Abstract:
We review recent efforts to detect small numbers of nuclear spins using magnetic resonance force microscopy. Magnetic resonance force microscopy (MRFM) is a scanning probe technique that relies on the mechanical measurement of the weak magnetic force between a microscopic magnet and the magnetic moments in a sample. Spurred by the recent progress in fabricating ultrasensitive force detectors, MRFM has rapidly improved its capability over the last decade. Today it boasts a spin sensitivity that surpasses conventional, inductive nuclear magnetic resonance detectors by about eight orders of magnitude. In this review we touch on the origins of this technique and focus on its recent application to nanoscale nuclear spin ensembles, in particular on the imaging of nanoscale objects with a three-dimensional (3D) spatial resolution better than 10 nm. We consider the experimental advances driving this work and highlight the underlying physical principles and limitations of the method. Finally, we discuss the challenges that must be met in order to advance the technique towards single nuclear spin sensitivity -- and perhaps -- to 3D microscopy of molecules with atomic resolution.

Abstract:
A method for high-field optically detected nuclear magnetic resonance (ODNMR) is developed sensitive to 10**8 nuclei. Nuclear spin transitions are induced using a radio frequency coil and detected through Faraday rotation spectroscopy. Unlike conventional ODNMR, which is limited to low fields and relies on the measurement of time-averaged luminescence polarization, this technique monitors nuclear polarization through time-resolved measurements of electron spin dynamics. Measurements in a (110) GaAs quantum well reveal Ga-69, Ga-71, and As-75 resonances and their quadrupolar splittings while resolving changes in nuclear polarization of 0.02%.

Abstract:
Using dynamic cantilever magnetometry, we study the vortex lattice and its corresponding melting transition in a micrometer-size crystallite of superconducting NbSe2. Measurements of the cantilever resonance frequency as a function of magnetic field and temperature respond to the magnetization of the vortex-lattice. The cantilever dissipation depends on thermally activated vortex creep motion, whose pinning energy barrier is found to be in good agreement with transport measurements on bulk samples. This approach reveals the phase diagram of the crystallite, and is applicable to other micro- or nanometer-scale superconducting samples.

Abstract:
We calculate the Overhauser frequency shifts in semiconductor nanostructures resulting from the hyperfine interaction between nonequilibrium electronic spins and nuclear spins. The frequency shifts depend on the electronic local density of states and spin polarization as well as the electronic and nuclear spin relaxation mechanisms. Unlike previous calculations, our method accounts for the electron confinement in low dimensional semiconductor nanostructures, resulting in both nuclear spin polarizations and Overhauser shifts that are strongly dependent on position. Our results explain previously puzzling measurements of Overhauser shifts in an Al$_x$Ga$_{1-x}$As parabolic quantum well by showing the connection between the electron spin lifetime and the frequency shifts.

Abstract:
We implement magnetic resonance force microscopy (MRFM) in an experimental geometry, where the long axis of the cantilever is normal to both the external magnetic field and the RF microwire source. Measurements are made of the statistical polarization of $^1$H in polystyrene with negligible magnetic dissipation, gradients greater than $10^5$ T/m within 100 nm of the magnetic tip, and rotating RF magnetic fields over 12 mT at 115 MHz. This geometry could facilitate the application of nanometer-scale MRFM to nuclear species with low gyro-magnetic ratios and samples with broadened resonances, such as In spins in quantum dots.

Abstract:
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 magneto-mechanical 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 magneto-mechanical noise.

Abstract:
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 (100nm)^3. In this work, 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. A protocol to periodically randomize the spin ensemble is demonstrated, allowing significant improvement in the signal-to-noise ratio for nanometer-scale magnetic resonance imaging.

Abstract:
Magnetic resonance imaging, based on the manipulation and detection of nuclear spins, is a powerful imaging technique that typically operates on the scale of millimeters to microns. Using magnetic resonance force microscopy, we have demonstrated that magnetic resonance imaging of nuclear spins can be extended to a spatial resolution better than 100 nm. The two-dimensional imaging of 19F nuclei was done on a patterned CaF2 test object, and was enabled by a detection sensitivity of roughly 1200 nuclear spins. To achieve this sensitivity, we developed high-moment magnetic tips that produced field gradients up to 1.4x10^6 T/m, and implemented a measurement protocol based on force-gradient detection of naturally occurring spin fluctuations. The resulting detection volume of less than 650 zl represents 60,000x smaller volume than previous NMR microscopy and demonstrates the feasibility of pushing magnetic resonance imaging into the nanoscale regime.

Abstract:
We cool the fundamental mechanical mode of an ultrasoft silicon cantilever from a base temperature of 2.2 K 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.

Abstract:
We measure the statistical polarization of quadrupolar nuclear spins in a sub-micrometer (0.6 um^3) particle of GaAs using magnetic resonance force microscopy. The crystalline sample is cut out of a GaAs wafer and attached to a micro-mechanical cantilever force sensor using a focused ion beam technique. Nuclear magnetic resonance is demonstrated on ensembles containing less than 5 x 10^8 nuclear spins and occupying a volume of around (300 nm)^3 in GaAs with reduced volumes possible in future experiments. We discuss how the further reduction of this detection volume will bring the spin ensemble into a regime where random spin fluctuations, rather than Boltzmann polarization, dominate its dynamics. The detection of statistical polarization in GaAs therefore represents an important ?rst step toward 3D magnetic resonance imaging of III-V materials on the nanometer-scale.