Overview#

A number of methods have been devised for detecting spin magnetic resonance using a cantilever. The methods are different enough that numerically calculating the effect of the spins on the cantilever requires a distinct approach for each method. We are most interested in simulating the signal from Degen et al. 1 and Longenecker et al. 2 experiments.

In these experiments, adiabatic rapid passages were used to repeatedly invert the sample’s spin magnetization in time with the natural oscillation period of the cantilever. The modulated spin magnetization interacted with a magnetic field gradient to produce a resonant force that excited the cantilever. The cantilever position was observed with a lock-in detector; spin resonance was registered as a change in the amplitude of the cantilever oscillation. In the experiments cited above, the number of spins in resonance was so small that the spin fluctuations exceeded the average thermal spin polarization. In this small-ensemble limit, nuclear magnetic resonance (NMR) was detected as a change in the variance of the cantilever position fluctuations observed in the in-phase channel of the lock-in detector.

  • experiment: summarizes all the experimental method

  • polarization: summarizes polarization and magnetization calculations

  • Trapezoid Integration: summarizes using Trapezoid integration to calculate the field change during cantilever motion.

Reference

1

Degen, C. L.; Poggio, M.; Mamin, H. J.; Rettner, C. T. & Rugar, D. “Nanoscale Magnetic Resonance Imaging”, Proc. Natl. Acad. Sci. U.S.A., 2009, 106, 1313 - 1317 [10.1073/pnas.0812068106].

2

Longenecker, J. G.; Mamin, H. J.; Senko, A. W.; Chen, L.; Rettner, C. T.; Rugar, D. & Marohn, J. A. “High-Gradient Nanomagnets on Cantilevers for Sensitive Detection of Nuclear Magnetic Resonance”, ACS Nano, 2012, 6, 9637 - 9645 [10.1021/nn3030628].