and hole wave functions, to produce effective couplings of random sign because the impurity spacing can be even or odd multiples of the Ni-Ni separation. With weak interchain coupling, the ground state is likely to be a spin glass, as deduced from other experiments (10) on Y 2Ϫx Ca x BaNiO 5 . The "incommensurate" nature of the excitations continues to follow from the structure factor of the spin part of the hole wave functions.In summary, we have measured the magnetic fluctuations in single crystals of a doped one-dimensional spin liquid. At energies above the spin gap, the triplet excitations of the parent compound, Y 2 BaNiO 5 , persist with doping. However, below the gap, we find new excitations with a broad spectrum and characteristic wave vectors that are displaced from the zone boundary by an amount of...

True atomic resolution of conductors and insulators is now routinely obtained in vacuum by frequency modulation atomic Ž force microscopy. So far, the imaging parameters i.e., eigenfrequency, stiffness and oscillation amplitude of the cantilever, . frequency shift which result in optimal spatial resolution for a given cantilever and sample have been found empirically. Here, we calculate the optimal set of parameters from first principles as a function of the tip-sample system. The result shows that the either the acquisition rate or the signal-to-noise ratio could be increased by up to two orders of magnitude by using stiffer cantilevers and smaller amplitudes than are in use today. q

Carbon, the backbone material of life on Earth, comes in three modifications: diamond, graphite, and fullerenes. Diamond develops tetrahedral sp 3 bonds, forming a cubic crystal structure, whereas graphite and fullerenes are characterized by planar sp 2 bonds. Polycrystalline graphite is the basis for many products of everyday life: pencils, lubricants, batteries, arc lamps, and brushes for electric motors. In crystalline form, highly oriented pyrolytic graphite is used as a diffracting element in monochromators for x-ray and neutron scattering and as a calibration standard for scanning tunneling microscopy (STM). The graphite surface is easily prepared as a clean atomically flat surface by cleavage. This feature is attractive and is used in many laboratories as the surface of choice for ''seeing atoms.'' Despite the proverbial ease of imaging graphite by STM with atomic resolution, every second atom in the hexagonal surface unit cell remains hidden, and STM images show only a single atom in the unit cell. Here we present measurements with a low-temperature atomic force microscope with pico-Newton force sensitivity that reveal the hidden surface atom. T he question of the existence of atoms is of central importance to the natural sciences, and the American Nobel physics laureate Richard P. Feynman has stated that in all scientific knowledge, the atomic hypothesis that "all things are made of atoms, little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another" contains the most information in the fewest words (1). Nevertheless, only 100 years ago some of the most distinguished scientists of that time were engaged in heated debates about the existence of atoms (2). To ''see'' atoms is therefore an important endeavor. E. W. Müller (3) achieved an important breakthrough 50 years ago with the invention of the field ion microscope that could later image single atoms on sharp tips with atomic resolution (4). Observing single atoms in real space on flat surfaces became possible 20 years ago with the invention of a marvelous instrument: the scanning tunneling microscope (STM) (5). (For a discussion of the relation between STM and other highresolution electron microscopy techniques, see chapter 1.8 in ref.6.) In particular, low-temperature STM provides exciting possibilities for arranging and studying matter on the nanoscale (7). STM creates images of the charge density of electrons at the Fermi level (8). In some cases, all surface atoms develop a local maximum of the charge density at the Fermi level and thus all surface atoms are observable by STM. In other cases, like GaAs (110), one type of surface atoms (As) is observable at negative sample bias and the other type (Ga) at positive sample bias (9). The graphite (0001) surface also has two types of atoms in the basis of the hexagonal surface unit cell (␣ and ␤, see Fig. 1A), but only one of these atom types is observed by STM, independent of the bias polarity. The...

The charge distribution in atoms with closed electron shells is spherically symmetric, whereas atoms with partially filled shells can form covalent bonds with pointed lobes of increased charge density. Covalent bonding in the bulk can also affect surface atoms, leading to four tiny humps spaced by less than 100 picometers in the charge density of adatoms on a (001) tungsten surface. We imaged these charge distributions by means of atomic force microscopy with the use of a light-atom probe (a graphite atom), which directly measured high-order force derivatives of its interaction with a tungsten tip. This process revealed features with a lateral distance of only 77 picometers.

Theory predicts that the currents in scanning tunneling microscopy (STM) and the attractive forces measured in atomic force microscopy (AFM) are directly related. Atomic images obtained in an attractive AFM mode should therefore be redundant because they should be similar to STM. Here, we show that while the distance dependence of current and force is similar for graphite, constant-height AFM-and STM images differ substantially depending on distance and bias voltage. We perform spectroscopy of the tunneling current, the frequency shift and the damping signal at high-symmetry lattice sites of the graphite (0001) surface. The dissipation signal is about twice as sensitive to distance as the frequency shift, explained by the Prandtl-Tomlinson model of atomic friction.The capability of scanning tunneling microscopy (STM) [1] and atomic force microscopy (AFM) [2] to resolve single atoms in real space makes them powerful tools for surface science and nanoscience. When operating AFM in the repulsive mode, protrusions in the images simply relate to the atoms because of Pauli's exclusion law. In contrast, the interpretation of STM images is more complicated. The Tersoff-Hamann approximation [3], valid for tips in an s-state, interprets STM images as a map of the charge density of the sample at the Fermi energy. Depending on the state of the tip, atoms can either be recorded as protrusions or holes, and tip changes can reverse the atomic contrast [4,5]. Theoretical predictions regarding the relation of forces and tunneling currents I state that tunneling currents and attractive forces are directly related, thus AFM would not provide any new physical insights over STM. Chen [5] has found that the square of the attractive energy between tip and sample should be proportional to I with experimental evidence in [6]. Hofer and Fisher [7] suggested that the interaction energy and I should be directly proportional, experimentally found in [8,9]. In this Letter, we investigate the experimental relationships between tunneling currents and conservative as well as dissipative forces for graphite probed with a W tip by performing local spectroscopy on specific lattice sites. While force spectroscopy on specific lattice sites [10] and combined force and tunneling spectroscopy on unspecific sample positions [8,9] have been performed before, the measurements reported here encompass site-specific spectra of currents and forces, supplemented by simultaneous constant-height measurements of currents and forces that allow a precise assessment of the validity of the theories regarding currents and forces in scanning probe experiments.In graphite (see Fig. 1), the electrons at E F are concentrated at the β sites, and only these atoms are 'seen' by STM at low-bias voltages. The state-of-theart method for atomic resolution force microscopy is frequency modulation AFM (FMAFM) [11], where the frequency shift ∆f of an oscillating cantilever with stiffness k, eigenfrequency f 0 and oscillation amplitude A is used as the imaging signal [12,13]. The b...

In frequency modulation atomic force microscopy, the stiffness, quality factor and oscillation amplitude of the cantilever are important parameters. While the first atomic resolution results were obtained with amplitudes of a few hundred ångstrom, it has subsequently been shown that smaller amplitudes should result in a better signal-to-noise ratio and an increased sensitivity to the short-range components of the tip-sample interaction. Stable oscillation at small amplitudes is possible if the product of stiffness and amplitude and the energy stored in the oscillating cantilever are large enough. For small amplitudes, stability can be achieved by using stiff cantilevers. Here, we discuss the physical requirements for small amplitude operation and present design criteria and technical details of the qPlus sensor, a self-sensing cantilever with large stiffness that allows small amplitude operation.

Abstract. The images obtained by atomic force microscopy (AFM) originate from a convolution of atomic tip and sample states. Since the vertical resolution of AFM is approaching the picometer level, the atomic and subatomic structure of the tip is becoming increasingly important. Here, we demonstrate the preparation of crystallographically oriented AFM tips by breaking a silicon wafer along its preferential cleavage planes. Assuming bulk termination, the front atom of this tip should expose a single dangling bond. Images derived with this tip are consistent with this speculated tip geometry and show unprecedented vertical distinction of the six different surface atom sites of the Si(111)-(7 × 7) structure. 07.79.Lh; 34.20.Cf; 68.37.E Recently, sub-atomic resolution on the surface of silicon (111)-(7 × 7) with frequency-modulation atomic force microscopy (FM-AFM) [1] has been demonstrated. The subatomic structure of the adatom images was attributed to a tip with a very special symmetry: a tip with a front atom exposing two unsaturated bonds. The experimental observation at subatomic resolution outlines the importance of both the chemical nature and the geometric orientation of the front atom with respect to its nearest neighbors in the tip. While the preparation of the silicon sample to obtain the 7 × 7 reconstruction is straightforward, the preparation of the tip is more challenging. Here, we report on the construction of a deliberately shaped tip with predetermined crystallographic orientation. PACS:Most force sensors for AFM are microfabricated, and the crystallographic orientation of the tip is determined by the manufacturing process of the whole cantilever. Typically, the tips of micromachined cantilevers point in the 100 direction of the crystallographic orientation between tip and sample is given by the tilt angle of the cantilever. To assure that the micromachined tip is closer to the flat sample than any other parts of the cantilever and mounting devices, tilt angles between 10 • and 25 • typically have to be applied. The angle between the orientations of tip and sample cannot be freely chosen. This constraint does not apply to force sensors based on a tuning fork ("qPlus" sensor, see Fig. 1 in [3]), since it is possible to attach large tips on these sensors with a deliberate crystallographic orientation.The natural cleavage planes of silicon are (111) planes, since the free surface energy is minimal for this orientation. Each Si-Si bond has a bonding energy of approximately 2.3 eV, and the density of unsaturated bonds (dangling bonds) is 7.8 nm −2 for the (111) orientation and 13.6 nm −2 for the (100) orientation. Therefore, silicon exhibits a very strong preference to form (111) limited planes as boundaries of mesoscopic structures. This is nicely evident in the work of Baumgärtner et al., where silicon has been deposited by molecular beam epitaxy onto a Si (100) wafer through a square shaped 350 nm × 350 nm aperture. The resulting structure was a pyramid with (111) plane boundaries, rather than a pi...

The noise performance of the force sensor is crucial for optimizing the resolution in non-contact atomic force microscopy. Sensing forces in vacuum and low temperatures is even more demanding than at ambient conditions. Here we analyze the noise performance and the sensitivity of a force sensor based on a quartz tuning fork of which one of the prongs is ®xed (qPlus sensor). The noise characteristic of the qPlus sensor, optical and piezoresistive detection schemes at room temperature are compared and the qPlus sensor is investigated at low temperatures. The frequency variation of quartz tuning forks as a function of temperature is experimentally determined for the temperature range from 4 to 300 K. #