Electron Spin-Lattice Relaxation at Defect Sites; <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>E</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math></span> Centers in Synthetic Quartz at 3 Kilo-Oersteds

J. G. Castle, Jr; D. W. Feldman; P. G. Klemens; R. A. Weeks

doi:10.1103/PhysRev.130.577

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Electron Spin-Lattice Relaxation at Defect Sites; $E^{'}$ Centers in Synthetic Quartz at 3 Kilo-Oersteds

J. G. Castle, Jr., D. W. Feldman, and P. G. Klemens

R. A. Weeks^*

Westinghouse Research Laboratories, Pittsburgh, Pennsylvania

Oak Ridge National Laboratory, Oak Ridge, Tennessee

^*Oak Ridge National Laboratory is operated by Union Carbide Corporation for the U. S. Atomic Energy Commission.

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Phys. Rev. 130, 577 – Published 15 April, 1963

DOI: https://doi.org/10.1103/PhysRev.130.577

Abstract

Measurements of the spin-lattice relaxation time $T_{1}$ by the inversion-recovery technique are reported for two paramagnetic centers in quartz over a wide temperature range: from 1.3 to 250°K for the ${E_{1}}^{'}$ center, and from 2 to 80°K the ${E_{2}}^{'}$ center. The data, extending over several orders of magnitude in $T_{1}$ , are interpreted in terms of cross relaxation, direct processes, and Raman processes. The dominant feature of the Raman relaxation is a temperature variation of about $T^{3}$ , which is much slower than expected by standard theory.

The theory of spin-lattice relaxation is extended to account for the modification at a defect site of the strain due to a lattice wave. Each defect has at least one characteristic frequency and the local strain due to a wave of higher frequency is enhanced, being essentially given by the displacement due to the wave, rather than its spatial derivative. If the characteristic frequency is sufficiently low compared to the Debye frequency, the Raman relaxation rate should vary as $T^{3}$ (or $T^{5}$ ) over a wide range of temperatures, instead of the usual $T^{7}$ (or $T^{9}$ ) variation.

A detailed comparison of the relaxation rates observed for the two $E^{'}$ centers with the above theory suggests that each center has two characteristic frequencies or temperatures $θ_{i}$ . For the ${E_{2}}^{'}$ center one of these ( $θ_{i} = 45 °$ K) is ascribed to the vibration of a neighboring impurity ion, probably a proton. The other temperature (≃5°K) may arise from the motion of oxygen ions at the defect. The ${E_{1}}^{'}$ center has the two characteristic temperatures of 140°K and 14°K.

A model for the ${E_{1}}^{'}$ center is proposed: An electron is trapped at a silicon ion located in an oxygen divacancy. This model leads to the likelihood of low characteristic frequencies through a non-rigid Si $O_{2}$ group, and also through a net negative charge, which should attract one or more interstitial impurity ions.

References (42)

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J. H. Van Vleck, Phys. Rev. 57, 426 (1941)
R. L. de Kronig, Physica 6, 33 (1939)
R. D. Mattuck and M. W. P. Strandberg, Phys. Rev. 119, 1204 (1960) M. Blume and R. L. Orbach, ibid. 127, 1587 (1962)
J. G. Castle, Jr., P. F. Chester, and P. E. Wagner, Phys. Rev. 119, 953 (1960)
J. G. Castle, Jr., and D. W. Feldman, Phys. Rev. 121, 1349 (1961)
A. A. Manenkov and A. M. Prokhorov, Soviet Phys.—JETP 15, 54 (1962)
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J. G. Castle, Jr., D. W. Feldman, and P. G. Klemens, Advances in Quantum Electronics (Columbia University Press, New York, 1961), p. 414
R. L. Orbach, Proc. Phys. Soc. (London) 77, 821 (1961)
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B. R. McAvoy, Rev. Sci. Instr. 33, 129 (1962)
R. L. Powell, M. D. Bunch, and R. J. Corruccini, Cryogenics 1, 139 (1961)
N. Bloembergen, S. Shapiro, P. S. Pershan, and J. O. Artman, Phys. Rev. 114, 445 (1959)
A. Kiel, Phys. Rev. 120, 137 (1960) ibid.123, 2202(E) (1961)
Omitted endnote
Omitted endnote
Omitted endnote
W. B. Mims, K. Nassau, and J. D. McGee, Phys. Rev. 123, 2059 (1961) A. Kiel, ibid. 125, 1451 (1962)
J. H. Van Vleck, Phys. Rev. 74, 1168 (1948) C. Kittel and E. Abrahams, ibid. 90, 238 (1953)
Omitted endnote
G. D. Watkins and J. W. Corbett, Discussions Faraday Soc. 31, 86 (1961)

[c1] J. H. Van Vleck, J. Chem. Phys. 7, 72 (1939)

[c2] J. H. Van Vleck, Phys. Rev. 57, 426 (1941)

[c3] R. L. de Kronig, Physica 6, 33 (1939)

[c4] R. D. Mattuck and M. W. P. Strandberg, Phys. Rev. 119, 1204 (1960) M. Blume and R. L. Orbach, ibid. 127, 1587 (1962)

[c5] J. G. Castle, Jr., P. F. Chester, and P. E. Wagner, Phys. Rev. 119, 953 (1960)

[c6] J. G. Castle, Jr., and D. W. Feldman, Phys. Rev. 121, 1349 (1961)

[c7] A. A. Manenkov and A. M. Prokhorov, Soviet Phys.—JETP 15, 54 (1962)

[c8] J. H. Pace, D. F. Sampson, and J. S. Thorp, Phys. Rev. Letters 4, 18 (1960) Proc. Phys. Soc. (London) 77, 257 (1961)

[c9] D. H. Paxman, Proc. Phys. Soc. (London) 78, 180 (1961)

[c10] T. Bray, G. C. Brown, Jr., and A. Kiel, Phys. Rev. 127, 730 (1962)

[c11] G. Feher and E. A. Gere, Phys. Rev. 114, 1245 (1959) D. K. Wilson and G. Feher, ibid. 124, 1068 (1961) A. Honig and E. Stupp, ibid. 117, 69 (1960)

[c12] J. G. Castle, Jr., D. W. Feldman, and P. G. Klemens, Advances in Quantum Electronics (Columbia University Press, New York, 1961), p. 414

[c13] R. L. Orbach, Proc. Phys. Soc. (London) 77, 821 (1961)

[c14] C. B. P. Finn, R. L. Orbach, and W. P. Wolf, Proc. Phys. Soc. (London) 77, 261 (1961) J. A. Cowen and D. E. Kaplan, Phys. Rev. 124, 1099 (1961)

[c15] P. L. Scott and C. D. Jeffries, Phys. Rev. 127, 32 (1962)

[c16] R. A. Weeks, preceding paper [Phys. Rev. 130, 570 (1963)]

[c17] R. A. Weeks, J. Appl. Phys. 27, 1376 (1956)

[c18] R. H. Silsbee, J. Appl. Phys. 32, 1459 (1961)

[c19] R. A. Weeks and C. M. Nelson, J. Am. Ceram. Soc. 43, 401 (1960)

[c20] C. M. Nelson and R. A. Weeks, J. Am. Ceram. Soc. 43, 399 (1960)

[c21] R. A. Weeks and E. Sonder, in Proceedings of the Conference on Paramagnetism, Jerusalem, Israel, July, 1962 (to be published)

[c22] J. H. E. Griffiths, J. Owen, and I. M. Ward, in Report of the Conference on Defects in Crystalline Solids (The Physical Society, London, 1955), p. 81

[c23] J. A. Weil and J. H. Anderson, J. Chem. Phys. 35, 1410 (1961)

[c24] P. G. Klemens, Phys. Rev. 125, 1795 (1962)

[c25] W. M. Rogers and R. L. Powell, Tables of Transport Integrals, National Bureau of Standards Circular No. 535 (U. S. Government Printing Office, Washington, D. C., 1958)

[c26] E. W. Montroll and R. B. Potts, Phys. Rev. 100, 525 (1955) H. B. Rosenstock and C. C. Klick, ibid. 119, 1198 (1960)

[c27] R. Brout and W. Visscher, Phys. Rev. Letters 9, 54 (1962)

[c28] H. B. Rosenstock, J. Phys. Chem. Sol. 23, 659 (1962)

[c29] A. B. Roitsin, Fiz. Tverd. Tela 3, 2879 (1961)

[c30] A. Abragam, Principles of Nuclear Magnetism (Oxford University Press, New York, 1961)

[c31] P. F. Chester, J. G. Castle, Jr., P. E. Wagner, and G. Conn, Rev. Sci. Instr. 30, 1127 (1959)

[c32] B. R. McAvoy, Rev. Sci. Instr. 33, 129 (1962)

[c33] R. L. Powell, M. D. Bunch, and R. J. Corruccini, Cryogenics 1, 139 (1961)

[c34] N. Bloembergen, S. Shapiro, P. S. Pershan, and J. O. Artman, Phys. Rev. 114, 445 (1959)

[c35] A. Kiel, Phys. Rev. 120, 137 (1960) ibid.123, 2202(E) (1961)

[c36] Omitted endnote

[c37] Omitted endnote

[c38] Omitted endnote

[c39] W. B. Mims, K. Nassau, and J. D. McGee, Phys. Rev. 123, 2059 (1961) A. Kiel, ibid. 125, 1451 (1962)

[c40] J. H. Van Vleck, Phys. Rev. 74, 1168 (1948) C. Kittel and E. Abrahams, ibid. 90, 238 (1953)

[c41] Omitted endnote

[c42] G. D. Watkins and J. W. Corbett, Discussions Faraday Soc. 31, 86 (1961)

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Electron Spin-Lattice Relaxation at Defect Sites; $E^{'}$ Centers in Synthetic Quartz at 3 Kilo-Oersteds

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Electron Spin-Lattice Relaxation at Defect Sites; E′ Centers in Synthetic Quartz at 3 Kilo-Oersteds

Abstract

References (42)

Electron Spin-Lattice Relaxation at Defect Sites; $E^{'}$ Centers in Synthetic Quartz at 3 Kilo-Oersteds