We report on Magnetic Resonance Force Microscopy measurements of the Boltzmann polarization of the 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 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 source of the rf field. We demonstrate a detection volume sensitivity of only (40 nm)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 (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.
@article{arxiv.1809.09351,
title = {Feasibility of imaging using Boltzmann polarization in nuclear Magnetic Resonance Force Microscopy},
author = {Martin de Wit and Gesa Welker and Jelmer Wagenaar and Freek Hoekstra and Tjerk Oosterkamp},
journal= {arXiv preprint arXiv:1809.09351},
year = {2019}
}