Reverse Monte Carlo reconstruction of electron spin-label coordinates from scanned-probe magnetic resonance microscope signals

TL;DR

This paper proposes a Bayesian reverse Monte Carlo method to reconstruct three-dimensional electron spin coordinates from scanned-probe magnetic resonance signals, enabling high-resolution imaging of spin-labeled molecules.

Contribution

It introduces a novel protocol and numerical simulation demonstrating the feasibility of 3D electron spin localization using a Bayesian reverse Monte Carlo algorithm.

Findings

Revealed nanometer-scale rings of frequency-shift signals during scanning.

Showed that full 3D electron coordinates can be reconstructed from 2D frequency maps.

Indicated potential for angstrom-resolution imaging of spin-labeled biomolecules.

Abstract

Individual electron spins have been observed using magnetic resonance in combination with a number of distinct detection approaches. The coordinates of an individual electron spin can then in principle be determined by introducing a 10 to 100 nm diameter magnetic needle, scanning the needle, and collecting signal as a function of the needle's position. Although individual electrons have recently been localized with nanometer precision in this way using a nitrogen-vacancy center in diamond as the spin detector, the experiment's low signal-to-noise ratio limited acquisition to two-dimensional scanning of just a few dozen data points and was incompatible with nitroxide spin labels widely used to label proteins and nucleic acids. We introduce and numerically simulate a protocol for detecting and imaging individual nitroxide electron spins mechanically with high spatial resolution. In our protocol a scanned magnet-tipped cantilever is brought near the sample, modulated microwaves are applied to resonantly excite electron spins, and changes in spin magnetization are detected as a shift in the mechanical frequency of the cantilever. By carefully applying resonant microwaves in short bursts in synchrony with the cantilever's oscillation, we propose to retain high spatial resolution even at large cantilever amplitude where sensitivity is highest. Numerical simulations reveal nanometer-diameter rings of frequency-shift signal as the tip is scanned. Our primary finding is that it is possible --- using a Bayesian, reverse Monte Carlo algorithm introduced here --- to obtain the full three-dimensional distribution of electron coordinates from the signal rings revealed in a two-dimensional frequency-shift map. This reduction in dimensionality brings within reach, on a practical timescale, the angstrom-resolution three-dimensional imaging of spin-labeled macromolecules.