Using a thermodynamic approach based upon the fluctuation-dissipation theorem we quantify the stochastic dynamics of rectangular and V-shaped microscale cantilevers immersed in a viscous fluid. We show that the stochastic cantilever dynamics as measured by the displacement of the cantilever tip or by the angle of the cantilever tip are different. We trace this difference to contributions from the higher modes of the cantilever. We find that contributions from the higher modes are significant in the dynamics of the cantilever tip-angle. For the V-shaped cantilever the resulting flow field is three-dimensional and complex in contrast to what is found for a long and slender rectangular cantilever. Despite this complexity the stochastic dynamics can be predicted using a two-dimensional model with an appropriately chosen length scale. We also quantify the increased fluid dissipation that results as a V-shaped cantilever is brought near a solid planar boundary.
We consider the stochastic dynamics of an array of two closely spaced atomic force microscope cantilevers in a viscous fluid for use as a possible biomolecule sensor. The cantilevers are not driven externally, as is common in applications of atomic force microscopy, and we explore the stochastic cantilever dynamics due to the constant buffeting of fluid particles by Brownian motion. The stochastic dynamics of two adjacent cantilevers are correlated due to long range effects of the viscous fluid. Using a recently proposed thermodynamic approach the hydrodynamic correlations are quantified for p…
We report a new spin manipulation protocol for periodically reversing the sample magnetization for Magnetic Resonance Force Microscopy. The protocol modulates the microwave excitation frequency synchronously with the position of the oscillating detection cantilever, thus allowing manipulation of the spin magnetization independent of both magnetic field gradient strength and cantilever response time. This allows continuous variation of the detected sample volume and is effective regardless of spin relaxation rate. This enhanced flexibility improves the utility of MRFM as a generally applicable …
We analyze the back-action influence of nuclear spins on the motion of the cantilever of a magnetic force resonance microscope. We calculate the contribution of nuclear spins to the damping and frequency shift of the cantilever. We show that, at the Rabi frequency, the energy exchange between the cantilever and the spin system cools or heats the cantilever depending on the sign of the high-frequency detuning. We also show that the spin noise leads to a significant damping of the cantilever motion.
An ongoing challenge in atomic force microscope (AFM) experiments is the quantitative measurement of cantilever motion. The vast majority of AFMs use the optical beam deflection (OBD) method to infer the deflection of the cantilever. The OBD method is easy to implement, has impressive noise performance and tends to be mechanically robust. However, it represents an indirect measurement of the cantilever displacement, since it is fundamentally an angular rather than a displacement measurement. Here, we demonstrate a metrological AFM that combines an OBD sensor with a laser Doppler vibrometer (LD…
Atomic force microscope (AFM) users often calibrate the spring constants of cantilevers using functionality built into individual instruments. This is performed without reference to a global standard, which hinders robust comparison of force measurements reported by different laboratories. In this article, we describe a virtual instrument (an internet-based initiative) whereby users from all laboratories can instantly and quantitatively compare their calibration measurements to those of others - standardising AFM force measurements - and simultaneously enabling non-invasive calibration of AFM …
A common use for atomic force microscopy is to quantify local forces through tip-sample interactions between the probe tip and a sample surface. The accuracy of these measurements depends on the accuracy to which the cantilever spring constant is known. Recent work has demonstrated that the measured spring constant of a cantilever can vary up to a factor of two, even for the exact same cantilever measured by different users on different microscopes. Here we demonstrate that a standard method for calibrating the spring constant (using the oscillations due to thermal energy) is susceptible to am…
Individual electron spins have been observed using magnetic resonance in combination with a number of distinct detection approaches. The coordinates of an individual electron spin can then in principle be determined by introducing a 10 to 100 nm diameter magnetic needle, scanning the needle, and collecting signal as a function of the needle's position. Although individual electrons have recently been localized with nanometer precision in this way using a nitrogen-vacancy center in diamond as the spin detector, the experiment's low signal-to-noise ratio limited acquisition to two-dimensional sc…
We present a "nanoladder" geometry that minimizes the mechanical dissipation of ultrasensitive cantilevers. A nanoladder cantilever consists of a lithographically patterned scaffold of rails and rungs with feature size $\sim$ 100 nm. Compared to a rectangular beam of the same dimensions, the mass and spring constant of a nanoladder are each reduced by roughly two orders of magnitude. We demonstrate a low force noise of $158 (+62)(-42)\,$zN and $190 (+42)(-33)\,$zN in a one-Hz bandwidth for devices made from silicon and diamond, respectively, measured at temperatures between 100--150 mK. As opp…
Atomic force microscopy is based on tip sample interaction, which is determined by the properties of tip and sample. Unfortunately, in particular in ambient conditions the tip as well as the sample are contaminated, and it is not clear how this contamination may affect data in Atomic Force Microscopy (AFM) applications. In the present work we propose to use on the one hand AFM imaging of the cantilever chips and on the other hand multidimensional AFM spectroscopy techniques to characterize the state of contamination of the tip sample system. We find that typically AFM cantilevers may be severe…
The frequency-dependent amplitude and phase in piezoresponse force microscopy (PFM) measurements are shown to be a consequence of the Euler-Bernoulli (EB) dynamics of atomic force microscope (AFM) cantilever beams used to make the measurements. Changes in the cantilever mode shape as a function of changes in the boundary conditions determine the sensitivity of cantilevers to forces between the tip and the sample. Conventional PFM and AFM measurements are made with the motion of the cantilever measured at one optical beam detector (OBD) spot location. A single OBD spot location provides a limit…
Exotic spin-dependent interactions may be generated by exchanging hypothetical bosons that have been proposed to solve some mysteries in physics by theories beyond the standard model of particle physics. The search for such interactions can be conducted by tabletop scale experiments using high precision measurement techniques. Here we report an experiment to explore the parity-odd interaction between moving polarized electrons and unpolarized nucleons using a magnetic force microscope. The polarized electrons are provided by the magnetic tip at the end of a silicon cantilever, and their polari…
We report achieving enhanced nuclear magnetization in a magnetic resonance force microscope experiment at 0.6 tesla and 4.2 kelvin using the dynamic nuclear polarization (DNP) effect. In our experiments a microwire coplanar waveguide delivered radiowaves to excite nuclear spins and microwaves to excite electron spins in a 250 nm thick nitroxide-doped polystyrene sample. Both electron and proton spin resonance were observed as a change in the mechanical resonance frequency of a nearby cantilever having a micron-scale nickel tip. NMR signal, not observable from Curie-law magnetization at 0.6 tes…
We constructed a $^3$He magnetic force microscope operating at the base temperature of 300 mK under a vector magnetic field of 2-2-9 T in the $x-y-z$ direction. Fiber optic interferometry as a detection scheme is employed in which two home-built fiber walkers are used for the alignment between the cantilever and the optical fiber. The noise level of the laser interferometer is close to its thermodynamic limit. The capabilities of the sub-Kelvin and vector field are demonstrated by imaging the coexistence of magnetism and superconductivity in a ferromagnetic superconductor (ErNi$_2$B$_2$C) at $…
We perform simulations and experiments on an oscillating atomic force microscope cantilever approaching a surface, where the intermodulation response of the cantilever driven with two pure harmonic tones is investigated. In the simulations, the tip and surface interact with a conservative nonlinear force, and the parameter space of approach distance and surface stiffness is explored. Approach experiments are carried out on three surfaces with widely varying stiffness. Qualitative similarities between simulations and experiment can be seen, but quantitative comparison is difficult due to the ov…
Various methods of force measurement with the Atomic Force Microscope (AFM) are compared for their ability to accurately determine the tip-surface force from analysis of the nonlinear cantilever motion. It is explained how intermodulation, or the frequency mixing of multiple drive tones by the nonlinear tip-surface force, can be used to concentrate the nonlinear motion in a narrow band of frequency near the cantilevers fundamental resonance, where accuracy and sensitivity of force measurement are greatest. Two different methods for reconstructing tip-surface forces from intermodulation spectra…
It is predicted that in force microscopy the quantum fluctuations responsible for the Casimir force can be directly observed as temperature-independent force fluctuations having spectral density $9π/(40\ln(4/e)) \hbar δk$, where $\hbar$ is Planck's constant and $δk$ is the observed change in spring constant as the microscope tip approaches a sample. For typical operating parameters the predicted force noise is of order $10^{-18}$ Newton in one Hertz of bandwidth. The Second Law is respected via the fluctuation-dissipation theorem. For small tip-sample separations the cantilever damping is pred…
Thermal fluctuation of the cantilever position sets a fundamental limit for the precision of any Scanning Force Microscope. In the present work we analyse how these fluctuations limit the determination of the resonance frequency of the tip-sample system. The basic principles of frequency detection in Dynamic Scanning Force Microscopy are revised and the precise response of a typical frequency detection unit to thermal fluctuation of the cantilever is analysed in detail. A general relation for thermal frequency noise is found as a function of measurement bandwidth and cantilever oscillation. Fo…
We present an alternative approach to pump-probe spectroscopy for measuring fast charge dynamics with an atomic force microscope (AFM). Our approach is based on coherent multifrequency lock-in measurement of the intermodulation between a mechanical drive and an optical or electrical excitation. In response to the excitation, the charge dynamics of the sample is reconstructed by fitting a theoretical model to the measured frequency spectrum of the electrostatic force near resonance of the AFM cantilever. We discuss the time resolution, which in theory is limited only by the measurement time, bu…
The possibility of the mechanical detection of the Casimir friction using the non-contact force microscope is discussed. On a SiO2 tip situated above a graphene-covered SiO2 substrate will act the frictional drag force mediated by a fluctuating electromagnetic field produced by a current in the graphene sheet. This friction force will produce the bending of the cantilever, which can be measured by state-of-art non-contact force microscope. Both the thermal and quantum contributions to the Casimir frictional drag force can be studied using this experimental setup. This result paves the ways for…
The Transient Fluctuation Theorem is used to calibrate an Atomic Force Microscope by measuring the fluctuations of the work performed by a time dependent force applied between a collo{ï}dal probe and the surface. From this measure one can easily extract the value of the interaction force and the relevant parameters of the cantilever. The results of this analysis are compared with those obtained by standard calibration methods. a) present adress: ISIS, Univ.
The functionalization of an Atomic Force Microscope (AFM) cantilever with a colloidal bead is a widely used technique when the geometry between the probe and the sample must be controlled, particularly in force spectroscopy. But some questions remain: how does a bead glued at the end of a cantilever influence its mechanical response ? And more important for quantitative measurements, can we still determine the stiffness of the AFM probe with traditional techniques? In this article, the influence of a colloidal mass loading on the eigenmodes shape and resonant frequency is investigated by measu…
Using an ultra-low temperature, high magnetic field scanning probe microscope, we have measured electric potentials of a deeply buried two dimensional electron gas (2DEG). Relying on the capacitive coupling between the 2DEG and a resonant tip/cantilever structure, we can extract electrostatic potential information of the 2DEG from the dynamics of the oscillator. We present measurements using a quartz tuning fork oscillator and a 2DEG with a cleaved edge overgrowth structure. The sensitivity of the quartz tuning fork as force sensor is demonstrated by observation of Shubnikov de Haas oscillatio…
Artificial diamond is created by exposing graphite to pressures on the order of 10\,GPa and temperatures of about 2000\,K. Here, we provide evidence that the pressure exerted by the tip of an atomic force microscope onto graphene over the carbon buffer layer of silicon carbide can lead to a temporary transition of graphite to diamond on the atomic scale. We perform atomic force microscopy with CO terminated tips and copper oxide (CuOx) tips to image graphene and to induce the structural transition. For a local transition, DFT predicts that a repulsive barrier of $\approx13$\,nN, followed by a …
Knowledge of surface forces is the key to understanding a large number of processes in fields ranging from physics to material science and biology. The most common method to study surfaces is dynamic atomic force microscopy (AFM). Dynamic AFM has been enormously successful in imaging surface topography, even to atomic resolution, but the force between the AFM tip and the surface remains unknown during imaging. Here, we present a new approach that combines high accuracy force measurements and high resolution scanning. The method, called amplitude-dependence force spectroscopy (ADFS) is based on…
Atomically-resolved imaging and force measurements using the atomic force microscope (AFM) are performed most commonly in a frequency-modulation (FM) mode. This has led to spectacular results, including direct observation of the atomic structure of complex molecules and quantification of chemical and frictional forces at the atomic scale. We address here a critical question: Is recovery of force from the measured frequency shift experienced by the AFM cantilever ill-posed - that is, unreliable in the presence of (unavoidable) measurement uncertainty? Resolution of this issue underlies all forc…
Near-field force and energy exchange between two objects due to quantum electrodynamic fluctuations give rise to interesting phenomena such as Casimir and van der Waals forces, and thermal radiative transfer exceeding Planck's theory of blackbody radiation. Although significant progress has been made in the past on the precise measurement of Casimir force related to zero-point energy, experimental demonstration of near-field enhancement of radiative heat transfer is difficult. In this work, we present a sensitive technique of measuring near-field radiative transfer between a microsphere and a …
