Feasibility of imaging in nuclear magnetic resonance force microscopy using Boltzmann polarization.

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 (40 nm) 3 , corresponding to about 1.6 × 10 4 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 (10 nm) 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. [ABSTRACT FROM AUTHOR]