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.

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.

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.

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.

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.

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.

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.

Scanned-probe detection of electron spin resonance from a nitroxide spin probe.

We report an approach that extends the applicability of ultrasensitive force-gradient detection of magnetic resonance to samples with spin-lattice relaxation times (T (1)) as short as a single cantilever period. To demonstrate the generality of the approach, which relies on detecting either cantilever frequency or phase, we used it to detect electron spin resonance from a T (1) = 1 ms nitroxide spin probe in a thin film at 4.2 K and 0.6 T. By using a custom-fabricated cantilever with a 4 microm-diameter nickel tip, we achieve a magnetic resonance sensitivity of 400 Bohr magnetons in a 1 Hz bandwidth. A theory is presented that quantitatively predicts both the lineshape and the magnitude of the observed cantilever frequency shift as a function of field and cantilever-sample separation. Good agreement was found between nitroxide T (1) 's measured mechanically and inductively, indicating that the cantilever magnet is not an appreciable source of spin-lattice relaxation here. We suggest that the new approach has a number of advantages that make it well suited to push magnetic resonance detection and imaging of nitroxide spin labels in an individual macromolecule to single-spin sensitivity.

Photogenerated exciton dissociation in highly coupled lead salt nanocrystal assemblies.

Internanocrystal coupling induced excitons dissociation in lead salt nanocrystal assemblies is investigated. By combining transient photoluminescence spectroscopy, grazing incidence small-angle X-ray scattering, and time-resolved electric force microscopy, we show that excitons can dissociate, without the aid of an external bias or chemical potential gradient, via tunneling through a potential barrier when the coupling energy is comparable to the exciton binding energy. Our results have important implications for the design of nanocrystal-based optoelectronic devices.

Quantifying electric field gradient fluctuations over polymers using ultrasensitive cantilevers.

An ultrasensitive cantilever, oscillating parallel to a surface in vacuum, is used to probe weak thermal electric field gradient fluctuations over thin polymer films. We measure the power spectrum of cantilever frequency fluctuations as a function of cantilever height and voltage over polymers of various compositions and thicknesses. The data are well described by a linear-response theory that calculates stochastic electric fields arising from thermally driven dielectric fluctuations.

Dielectric fluctuations in force microscopy: noncontact friction and frequency jitter.

Electric force microscopy, in which a charged probe oscillates tens to hundreds of nanometers above a sample surface, provides direct mechanical detection of relaxation in molecular materials. Noncontact friction, the damping of the probe's motions, reflects the dielectric function at the resonant frequency of the probe, while fluctuations in the probe frequency are induced by slower molecular motions. We present a unified theoretical picture of both measurements, which relates the noncontact friction and the power spectrum of the frequency jitter to dielectric properties of the sample and to experimental geometry. Each observable is related to an equilibrium correlation function associated with electric field fluctuations, which is determined by two alternative, complementary strategies for a dielectric continuum model of the sample. The first method is based on the calculation of a response function associated with the polarization of the dielectric by a time-varying external charge distribution. The second approach employs a stochastic form of Maxwell's equations, which incorporate a fluctuating electric polarization, to compute directly the equilibrium correlation function in the absence of an external charge distribution. This approach includes effects associated with the propagation of radiation. In the experimentally relevant limit that the tip-sample distance is small compared to pertinent wavelengths of radiation, the two methods yield identical results. Measurements of the power spectrum of frequency fluctuations of an ultrasensitive cantilever together with measurements of the noncontact friction over a poly(methylmethacrylate) film are used to estimate the minimum experimentally detectable frequency jitter. The predicted jitter for this polymer is shown to exceed this threshold, demonstrating the feasibility of the measurement.

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.

Time-resolved electric force microscopy of charge trapping in polycrystalline pentacene.

Here we introduce time-resolved electric force microscopy measurements to directly and locally probe the kinetics of charge trap formation in a polycrystalline pentacene thin-film transistor. We find that the trapping rate depends strongly on the initial concentration of free holes and that trapped charge is highly localized. The observed dependence of trapping rate on the hole chemical potential suggests that the trapping process should not be viewed as a filling of midgap energy levels, but instead as a process in which the very creation of trapped states requires the presence of free holes.

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.

Noncontact dielectric friction.

Dielectric fluctuations are shown to be the dominant source of noncontact friction in high-sensitivity scanning probe microscopy of dielectric materials. Recent measurements have directly determined the friction acting on custom-fabricated single-crystal silicon cantilevers whose capacitively charged tips are located 3-200 nm above thin films of poly(methyl methacrylate), poly(vinyl acetate), and polystyrene. Differences in measured friction among these polymers are explained here by relating electric field fluctuations at the cantilever tip to dielectric relaxation of the polymer.

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.

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.

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.