Multiple Electron-Spin Echoes in Ti<span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>: <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi mathvariant="normal">V</mi></mrow><mrow><mn>4</mn><mo>+</mo></mrow></msup></mrow></math></span>

L. G. Rowan

doi:10.1103/PhysRev.167.326

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Multiple Electron-Spin Echoes in Ti $O_{2}$ : $V^{4 +}$

L. G. Rowan

Department of Physics, University of North Carolina, Chapel Hill, North Carolina

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Phys. Rev. 167, 326 – Published 10 March, 1968

DOI: https://doi.org/10.1103/PhysRev.167.326

Abstract

An electron-spin-echo experiment has been performed on $V^{4 +}$ paramagnetic impurities in a single crystal of Ti $O_{2}$ . The high microwave dielectric constant of Ti $O_{2}$ and the simple geometry of the sample give rise to high- $Q$ dielectric resonant modes in the sample. The strong interaction between the paramagnetic impurities and the dielectric modes produces multiple spin echoes when two microwave pulses are applied under certain conditions. A simple model is presented to explain the process of multiple-echo formation, and a quantum-mechanical description is given.

References (9)

M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Clarendon Press, Oxford, England, 1954) R. H. Lyddane and K. F. Herzfeld, Phys. Rev. 54, 846 (1948)
J. J. Hopfield, Phys. Rev. 112, 1555 (1958) U. Fano, ibid. 103, 1202 (1956) P. Pincus, J. Appl. Phys. 33, 553 (1962)
E. L. Hahn, Phys. Rev. 80, 580 (1950) K. D. Bowers and W. B. Mims, ibid. 115, 285 (1959)
C. Kittel, Quantum Theory of Solids (John Wiley & Sons, Inc., New York, 1963), pp. 46-47
L. R. Walker, Phys. Rev. 105, 390 (1957) P. Fletcher and C. Kittel ibid. 120, 2004 (1960) R. Damon and J. Eshbach, Phys. Chem. Solids 19, 308 (1961)
R. DamonJ. EshbachPrinciples of Microwave Circuits, edited by C. G. Montgomery, R. H. Dicke, and E. M. Purcell (Dover Publications, Inc., New York, 1965)
R. DamonJ. EshbachQuantum Optics and Electronics, edited by C. DeWitt (Gordon and Breach Science Publishers, Inc., New York, 1965), pp. 14-15
N. A. Kurnit, I. D. Abella, and S. R. Hartmann, Phys. Rev. Letters 13, 567 (1964) A. G. Fox and P. W. Smith, ibid. 18, 826 (1967) S. L. McCall and E. L. Hahn, ibid. 18, 908 (1967)
M. Sparks, Ferromagnetic Relaxation Theory, (McGraw-Hill Book Co., Inc., New York, 1964)

[c1] M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Clarendon Press, Oxford, England, 1954) R. H. Lyddane and K. F. Herzfeld, Phys. Rev. 54, 846 (1948)

[c2] J. J. Hopfield, Phys. Rev. 112, 1555 (1958) U. Fano, ibid. 103, 1202 (1956) P. Pincus, J. Appl. Phys. 33, 553 (1962)

[c3] E. L. Hahn, Phys. Rev. 80, 580 (1950) K. D. Bowers and W. B. Mims, ibid. 115, 285 (1959)

[c4] C. Kittel, Quantum Theory of Solids (John Wiley & Sons, Inc., New York, 1963), pp. 46-47

[c5] L. R. Walker, Phys. Rev. 105, 390 (1957) P. Fletcher and C. Kittel ibid. 120, 2004 (1960) R. Damon and J. Eshbach, Phys. Chem. Solids 19, 308 (1961)

[c6] R. DamonJ. EshbachPrinciples of Microwave Circuits, edited by C. G. Montgomery, R. H. Dicke, and E. M. Purcell (Dover Publications, Inc., New York, 1965)

[c7] R. DamonJ. EshbachQuantum Optics and Electronics, edited by C. DeWitt (Gordon and Breach Science Publishers, Inc., New York, 1965), pp. 14-15

[c8] N. A. Kurnit, I. D. Abella, and S. R. Hartmann, Phys. Rev. Letters 13, 567 (1964) A. G. Fox and P. W. Smith, ibid. 18, 826 (1967) S. L. McCall and E. L. Hahn, ibid. 18, 908 (1967)

[c9] M. Sparks, Ferromagnetic Relaxation Theory, (McGraw-Hill Book Co., Inc., New York, 1964)

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Multiple Electron-Spin Echoes in Ti $O_{2}$ : $V^{4 +}$

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Multiple Electron-Spin Echoes in TiO2: V4+

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References (9)

Multiple Electron-Spin Echoes in Ti $O_{2}$ : $V^{4 +}$