Skip to main content
SpringerLink
Log in

Spin Diffusion and Spin–Lattice Relaxation in the Zeeman and Dipolar Systems

  • Original Paper
  • Published:
Applied Magnetic Resonance Aims and scope Submit manuscript

Abstract

Relaxation in the Zeeman and dipolar spin systems is considered. To shorten the spin–lattice relaxation time in the samples containing paramagnetic impurities, we propose to transfer order from the Zeeman to the dipolar systems. The diffusion equations for the inverse Zeeman and dipolar spin temperatures are solved numerically. It is shown that the dipolar system relaxes faster than the Zeeman one. At the initial stage, the relaxation in the Zeeman and dipolar spin systems is nonexponential. Then, the relaxation regimes in both cases are asymptotically changed to be described by exponential functions of time. The acceleration of the relaxation is achieved due to the following factors: the diffusion coefficient of the dipolar energy is larger than one of the Zeeman energy, and the energy transfer from the Zeeman system into the dipolar one allows us to overcome the obstacle of the diffusion barrier.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Abragam, The Principles of Nuclear Magnetism (Clarendon Press, Oxford, 1961)

    Google Scholar 

  2. P.T. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy (Clarendon Press, Oxford, 1991)

    Google Scholar 

  3. W.T. Wenckebach, Essentials of Dynamic Nuclear Polarization (Spindrift Publications, Dodrecht, 2016)

    Google Scholar 

  4. Y. Hovav, A. Feintuch, S. Vega, Theoretical aspects of dynamic nuclear polarization in the solid state – the cross effect. J. Mag. Resonance 214, 29–41 (2012)

    ADS  Google Scholar 

  5. W. Kockenberger, Dissolution dynamic nuclear polarization. eMagRes 3, 161–170 (2014). https://doi.org/10.1002/9780470034590.emrstm1311

    Article  Google Scholar 

  6. K.O. Tan, M. Mardini, C. Yang, J.H. Ardenkjr-Larsen, R.G. Griffin, Three-spin solid effect and the spin diffusion barrier in amorphous solids. Sci. Adv. 5, 2743 (2019)

    ADS  Google Scholar 

  7. W.T. Wenckebach, T.J.B. Swanenburg, N.J. Poulis, Thermodynamics of spin systems in paramagnetic crystals. Phys. Rep. 14, 181–255 (1974)

    ADS  Google Scholar 

  8. M. Goldman, A. Abragam, Principles of dynamic nuclear polarisation. Rep. Progr. Phys. 41, 395–467 (1978)

    ADS  Google Scholar 

  9. V.A. Atsarkin, Dynamic polarization of nuclei in solid dielectrics. Sov. Phys. Uspekhi 126, 3–39 (1978)

    Google Scholar 

  10. Y. Xia, K. Momot, Biophysics and Biochemistry of Cartilage by NMR and MRI (The Royal Society of Chemistry, Cambridge, 2016).

    Google Scholar 

  11. W.E. Blumberg, Nuclear spin-lattice relaxation caused by paramagnetic impurities. Phys. Rev. 119, 79 (1960)

    ADS  Google Scholar 

  12. G.R. Khutsishvili, Spin diffusion. Sov. Phys. Usp. 8, 743 (1966)

    ADS  Google Scholar 

  13. I.J. Lowe, D. Tse, Nuclear spin-lattice relaxation via paramagnetic centers. Phys. Rev. 166, 279 (1968)

    ADS  Google Scholar 

  14. G.B. Furman, E.M. Kunoff, S.D. Goren, V. Pasquier, D. Tinet, Nuclear spin-lattice relaxation via paramagnetic impurities in solids with arbitrary space dimension. Phys. Rev. B 52, 182 (1995)

    Google Scholar 

  15. G.B. Furman, A.M. Panich, A. Yochels, E.M. Kunoff, S.D. Goren, Nuclear spin-lattice relaxation of dipolar order caused by paramagnetic impurities. Phys. Rev. B 55, 438–446 (1997)

    ADS  Google Scholar 

  16. G.B. Furman, S.D. Goren, The spin-diffusion effect in the dipolar ordering state. J. Phys. 11, 4045–4052 (1999)

    Google Scholar 

  17. G.B. Furman, S.D. Goren, Spin diffusion and spin lattice relaxation in pulse spin-locking in solids containing paramagnetic impurities. J. Phys. 11, 8275–8282 (1999)

    Google Scholar 

  18. G.B. Furman, S.D. Goren, A.M. Panich, A.I. Shames, Spin diffusion and nuclear spin-lattice relaxation in irradiated solids: a multiple-pulse NQR study. Sol. St. Nucl. Magn. Res. 14, 145–155 (1999)

    Google Scholar 

  19. G.B. Furman, L. Frenkel Ben-Yakar, A.I. Shames, C. Korn, S.D. Goren, Nuclear spin-lattice relaxation and spin diffusion in the mixed state of type II layered superconductors. Phys. Rev. B 61, 7021–7028 (2000)

    ADS  Google Scholar 

  20. G.B. Furman, S.D. Goren, A.M. Panich, A.I. Shames, Spin diffusion in pure multiple-pulse NQR. Z. Naturforsch. 55, 54–60 (2000)

    ADS  Google Scholar 

  21. E.P. Horvitz, Nuclear spin diffusion induced by paramagnetic impurities in nonconducting solids. Phys. Rev. B 3, 2868 (1971)

    ADS  Google Scholar 

  22. J.P. Wolfe, Direct observation of a nuclear spin diffusion barrier. Phys. Rev. Lett. 31, 907 (1973)

    ADS  Google Scholar 

  23. A.Z. Genack, A.G. Redfield, Nuclear Spin Diffusion and Its Thermodynamic Quenching in the Field Gradients of a Type-II Superconductor. Phys. Rev. Lett. 31, 1204 (1973)

    ADS  Google Scholar 

  24. A.Z. Genack, A.G. Redfield, Theory of nuclear spin diffusion in a spatially varying magnetic field. Phys. Rev. B 12, 78 (1975)

    ADS  Google Scholar 

  25. S.F.J. Cox, S.F.J. Read, WTh. Wenckebach, The behaviour of nuclear spins near highly polarised paramagnetic centres. J. Phys. C: Solid State Phys. 10, 2917 (1977)

    ADS  Google Scholar 

  26. G.S. Boutis, D. Greenbaum, H. Cho, D.G. Cory, C. Ramanathan, Spin diffusion of correlated two-spin states in a dielectric crystal. PRL 92, 137201–137211 (2004)

    ADS  Google Scholar 

  27. A.E. Dementyev, D.G. Cory, C. Ramanathan, Rapid diffusion of dipolar order enhances dynamic nuclear polarization. Phys. Rev. B 277, 024413 (2008)

    ADS  Google Scholar 

  28. G.B. Furman, S.D. Goren, V.M. Meerovich, V.L. Sokolovsky, Dipolar nuclear polarization via the spin diffusion of a dipole order. J. Mag. Resonance 320, 106847 (2020)

    Google Scholar 

  29. A. Abragam, M. Goldman, Nuclear Magnetism, Order and Disorder (Clarendon Press, Oxford, 1982).

    Google Scholar 

  30. M. Goldman, Spin Temperature and Nuclear Resonance in Solids (Oxford at the Claredon Press, 1970).

  31. C.P. Slichter, Principles of Magnetic Resonance (Springer-Verlag, Berlin, 1980)

    Google Scholar 

  32. J. Jeneer, P. Broekaert, Nuclear magnetic resonance in solids: thermodynamic effects of a pair of rf pulses. Phys. Rev. 157, 232 (1967)

    ADS  Google Scholar 

  33. N. Bloembergen, The interaction of nuclear spins in a crystalline lattice. Physica 15, 386 (1949)

    ADS  Google Scholar 

  34. L.L. Buishvili, D.N. Zubarev, The statistical theory of nuclear spin diffusion. Sov. Phys. Solid State 3, 580 (1965)

    MathSciNet  Google Scholar 

  35. L. L. Buishvili and M. D. Zviadadze, Fiz. Tverd. Tela 9, 1969–1973 (1967) [Soviet Phys. - Solid State 9, 1545 (1968)]

  36. D.N. Zubarev, Nonequilibrium Statistical Thermodynamics (Imprint Consultannts Bureau, New York, 1974)

    Google Scholar 

  37. L.J. Humphries, S.D. Day, Spin-lattice relaxation of dipolar order in paramagnetic-impurity-doped CaF2. Phys. Rev. B 12, 2601 (1975)

    ADS  Google Scholar 

  38. G.B. Furman, S.D. Goren, A.M. Panich, A.I. Shames, T. Nakajima, Spin diffusion in multiple pulse spin-locking in solids containing paramagnetic impurities. Sol. St. Nucl. Magn. Res. 38, 84–89 (2010)

    Google Scholar 

  39. G.B. Furman, S.D. Goren, Nuclear magnetic resonance detection of the nuclear spins near paramagnetic impurities in solids. J. Phys. 14, 873–881 (2002)

    Google Scholar 

  40. G.B. Furman, E.M. Kunoff, S.D. Goren, V. Pasquier, D. Tinet, Nuclear spin-lattice relaxation via paramagnetic impurities in solids with arbitrary space dimension. Phys. Rev. B 52, 10182–10187 (1995)

    ADS  Google Scholar 

  41. G.B. Furman, A.M. Panich, A. Yochelis, E.M. Kunoff, S.D. Goren, Nuclear spin-lattice relaxation of dipolar order caused by paramagnetic impurities. Phys. Rev. B 55, 439–444 (1997)

    ADS  Google Scholar 

  42. H. Cho, D.G. Cory, C. Ramanathan, Spin counting experiments in the dipolar-ordered state. J. Chem. Phys. 118, 3686 (2003)

    ADS  Google Scholar 

  43. G.W. Leppelmeier, J. Jeener, Measurement of the nuclear spin diffusion coefficient in CaF2. Phys. Rev. 175, 498 (1968)

    ADS  Google Scholar 

  44. W. Zhang, D.G. Cory, First direct measurement of the spin diffusion rate in a homogenous solid. Phys. Rev. Lett. 80, 1324 (1998)

    ADS  Google Scholar 

Download references

Acknowledgements

This research was supported by a grant from the United States—Israel Binational Science Foundation (BSF), Jerusalem, Israel. This manuscript is dedicated to Professor Vadim Atsarkin, on the occasion of his 85th birthday.

Author information

Authors and Affiliations

  1. Department of Physics, Ben-Gurion University, POB 653, 84104, Be’er-Sheva, Israel

    G. B. Furman, S. D. Goren, V. M. Meerovich & V. L. Sokolovsky

Authors
  1. G. B. Furman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. D. Goren
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. M. Meerovich
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. V. L. Sokolovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. B. Furman.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Furman, G.B., Goren, S.D., Meerovich, V.M. et al. Spin Diffusion and Spin–Lattice Relaxation in the Zeeman and Dipolar Systems. Appl Magn Reson 52, 781–796 (2021). https://doi.org/10.1007/s00723-021-01349-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00723-021-01349-8

Search

Navigation