Feasibility of imaging using Boltzmann polarization in nuclear Magnetic Resonance Force Microscopy

TL;DR

This paper demonstrates the detection of nuclear spin polarization in copper using Magnetic Resonance Force Microscopy, achieving high sensitivity and proposing potential for sub-10 nm resolution imaging based on Boltzmann polarization.

Contribution

It introduces a theoretical framework for rf effects on spins in high gradients and applies it to copper, achieving detection of 40 nm^3 volume and proposing future proton imaging improvements.

Findings

Detection volume sensitivity of 40 nm^3

Approximately 16,000 polarized copper nuclear spins detected

Potential for sub-10 nm^3 resolution imaging with technical advancements

Abstract

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$\cdot 10^4$ 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.