An analysis of double-quantum coherence ESR in an N-spin system: Analytical expressions and predictions.

Electron spin resonance pulsed dipolar spectroscopy (PDS) has become popular in protein 3D structure analysis. PDS studies yield distance distributions between a pair or multiple pairs of spin probes attached to protein molecules, which can be used directly in structural studies or as constraints in theoretical predictions. Double-quantum coherence (DQC) is a highly sensitive and accurate PDS technique to study protein structures in the solid state and under physiologically relevant conditions. In this work, we have derived analytical expressions for the DQC signal for a system with N-dipolar coupled spin-1/2 particles in the solid state. The expressions are integrated over the relevant spatial parameters to obtain closed form DQC signal expressions. These expressions contain the concentration-dependent "instantaneous diffusion" and the background signal. For micromolar and lower concentrations, these effects are negligible. An approximate analysis is provided for cases of finite pulses. The expressions obtained in this work should improve the analysis of DQC experimental data significantly, and the analytical approach could be extended easily to a wide range of magnetic resonance phenomena.

The Landau-Zener-Stückelberg-Majorana transition in the T2 ≪ T1 limit.

Landau-Zener-Stückelberg-Majorana (LZSM) transitions occur between quantum states when parameters in the system's Hamiltonian are varied continuously and rapidly. In magnetic resonance, losses in adiabatic rapid passage can be understood using the physics of LZSM transitions. Most treatments of LZSM transitions ignore the T2 dephasing of coherences, however. Motivated by ongoing work in magnetic resonance force microscopy, we employ the Bloch equations, coordinate transformation, and the Magnus expansion to derive expressions for the final magnetization following a rapid field sweep at fixed irradiation intensity that include T2 losses. Our derivation introduces an inversion-function, Fourier transform method for numerically evaluating highly oscillatory integrals. Expressions for the final magnetization are given for low and high irradiation intensity, valid in the T2≪T1 limit. Analytical results are compared to numerical simulations and nuclear magnetic resonance experiments. Our relatively straightforward calculation reproduces semiquantitatively the well known LZSM result in the T2→0 limit.

mmodel: A workflow framework to accelerate the development of experimental simulations.

Simulation has become an essential component of designing and developing scientific experiments. The conventional procedural approach to coding simulations of complex experiments is often error-prone, hard to interpret, and inflexible, making it hard to incorporate changes such as algorithm updates, experimental protocol modifications, and looping over experimental parameters. We present mmodel, a Python framework designed to accelerate the writing of experimental simulation packages. mmodel uses a graph-theory approach to represent the experiment steps and can rewrite its own code to implement modifications, such as adding a loop to vary simulation parameters systematically. The framework aims to avoid duplication of effort, increase code readability and testability, and decrease development time.

A Non-Perturbative, Low-Noise Surface Coating for Sensitive Force-Gradient Detection of Electron Spin Resonance in Thin Films.

The sensitivity of magnetic resonance force microscopy (MRFM) is limited by surface noise. Coating a thin-film polymer sample with metal has been shown to decrease, by orders of magnitude, sample-related force noise and frequency noise in MRFM experiments. Using both MRFM and inductively detected measurements of electron-spin resonance, we show that thermally evaporating a 12 nm gold layer on a 40 nm nitroxide-doped polystyrene film inactivates the nitroxide spin labels to a depth of 20 nm, making single-spin measurements difficult or impossible. We introduce a "laminated sample" protocol in which the gold layer is first evaporated on a sacrificial polymer. The sample is deposited on the room-temperature gold layer, removed using solvent lift-off, and placed manually on a coplanar waveguide. Electron spin resonance (ESR) of such a laminated sample was detected via MRFM at cryogenic temperatures using a high-compliance cantilever with an integrated 100-nm-scale cobalt tip. A 20-fold increase of spin signal was observed relative to a thin-film sample prepared instead with an evaporated metal coating. The observed signal is still somewhat smaller than expected, and we discuss possible remaining sources of signal loss.

Cryogenic positioning and alignment with micrometer precision in a magnetic resonance force microscope.

Aligning a microcantilever to an area of interest on a sample is a critical step in many scanning probe microscopy experiments, particularly those carried out on devices and rare, precious samples. We report a series of protocols that rapidly and reproducibly align a high-compliance microcantilever to a <10 µm sample feature under high vacuum and at cryogenic temperatures. The first set of protocols, applicable to a cantilever oscillating parallel to the sample surface, involve monitoring the cantilever resonance frequency while laterally scanning the tip to map the sample substrate through electrostatic interactions of the substrate with the cantilever. We demonstrate that when operating a cantilever a few micrometers from the sample surface, large shifts in the cantilever resonance frequency are present near the edges of a voltage-biased sample electrode. Surprisingly, these "edge-finder" frequency shifts are retained when the electrode is coated with a polymer film and a ∼10 nm thick metallic ground plane. The second series of methods, applicable to any scanning probe microscopy experiment, integrate a single-optical fiber to image line scans of the sample surface. The microscope modifications required for these methods are straightforward to implement, provide reliable micrometer-scale positioning, and decrease the experimental setup time from days to hours in a vacuum, cryogenic magnetic resonance force microscope.

Microsecond photocapacitance transients observed using a charged microcantilever as a gated mechanical integrator.

How light is converted to electricity in blends of organic donor and acceptor molecules is an unsettled question, partly because the spatial heterogeneity present in these blends makes them challenging to characterize. Although scanned-probe measurements have provided crucially important microscopic insights into charge generation and transport in these blends, achieving the subnanosecond time resolution needed to directly observe the fate of photogenerated charges has proven difficult. We use a charged microcantilever as a gated mechanical integrator to record photocapacitance indirectly by measuring the accumulated change in cantilever phase as a function of the time delay between precisely synchronized voltage and light pulses. In contrast with previous time-resolved scanned-probe photocapacitance measurements, the time resolution of this method is set by the rise and fall time of the voltage and light pulses and not by the inverse detection bandwidth. We demonstrate in an organic donor-acceptor blend the ability of this indirect, "phase-kick" technique to record multiexponential photocapacitance transients on time scales ranging from 40 µs to 10 ms. The technique's ability to measure subcycle, nanosecond charge dynamics is demonstrated by measuring the tens of nanosecond sample electrical charging time.

Correction: Dynamic nuclear polarization in a magnetic resonance force microscope experiment.

Correction for 'Dynamic nuclear polarization in a magnetic resonance force microscope experiment' by Corinne E. Isaac et al., Phys. Chem. Chem. Phys., 2016, 18, 8806-8819.

Dynamic nuclear polarization in a magnetic resonance force microscope experiment.

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 T, became observable when microwave irradiation was applied to saturate the electron spins. The resulting NMR signal's size, buildup time, dependence on microwave power, and dependence on irradiation frequency was consistent with a transfer of magnetization from electron spins to nuclear spins. Due to the presence of an inhomogeneous magnetic field introduced by the cantilever's magnetic tip, the electron spins in the sample were saturated in a microwave-resonant slice 10's of nm thick. The spatial distribution of the nuclear polarization enhancement factor ε was mapped by varying the frequency of the applied radiowaves. The observed enhancement factor was zero for spins in the center of the resonant slice, was ε = +10 to +20 for spins proximal to the magnet, and was ε = -10 to -20 for spins distal to the magnet. We show that this bipolar nuclear magnetization profile is consistent with cross-effect DNP in a ∼10(5) T m(-1) magnetic field gradient. Potential challenges associated with generating and using DNP-enhanced nuclear magnetization in a nanometer-resolution magnetic resonance imaging experiment are elucidated and discussed.

Electric force microscopy of semiconductors: theory of cantilever frequency fluctuations and noncontact friction.

An electric force microscope employs a charged atomic force microscope probe in vacuum to measure fluctuating electric forces above the sample surface generated by dynamics of molecules and charge carriers. We present a theoretical description of two observables in electric force microscopy of a semiconductor: the spectral density of cantilever frequency fluctuations (jitter), which are associated with low-frequency dynamics in the sample, and the coefficient of noncontact friction, induced by higher-frequency motions. The treatment is classical-mechanical, based on linear response theory and classical electrodynamics of diffusing charges in a dielectric continuum. Calculations of frequency jitter explain the absence of contributions from carrier dynamics to previous measurements of an organic field effect transistor. Calculations of noncontact friction predict decreasing friction with increasing carrier density through the suppression of carrier density fluctuations by intercarrier Coulomb interactions. The predicted carrier density dependence of the friction coefficient is consistent with measurements of the dopant density dependence of noncontact friction over Si. Our calculations predict that in contrast to the measurement of cantilever frequency jitter, a noncontact friction measurement over an organic semiconductor could show appreciable contributions from charge carriers.

Long-lived frequency shifts observed in a magnetic resonance force microscope experiment following microwave irradiation of a nitroxide spin probe.

We introduce a spin-modulation protocol for force-gradient detection of magnetic resonance that enables the real-time readout of longitudinal magnetization in an electron spin resonance experiment involving fast-relaxing spins. We applied this method to observe a prompt change in longitudinal magnetization following the microwave irradiation of a nitroxide-doped perdeuterated polystyrene film having an electron spin-lattice relaxation time of [Formula: see text]. The protocol allowed us to discover a large, long-lived cantilever frequency shift. Based on its magnitude, lifetime, and field dependence, we tentatively attribute this persistent signal to deuteron spin magnetization created via transfer of polarization from nitroxide spins.

Magnetic Resonance Force Microscopy Detected Long-Lived Spin Magnetization.

Magnetic resonance force microscopy (MRFM), which combines magnetic resonance imaging with scanning probe microscopy together, is capable of performing ultra-sensitive detection of spin magnetization. In an attempt to observe dynamic nuclear polarization (DNP) in an MRFM experiment, which could possibly further improve its sensitivity towards a single proton spin, a film of perdeuterated polystyrene doped with a nitroxide electron-spin probe was prepared. A high-compliance cantilever with a 4 µm diameter magnetic tip was brought near the film at a temperature of 7.3 K and in a background magnetic field of ~0.6 T. The film was irradiated with 16.7 GHz microwaves while the resulting transient change in cantilever frequency was recorded in real time. In addition to observing the expected prompt change in cantilever frequency due to saturation of the nitroxide's electron-spin magnetization, we observed a persistent cantilever frequency change. Based on its magnitude, lifetime, and field dependence, we tentatively attribute the persistent signal to polarized deuteron magnetization created via transfer of magnetization from electron spins. Further measurements of the persistent signal's dependence on the cantilever amplitude and tip-sample separation are presented and explained by the cross-effect DNP mechanism in high magnetic field gradients.

Charge carrier dynamics and interactions in electric force microscopy.

In electric force microscopy, a charged atomic force microscope tip in vacuum senses a fluctuating electrical force generated by the sample. Such measurements can in principle probe electrical noise generated by moving charge carriers in an organic semiconductor. We present a theory of cantilever frequency fluctuations in electric force microscopy, driven by coupled charge carrier dynamics and dielectric fluctuations. The connection between observable frequency fluctuations in electric force microscopy and the Casimir-Lifshitz force is described. This classical electrodynamic calculation is based on Maxwell's equations coupled to diffusive carrier transport. The effects of carrier transport and inter-carrier interactions on the spectrum of cantilever frequency noise are elucidated. We find that a simplified model of freely diffusing carriers can overestimate cantilever frequency noise by several orders of magnitude because of the neglect of interactions. Electric force microscopy measurements on an organic field effect transistor are reported and qualitatively interpreted in terms of the suppression of electrical noise from charge carriers by Coulomb interactions.

Spectroscopic imaging of photopotentials and photoinduced potential fluctuations in a bulk heterojunction solar cell film.

We present spatially resolved photovoltage spectra of a bulk heterojunction solar cell film composed of phase-separated poly(9,9'-dioctylfluorene-co-benzothiadiazole) (F8BT) and poly(9,9'-dioctylfluorene-co-bis-N,N'-(4-butylphenyl)-bis-N,N'-phenyl-1,4-phenylenediamine) (PFB) polymers prepared on ITO/PEDOT:PSS and aluminum substrates. Over both PFB- and F8BT-rich domains, the photopotential spectra were found to be proportional to a linear combination of the polymers' absorption spectra. Charge trapping in the film was studied using photopotential fluctuation spectroscopy, in which low-frequency photoinduced electrostatic potential fluctuations were measured by observing noise in the oscillation frequency of a nearby charged atomic force microscope cantilever. Over both F8BT- and PFB-rich regions, the magnitude, distance dependence, frequency dependence, and illumination wavelength dependence of the observed cantilever frequency noise are consistent with photopotential fluctuations arising from stochastic light-driven trapping and detrapping of charges in F8BT. Taken together, our findings suggest a microscopic mechanism by which intermixing of phases leads to charge trapping and thereby to suppressed open-circuit voltage and decreased efficiency in this prototypical bulk heterojunction solar cell film.

High-gradient nanomagnets on cantilevers for sensitive detection of nuclear magnetic resonance.

Detection of magnetic resonance as a force between a magnetic tip and nuclear spins has previously been shown to enable sub-10 nm resolution 1H imaging. Maximizing the spin force in such a magnetic resonance force microscopy (MRFM) experiment demands a high field gradient. In order to study a wide range of samples, it is equally desirable to locate the magnetic tip on the force sensor. Here we report the development of attonewton-sensitivity cantilevers with high-gradient cobalt nanomagnet tips. The damage layer thickness and saturation magnetization of the magnetic material were characterized by X-ray photoelectron spectroscopy and superconducting quantum interference device magnetometry. The coercive field and saturation magnetization of an individual tip were quantified in situ using frequency-shift cantilever magnetometry. Measurements of cantilever dissipation versus magnetic field and tip­sample separation were conducted. MRFM signals from protons in a polystyrene film were studied versus rf irradiation frequency and tip­sample separation, and from this data the tip field and tip-field gradient were evaluated. Magnetic tip performance was assessed by numerically modeling the frequency dependence of the magnetic resonance signal. We observed a tip-field gradient ∂B(z)(tip)/∂z estimated to be between 4.4 and 5.4 MT m(­1), which is comparable to the gradient used in recent 4 nm resolution 1H imaging experiments and larger by nearly an order of magnitude than the gradient achieved in prior magnet-on-cantilever MRFM experiments.

Switching through intermediate states seen in a single nickel nanorod by cantilever magnetometry.

In-plane to out-of-plane magnetization switching in a single nickel nanorod affixed to an attonewton-sensitivity cantilever was studied at cryogenic temperatures. We observe multiple sharp, simultaneous transitions in cantilever frequency, dissipation, and frequency jitter associated with magnetic switching through distinct intermediate states. These findings suggest a new route for detecting magnetic fields at the nanoscale.

Single-shot nuclear magnetization recovery curves with force-gradient detection.

We measure the spin-lattice relaxation time as a function of sample temperature in GaAs in a real-time single-shot inversion recovery experiment using spin force gradients acting on a magnetic tipped cantilever. After inverting 69Ga spins localized near the magnet with a single 20 ms adiabatic rapid passage sweep, the spins' magnetization recovery was passively tracked by recording the cantilever's frequency change, which is proportional to the longitudinal component of the spins' magnetization. The cantilever's frequency was recorded for a time 3*T1 for sample temperatures ranging from 4.8 to 25 K. The temperature dependence was observed for the 69Ga quadrupolar relaxation interaction.

A Unified Picture of Cantilever Frequency-Shift Measurements of Magnetic Resonance.

We report a unified framework describing all existing protocols for spin manipulation and signal creation in frequency-modulation magnetic resonance force microscopy using classical perturbation theory. The framework is well suited for studying the dependence of the frequency shift on the cantilever amplitude via numerical simulation. We demonstrate the formalism by recovering an exact result for a single spin signal and by simulating, for the first time as a function of cantilever amplitude, the frequency shift due to a volume of noninteracting spins inverted by an adiabatic rapid passage. We show that an optimal cantilever amplitude exists that maximizes the signal. Our findings suggest that understanding the amplitude dependence of the spin signal will be important for designing future high-sensitivity experiments.

Dielectric fluctuations over polymer films detected using an atomic force microscope.

We present a systematic study of the frequency noise experienced by a charged atomic force microscope cantilever due to thermal dielectric fluctuations in a thin-film sample of poly(vinyl acetate). Here, the tip of the commercial atomic force microscope cantilever oscillates in the conventional direction, normal to the surface of the film, complementing our previous studies of dielectric fluctuations carried out using an ultrasensitive custom-fabricated cantilever oscillating parallel to the film surface. We show that frequency noise induced by mechanical vibrations can be distinguished from frequency noise resulting from thermal dielectric fluctuations by the dependence on applied voltage and tip-sample separation, allowing molecular information to be unambiguously extracted. A linear response theory for cantilever frequency noise over a molecular material correctly reproduces the observed dependences on frequency, voltage, and tip-sample separation. The technique is shown to measure primarily fluctuations in the electric field gradient over the surface, which in these measurements are generated by orientational relaxation of polar polymer segments.

Spectroscopic characterization of charged defects in polycrystalline pentacene by time- and wavelength-resolved electric force microscopy.

Spatial maps of topography and trapped charge are acquired for polycrystalline pentacene thin-film transistors using electric and atomic force microscopy. In regions of trapped charge, the rate of trap clearing is studied as a function of the wavelength of incident radiation.