Nanoscale Fourier-Transform Magnetic Resonance Imaging

(Clockwise from Top Left) John M. Nichol, Tyler R. Naibert, Raffi Budakian, Lincoln J. Lauhon

Authors:
John M. Nichol¹, Tyler R. Naibert¹, Eric R. Hemesath², Lincoln J. Lauhon², Raffi Budakian¹

Affiliation:
¹Dept of Physics, University of Illinois at Urbana-Champaign, USA
²Dept of Materials Science and Engineering, Northwestern University, USA

Magnetic resonance imaging (MRI) has had a profound impact on biology and medicine [1]. Key to its success has been the unique ability to combine imaging with nuclear magnetic resonance spectroscopy—a capability that has led to a host of powerful modalities for imaging. Common examples include spin-relaxation weighted imaging [2], chemical shift imaging [2], and functional MRI [3]. These and most other modern MRI techniques involve applying a combination of sophisticated radiofrequency and static magnetic field pluses to image the sample. These “pulsed” magnetic resonance methods [4] enable highly-efficient imaging by acquiring data from the entire sample at all times.

The spatial resolution of inductive MRI remains limited to millimeter lengths scales in common practice and to a few micrometers in the highest-resolution experimental instruments [5]. Although it remains a significant challenge, there is considerable interest to extend these powerful spectroscopic and imaging capabilities to the nanometer scale as the capability to perform nanoscale MRI would revolutionize biology and medicine. Promising work towards this goal includes force-detected magnetic resonance [6], which has been used to perform three-dimensional imaging of single tobacco mosaic virus particles with 5 nm resolution [7], and nitrogen-vacancy-based magnetic resonance [8, 9], which has been used to detect proton resonance in volumes as small as (5 nm)³ [10, 11]. The difficulties associated with the detection of nanometer-size volumes of nuclear spins, however, have required techniques such as these -- that are strikingly different from conventional inductive MRI. Moreover, it remains difficult to apply classic pulsed magnetic resonance techniques to nanometer-size samples.

In a recent proof-of-concept experimental work [12], we demonstrate a new technique, which allows us to perform pulsed nuclear magnetic resonance imaging and spectroscopy with nanometer-scale spatial resolution. Two unique components central to this work are (1) the ability to generate intense time-dependent magnetic fields on the nanometer scale, and (2) the development of a novel spin manipulation protocol, which allows us to encode the quantum spin noise in nanometer-scale ensembles of nuclear spins.

In particular, we perform nanometer-scale solid-state Fourier-transform MRI with roughly 10-nm spatial resolution. Fourier-transform imaging [13, 14], a pulsed magnetic resonance technique that relies on coherent manipulation of spins in the sample, is the most common method of MRI because it is highly efficient [15]. We use a nanometer-scale metal wire, or constriction, to generate intense static and radiofrequency magnetic field gradient pulses, which create temporal correlations in the statistical spin fluctuations in the sample. The correlations are recorded for a set of pulse configurations and Fourier-transformed to give the spin density. The sample used in this study is a nanometer-sized volume of polystyrene, a solid organic material containing a high proton density (Fig. 1).

Figure 1. Schematic of the experimental apparatus. A silicon nanowire coated with polystyrene is positioned near a constriction in a lithographically fabricated Ag wire. Electric current through the constriction generates static and radiofrequency magnetic field pulses, which are used to image protons in the polystyrene coating.

The magnetic resonance sensor we use is an ultra-sensitive silicon-nanowire mechanical oscillator [16], and the sample is mounted on the tip of the nanowire (Fig. 1). In addition to providing pulses for magnetic resonance, the metal constriction also produces a magnetic field gradient that oscillates at the silicon nanowire mechanical resonance frequency. The force of interaction between the protons in the sample and the magnetic field gradient from the constriction induces an angstrom-scale vibration of the nanowire, which we measure using a fiber-optic interferometer [17]. The silicon nanowire is an exceptionally sensitive mechanical oscillator and is well-suited to detecting the minute forces originating from small ensembles of nuclear spins [16].

Looking forward, our technique establishes a paradigm by which all other pulsed magnetic resonance techniques can be implemented for nanoscale imaging and spectroscopy. Constrictions capable of producing two orthogonal static gradients could be fabricated, and such devices would enable full three-dimensional imaging. A small coil near the sample could also provide a uniform radiofrequency field throughout the sample, which would enable the use of solid-state nuclear magnetic resonance spectroscopy techniques. More generally, our approach serves as a model for leveraging these and other sophisticated pulsed magnetic resonance tools to aid nanoscale MRI in its progress toward atomic-scale imaging.

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[16] John M. Nichol, Eric R. Hemesath, Lincoln J. Lauhon, Raffi Budakian, "Nanomechanical detection of nuclear magnetic resonance using a silicon nanowire oscillator", Physical Review B, 85, 054414 (2012). Abstract.
[17] John M. Nichol, Eric R. Hemesath, Lincoln J. Lauhon, Raffi Budakian, "Displacement detection of silicon nanowires by polarization-enhanced fiber-optic interferometry", Applied Physics Letters, 93, 193110 (2008). Abstract.