Decoherence of Near-Surface Nitrogen-Vacancy Centers Due to Electric Field Noise.

We show that electric field noise from surface charge fluctuations can be a significant source of spin decoherence for near-surface nitrogen-vacancy (NV) centers in diamond. This conclusion is based on the increase in spin coherence observed when the diamond surface is covered with high-dielectric-constant liquids, such as glycerol. Double-resonance experiments show that improved coherence occurs even though the coupling to nearby electron spins is unchanged when the liquid is applied. Multipulse spin-echo experiments reveal the effect of glycerol on the spectrum of NV frequency noise.

Proton magnetic resonance imaging using a nitrogen-vacancy spin sensor.

Magnetic resonance imaging, with its ability to provide three-dimensional, elementally selective imaging without radiation damage, has had a revolutionary impact in many fields, especially medicine and the neurosciences. Although challenging, its extension to the nanometre scale could provide a powerful new tool for the nanosciences, especially if it can provide a means for non-destructively visualizing the full three-dimensional morphology of complex nanostructures, including biomolecules. To achieve this potential, innovative new detection strategies are required to overcome the severe sensitivity limitations of conventional inductive detection techniques. One successful example is magnetic resonance force microscopy, which has demonstrated three-dimensional imaging of proton NMR with resolution on the order of 10 nm, but with the requirement of operating at cryogenic temperatures. Nitrogen-vacancy (NV) centres in diamond offer an alternative detection strategy for nanoscale magnetic resonance imaging that is operable at room temperature. Here, we demonstrate two-dimensional imaging of (1)H NMR from a polymer test sample using a single NV centre in diamond as the sensor. The NV centre detects the oscillating magnetic field from precessing protons as the sample is scanned past the NV centre. A spatial resolution of ∼12 nm is shown, limited primarily by the scan resolution.

Multipulse double-quantum magnetometry with near-surface nitrogen-vacancy centers.

We discuss multipulse magnetometry that exploits all three magnetic sublevels of the S=1 nitrogen-vacancy center in diamond to achieve enhanced magnetic field sensitivity. Based on dual frequency microwave pulsing, the scheme is twice as sensitive to ac magnetic fields as conventional two-level magnetometry. We derive the spin evolution operator for dual frequency microwave excitation and show its effectiveness for double-quantum state swaps. Using multipulse sequences of up to 128 pulses under optimized conditions, we show enhancement of the SNR by up to a factor of 2 in detecting NMR statistical signals, with a 4× enhancement theoretically possible.

Nanoscale nuclear magnetic resonance with a nitrogen-vacancy spin sensor.

Extension of nuclear magnetic resonance (NMR) to nanoscale samples has been a longstanding challenge because of the insensitivity of conventional detection methods. We demonstrated the use of an individual, near-surface nitrogen-vacancy (NV) center in diamond as a sensor to detect proton NMR in an organic sample located external to the diamond. Using a combination of electron spin echoes and proton spin manipulation, we showed that the NV center senses the nanotesla field fluctuations from the protons, enabling both time-domain and spectroscopic NMR measurements on the nanometer scale.

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.

Isotope-selective detection and imaging of organic nanolayers.

Magnetic resonance force microscopy (MRFM) makes use of the spectroscopic nature of magnetic resonance to add unambiguous elemental selectivity to scanning probe microscopy. We show isotopic selectivity of MRFM for three nuclei, (1)H, (31)P, and (13)C, in organic materials. We also detect a roughly 1 nm thick layer of naturally occurring adsorbates on a gold surface by measuring the magnetic resonance signal of the hydrogen contained in the layer. Finally, we detect the signal from hydrogen present on a carbon nanotube and use it to perform a three-dimensional magnetic resonance image of the 10 nm diameter object.

Nuclear double resonance between statistical spin polarizations.

We demonstrate nuclear double resonance for nanometer-scale volumes of spins where random fluctuations rather than Boltzmann polarization dominate. When the Hartmann-Hahn condition is met in a cross-polarization experiment, flip-flops occur between two species of spins and their fluctuations become coupled. We use magnetic resonance force microscopy to measure this effect between 1H and 13C spins in 13C-enriched stearic acid. The development of a cross-polarization technique for statistical ensembles adds an important tool for generating chemical contrast in nanometer-scale magnetic resonance.

Nanoscale magnetic resonance imaging.

We have combined ultrasensitive magnetic resonance force microscopy (MRFM) with 3D image reconstruction to achieve magnetic resonance imaging (MRI) with resolution <10 nm. The image reconstruction converts measured magnetic force data into a 3D map of nuclear spin density, taking advantage of the unique characteristics of the "resonant slice" that is projected outward from a nanoscale magnetic tip. The basic principles are demonstrated by imaging the (1)H spin density within individual tobacco mosaic virus particles sitting on a nanometer-thick layer of adsorbed hydrocarbons. This result, which represents a 100 million-fold improvement in volume resolution over conventional MRI, demonstrates the potential of MRFM as a tool for 3D, elementally selective imaging on the nanometer scale.

Nuclear spin relaxation induced by a mechanical resonator.

We report on measurements of the spin lifetime of nuclear spins strongly coupled to a micromechanical cantilever as used in magnetic resonance force microscopy. We find that the rotating-frame correlation time of the statistical nuclear polarization is set by the magnetomechanical noise originating from the thermal motion of the cantilever. Evidence is based on the effect of three parameters: (1) the magnetic field gradient (the coupling strength), (2) the Rabi frequency of the spins (the transition energy), and (3) the temperature of the low-frequency mechanical modes. Experimental results are compared to relaxation rates calculated from the spectral density of the magnetomechanical noise.

Feedback cooling of a cantilever's fundamental mode below 5 mK.

We cool the fundamental mechanical mode of an ultrasoft silicon cantilever from a base temperature of 2.2 K down to 2.9+/-0.3 mK using active optomechanical feedback. The lowest observed mode temperature is consistent with limits determined by the properties of the cantilever and by the measurement noise. For high feedback gain, the driven cantilever motion is found to suppress or "squash" the optical interferometer intensity noise below the shot noise level.

Role of spin noise in the detection of nanoscale ensembles of nuclear spins.

When probing nuclear spins in materials on the nanometer scale, random fluctuations of the spin polarization will exceed the mean Boltzmann polarization for sample volumes below about (100 nm){3}. In this Letter, we use magnetic resonance force microscopy to observe nuclear spin fluctuations in real time. We show how reproducible measurements of the polarization variance can be obtained by controlling the spin correlation time and rapidly sampling a large number of independent spin configurations. This allows significant improvement in the signal-to-noise ratio for nanometer-scale magnetic resonance imaging.

Nuclear magnetic resonance imaging with 90-nm resolution.

Magnetic resonance imaging (MRI) is a powerful imaging technique that typically operates on the scale of millimetres to micrometres. Conventional MRI is based on the manipulation of nuclear spins with radio-frequency fields, and the subsequent detection of spins with induction-based techniques. An alternative approach, magnetic resonance force microscopy (MRFM), uses force detection to overcome the sensitivity limitations of conventional MRI. Here, we show that the two-dimensional imaging of nuclear spins can be extended to a spatial resolution better than 100 nm using MRFM. The imaging of 19F nuclei in a patterned CaF(2) test object was enabled by a detection sensitivity of roughly 1,200 nuclear spins at a temperature of 600 mK. To achieve this sensitivity, we developed high-moment magnetic tips that produced field gradients up to 1.4 x 10(6) T m(-1), and implemented a measurement protocol based on force-gradient detection of naturally occurring spin fluctuations. The resulting detection volume was less than 650 zeptolitres. This is 60,000 times smaller than the previous smallest volume for nuclear magnetic resonance microscopy, and demonstrates the feasibility of pushing MRI into the nanoscale regime.

Creating order from random fluctuations in small spin ensembles.

We demonstrate the ability to create spin order by using a magnetic resonance force microscope to harness the naturally occurring statistical fluctuations in small ensembles of electron spins. In one method, we hyperpolarized the spin system by selectively capturing the transient spin order created by the statistical fluctuations. In a second method, we took a more active approach and rectified the spin fluctuations by applying real-time feedback to the entire spin ensemble. The created spin order can be stored in the laboratory frame for a period on the order of the longitudinal relaxation time of 30 seconds and then read out.

Single spin detection by magnetic resonance force microscopy.

Magnetic resonance imaging (MRI) is well known as a powerful technique for visualizing subsurface structures with three-dimensional spatial resolution. Pushing the resolution below 1 micro m remains a major challenge, however, owing to the sensitivity limitations of conventional inductive detection techniques. Currently, the smallest volume elements in an image must contain at least 10(12) nuclear spins for MRI-based microscopy, or 10(7) electron spins for electron spin resonance microscopy. Magnetic resonance force microscopy (MRFM) was proposed as a means to improve detection sensitivity to the single-spin level, and thus enable three-dimensional imaging of macromolecules (for example, proteins) with atomic resolution. MRFM has also been proposed as a qubit readout device for spin-based quantum computers. Here we report the detection of an individual electron spin by MRFM. A spatial resolution of 25 nm in one dimension was obtained for an unpaired spin in silicon dioxide. The measured signal is consistent with a model in which the spin is aligned parallel or anti-parallel to the effective field, with a rotating-frame relaxation time of 760 ms. The long relaxation time suggests that the state of an individual spin can be monitored for extended periods of time, even while subjected to a complex set of manipulations that are part of the MRFM measurement protocol.

Suppression of spin diffusion near a micron-size ferromagnet.

We have used the large gradients generated near the ferromagnetic tip of a magnetic resonance force microscope to locally suppress spin diffusion in a silica sample containing paramagnetic electron spins. By controlling the slice location with respect to the tip, the magnetic field gradient was varied from 0.01 to 36 mT/microm, resulting in a fourfold decrease in T-11 and a similar decrease in T(-1)(1 rho). The observed dependence of the relaxation rates on field gradient is consistent with the quenching of flip-flop interactions that mediate the transport of magnetization between slow and fast relaxing spins.

Detection and manipulation of statistical polarization in small spin ensembles.

We report the detection of the square root of N statistical polarization in a small ensemble of electron spin centers in SiO2 by magnetic resonance force microscopy. A novel detection technique was employed that captures the statistical polarization and cycles it between states that are either locked or antilocked to the effective field in the rotating frame. Using field gradients as high as 5 G/nm, we achieved a detection sensitivity equivalent to roughly two electron spins, and observed ultralong spin-lock lifetimes, as long as 20 s. Given a sufficient signal-to-noise ratio, this scheme should be extendable to single electron spin detection.

Noncontact friction and force fluctuations between closely spaced bodies.

Noncontact friction between a Au(111) surface and an ultrasensitive gold-coated cantilever was measured as a function of tip-sample spacing, temperature, and bias voltage using observations of cantilever damping and Brownian motion. The importance of the inhomogeneous contact potential is discussed and comparison is made to measurements over dielectric surfaces. Using the fluctuation-dissipation theorem, the force fluctuations are interpreted in terms of near-surface fluctuating electric fields interacting with static surface charge.

Magnetic dissipation and fluctuations in individual nanomagnets measured by ultrasensitive cantilever magnetometry.

Cantilever magnetometry with moment resolution better than 10(4)micro(B) was used to study individual nanomagnets. By using the fluctuation-dissipation theorem to interpret measurements of field-induced cantilever damping, the low frequency spectral density of magnetic fluctuations could be determined with resolution better than 1micro(B) Hz-1/2. Cobalt nanowires exhibited significant magnetic dissipation and the associated magnetic fluctuations were found to have 1/f frequency dependence. In individual submicron rare-earth alloy magnets, the dissipation/fluctuation was very small and not distinguishable from that of a bare silicon cantilever.

Electron spin relaxation near a micron-size ferromagnet.

Magnetic resonance force microscopy was used to study the behavior of small ensembles of unpaired electron spins in silica near a micrometer-size ferromagnetic tip. Using a cantilever-driven spin manipulation protocol and a magnetic field gradient greater than 10(5) T/m, signals from as few as 100 net spins within a 20 nm thick resonant slice could be studied. A sixfold increase in the spin-lattice relaxation rate was found within 800 nm of the ferromagnet, while no effect due to silica surface proximity was detected. The results are interpreted in terms of Larmor-frequency magnetic field fluctuations emanating from the ferromagnet.