Effect of Linear Jahn-Teller Coupling on Paramagnetic Resonance in a <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>E</mi></mrow><mprescripts></mprescripts><mrow></mrow><mrow><mn>2</mn></mrow><mrow></mrow><mrow></mrow></mmultiscripts></mrow></math></span> State

Frank S. Ham

doi:10.1103/PhysRev.166.307

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Effect of Linear Jahn-Teller Coupling on Paramagnetic Resonance in a ${}^{2}E$ State

Frank S. Ham

General Electric Research and Development Center, Schenectady, New York

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Phys. Rev. 166, 307 – Published 10 February, 1968

DOI: https://doi.org/10.1103/PhysRev.166.307

Abstract

The theory of the effect of a dynamic Jahn-Teller effect on the electron-paramagnetic-resonance spectrum of a ${}^{2}E$ state is developed from the limit of weak Jahn-Teller coupling taking account only of linear coupling. The principal changes produced in the EPR spectrum of the vibronic ground state may be represented simply by introducing appropriate reduction factors into the spin Hamiltonian which describes the splitting of the electronic ${}^{2}E$ state by a magnetic field, strain, or hyperfine interaction. These reduction factors affect the anisotropic part of the spin Hamiltonian but not the isotropic part; they are diminished from unity by the Jahn-Teller coupling; and they are analogous to the reduction factors introduced earlier in the theory of a triplet state. The theory is used to discuss Höchli's data for ${Sc}^{2 +}$ in Ca $F_{2}$ and Sr $F_{2}$ and Coffman's data for ${Cu}^{2 +}$ in MgO. While the latter case is consistent with either a moderately strong linear Jahn-Teller coupling or with the tunneling model, the present theory applied to ${Sc}^{2 +}$ in Ca $F_{2}$ and Sr $F_{2}$ indicates that in these cases the Jahn-Teller coupling is quite weak.

References (41)

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B. Bleaney and K. D. Bowers, Proc. Phys. Soc. (London) A65, 667 (1952)
H. A. Jahn and E. Teller, Proc. Roy. Soc. (London) A161, 220 (1937)
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W. Moffitt and A. D. Liehr, Phys. Rev. 106, 1195 (1957)
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W. Low and A. Rosenthal, Bull. Am. Phys. Soc. 11, 906 (1966)
G. A. Slack, F. S. Ham, and R. M. Chrenko, Phys. Rev. 152, 376 (1966)
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Omitted endnote
([23])
Omitted endnote
Omitted endnote
[28]
[15]
[14,15]
W. Hayes and J. Wilkens, Proc. Roy. Soc. (London) A281, 340 (1964)
Omitted endnote
A. Abragam and M. H. L. Pryce, Proc. Roy. Soc. A205, 135 (1951)
[25]
Omitted endnote

[c1] B. Bleaney and D. J. E. Ingram, Proc. Phys. Soc. (London) A63, 408 (1950)

[c2] A. Abragam and M. H. L. Pryce, Proc. Phys. Soc. (London) A63, 409 (1950)

[c3] B. Bleaney and K. D. Bowers, Proc. Phys. Soc. (London) A65, 667 (1952)

[c4] H. A. Jahn and E. Teller, Proc. Roy. Soc. (London) A161, 220 (1937)

[c5] M. D. Sturge, in Solid State Physics, edited by F. Seitz, D. Turnbull, and H. Ehrenreich (Academic Press Inc., New York, 1967), Vol. 20, p. 91, Sec. II

[c6] J. H. Van Vleck, J. Chem. Phys. 7, 72 (1939)

[c7] U. Opik and M. H. L. Pryce, Proc. Roy. Soc. (London) A238, 425 (1957)

[c8] A. D. Liehr and C. J. Ballhausen, Ann. Phys. (N.Y.) 3, 304 (1958)

[c9] A. D. Liehr, J. Phys. Chem. 67, 389 (1963)

[c10] J. B. Goodenough, J. Phys. Chem. Solids 25, 151 (1964)

[c11] W. Moffitt and A. D. Liehr, Phys. Rev. 106, 1195 (1957)

[c12] W. Moffitt and W. Thorson, Phys. Rev. 108, 1251 (1957)

[c13] W. Moffitt and W. Thorson, in Calcul des Fonctions d'Onde M oleculaire, edited by R. Daudel (Rec. Mem. Centre Nat. Rech. Sci., Paris, 1958), p. 141

[c14] H. C. Longuet-Higgins, U. Opik, M. H. L. Pryce, and R. A. Sack, Proc. Roy. Soc. (London) A244, 1 (1958)

[c15] M. S. Child and H. C. Longuet-Higgins, Phil. Trans. Roy. Soc. (London) A254, 259 (1961)

[c16] M. C. M. O'Brien, Proc. Roy. Soc. (London) A281, 323 (1964)

[c17] I. B. Bersuker, Zh. Eksperim. i Teor. Fiz. 43, 1315 (1962) [English transl.: Soviet Phys.—JETP 16, 933 (1963)]

[c18] J. C. Slonczewski, Phys. Rev. 131, 1596 (1963)

[c19] I. B. Bersuker, Zh. Eksperim. i Teor. Fiz. 44, 1239 (1963) [English transl.: Soviet Phys—JETP 17, 836 (1963)]

[c20] R. Englman and D. Horn, in Proceedings of the First International Conference on Paramagnetic Resonance, edited by W. Low (Academic Press Inc., New York, 1963), p. 329

[c21] I. B. Bersuker, S. S. Budnikov, B. C. Vekhter, and B. I. Chinik, Fiz. Tverd. Tela 6, 2583 (1964) [English transl.: Soviet Phys.—Solid State 6, 2059 (1965)]

[c22] C. W. Struck and F. Herzfeld, J. Chem. Phys. 44, 464 (1966)

[c23] D. C. Krupka and R. H. Silsbee, Phys. Rev. 152, 816 (1966)

[c24] R. E. Coffman, Phys. Letters 19, 475 (1965) ibid.21, 381 (1966) (unpublished)

[c25] U. T. Höchli and T. L. Estle, Phys. Rev. Letters 18, 128 (1967) U. T. Höchli, Phys. Rev. 162, 262 (1967)

[c26] F. S. Ham, Phys. Rev. 138, A1727 (1965)

[c27] W. Low and A. Rosenthal, Bull. Am. Phys. Soc. 11, 906 (1966)

[c28] G. A. Slack, F. S. Ham, and R. M. Chrenko, Phys. Rev. 152, 376 (1966)

[c29] G. A. Slack, S. Roberts, and F. S. Ham, Phys. Rev. 155, 170 (1967)

[c30] Omitted endnote

[c31] ([23])

[c32] Omitted endnote

[c33] Omitted endnote

[c34] [28]

[c35] [15]

[c36] [14,15]

[c37] W. Hayes and J. Wilkens, Proc. Roy. Soc. (London) A281, 340 (1964)

[c38] Omitted endnote

[c39] A. Abragam and M. H. L. Pryce, Proc. Roy. Soc. A205, 135 (1951)

[c40] [25]

[c41] Omitted endnote

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Effect of Linear Jahn-Teller Coupling on Paramagnetic Resonance in a ${}^{2}E$ State

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Effect of Linear Jahn-Teller Coupling on Paramagnetic Resonance in a E2 State

Abstract

References (41)

Effect of Linear Jahn-Teller Coupling on Paramagnetic Resonance in a ${}^{2}E$ State