Abstract
We report on magnetic resonance force microscopy measurements of the Boltzmann polarization of nuclear spins in copper by detecting the frequency shift of a soft cantilever. We use the time-dependent solution of the Bloch equations to derive a concise equation describing the effect of radio-frequent (RF) magnetic fields on both on- and off-resonant spins in high magnetic field gradients. We then apply this theory to saturation experiments performed on a 100 nm thick layer of copper, where we use the higher modes of the cantilever as a source of the RF field. We demonstrate a detection volume sensitivity of only (40nm)3, corresponding to about 1.6×104 polarized copper nuclear spins. We propose an experiment on protons where, with the appropriate technical improvements, frequency-shift based magnetic resonance imaging with a resolution better than (10nm)3 could be possible. Achieving this resolution would make imaging based on the Boltzmann polarization competitive with the more traditional stochastic spin-fluctuation based imaging, with the possibility to work at millikelvin temperatures.
Highlights
Magnetic resonance force microscopy (MRFM) is a technique that combines magnetic resonance protocols with an ultrasensitive cantilever to measure the forces exerted by extremely small numbers of spins, with the immense potential of imaging biological samples with nanometer resolution.[1,2,3] In the last 20 years, great steps have been taken towards this goal, with some milestones including the detection of a single electron spin,[4] the magnetic resonance imaging of a tobacco mosaic virus with a spatial resolution of 4 nm,[5] and more recently the demonstration of a one-dimensional slice thickness below 2 nm for the imaging of a polystyrene film.[6]
We have used the time-dependent solution of the Bloch equation to derive a concise equation to calculate the frequency shifts in MRFM experiments and applied this to saturation experiments on a thin copper film
By using the higher modes of the cantilever as a source for the RF fields, we have demonstrated that it is possible to make one-dimensional scans of the copper film with near-negligible dissipation, and that the measured direct frequency shifts are well reproduced by the presented theory
Summary
Magnetic resonance force microscopy (MRFM) is a technique that combines magnetic resonance protocols with an ultrasensitive cantilever to measure the forces exerted by extremely small numbers of spins, with the immense potential of imaging biological samples with nanometer resolution.[1,2,3] In the last 20 years, great steps have been taken towards this goal, with some milestones including the detection of a single electron spin,[4] the magnetic resonance imaging of a tobacco mosaic virus with a spatial resolution of 4 nm,[5] and more recently the demonstration of a one-dimensional slice thickness below 2 nm for the imaging of a polystyrene film.[6]. We demonstrate that we can use higher modes of the cantilever as the source of the alternating field in order to generate the required RF fields to saturate the magnetization of the spins with minimal dissipation.[13] These results suggest that imaging based on the Boltzmann polarization could be possible, allowing for the first MRFM imaging experiments performed at temperatures down to 10 mK and using the magnet-on-tip geometry, as opposed to the sample-on-tip geometry more commonly found. We substantiate this claim by using the specifications of the current experiments to calculate the resolution for an imaging experiment on protons based on measuring the Boltzmann polarization
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