Nanoscale Torsional Resonator for Polarization and Spectroscopy of Nuclear Spins

We propose a torsional resonator that couples to the transverse spin dipole of an attached sample. The absence of relative motion eliminates a source of friction that would otherwise hinder nanoscale implementation. Enhanced spontaneous emission induced by the resonator relaxes the longitudinal spin dipole at a rate of $\sim 1{\mathrm{s}}^{-1}$ in the low-temperature limit. With signal averaging, single-proton magnetic resonance spectroscopy appears feasible at $\sim 10\mathrm{mK}$ and a high magnetic field, while single-shot sensitivity is practical for samples with at least tens of protons in a volume of $\sim 5{\mathrm{nm}}^3$.

Figure 1

Prototypical resonator design for NMR spectroscopy of nanoscale samples. The sample is “sandwiched” between magnetic cylinders and rotates with the sandwich about the torsional beam. The spin dipole couples to the oscillating transverse field generated by the cylinders.

Figure 2

Simulated polarization of 50 spins, with $R_h=1{\mathrm{s}}^{-1}$ and $T_h=0$. The dashed curve shows relaxation by noninteracting spins to a trapped state, while the dash-dotted curve corresponds to the regime in which the spin Hamiltonian efficiently equalizes the population within each eigenspace of $I_z$ during the relaxation. The solid curve shows exponential relaxation with rate constant $R_h$.

Figure 3

Simulation of the proton NMR spectrum of a single molecule of vinyl bromide adsorbed on Si. The noise sources are spin fluctuations, thermal motion in the resonator, and noise added during detection of the mechanical motion. A chemical shift of 0.6 ppm and a secular dipolar coupling of 1840 Hz were used for the simulation. Thermal polarization was assumed at the beginning of each transient. Acquisition would require $\sim 60\mathrm{h}$.