Dynamic Jahn-Teller Effect in an Orbital Triplet State Coupled to Both <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></math></span> and <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mn>2</mn><mi>σ</mi></mrow></msub></mrow></math></span> Vibrations

Mary C. M. O'Brien

doi:10.1103/PhysRev.187.407

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Dynamic Jahn-Teller Effect in an Orbital Triplet State Coupled to Both $E_{g}$ and $T_{2 σ}$ Vibrations

Mary C. M. O'Brien^*

Mason Laboratory, Yale University, New Haven, Connecticut 06520

^*Permanent address: Department of Theoretical Physics, Oxford University, Oxford, England.

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Phys. Rev. 187, 407 – Published 10 November, 1969

DOI: https://doi.org/10.1103/PhysRev.187.407

Abstract

The Jahn-Teller coupling of a triplet state in cubic surroundings to both $E_{g}$ and $T_{2 g}$ modes of vibration can lead to a vibronic ground state that includes both tetragonal and trigonal distortions if the energy difference between the static distortions is small. A simple model is set up to study the properties of this ground state, assuming the Jahn-Teller coupling is strong, so that the adiabatic approximation can be used. Expressions for the reduction factors $K (E)$ and $K (T_{2})$ , the $g$ values, and their sensitivity to strains in the crystal are derived. These properties interpolate nicely between those appropriate to coupling to $E_{g}$ or $T_{2 g}$ modes separately. The ground state is a triplet belonging to the same irreducible representation as the original triplet throughout the range of parameters considered.

References (17)

F. S. Ham, in Electron Paramagnetic Resonance, edited by S. Geschwind (Plenum Press, Inc., New York, to be published)
M. D. Sturge, in Solid State Physics, edited by F. Seitz, D. Turnbull, and H. Ehrenreich (Academic Press Inc., New York, 1967), Vol. 20
J. H. Van Vleck, J. Chem. Phys. 7, 72 (1939)
F. S. Ham, Phys. Rev. 138, A1727 (1965)
M. Caner and R. Englman, J. Chem. Phys. 44, 4054 (1966)
U. Öpik and M. H. L. Pryce, Proc. Roy. Soc. (London), A238, 425 (1957)
A. F. Devonshire, Proc. Roy. Soc. (London) 153, 601 (1936) P. Sauer, Z. Physik 194, 360 (1966)
G. F. Koster, J. O. Dimmock, R. G. Wheeler, and H. Statz, Properties of the 32 Point Groups (MIT Press, Inc., Cambridge, Mass. 1966)
A. Abragam and M. H. L. Pryce, Proc. Roy. Soc. (London) A205, 135 (1951)
F. S. Ham. Phys. Rev. 166, 307 (1968)
F. I. B. Williams, D. C. Krupka, and D. P. Breen, Phys. Rev. 179, 255 (1969)
J. C. Kemp, W. M. Ziniker, J. A. Glaze, and J. C. Cheng, Phys. Rev. 171, 1024 (1968)
R. G. Bessent, B. C. Cavenett, and I. C. Hunter, J. Phys. Chem. Solids 29, 1523 (1968)
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M. D. Sturge, Phys. Rev. 140, A880 (1965)
F. S. Ham, in Optical Properties of Ions in Crystals, edited by H. M. Crosswhite and H. W. Moos (Wiley-Interscience, Inc., New York, 1967), p. 357
G. D. Watkins, J. Phys. Soc. Japan 18, Suppl. II, 22 (1963)

[c1] F. S. Ham, in Electron Paramagnetic Resonance, edited by S. Geschwind (Plenum Press, Inc., New York, to be published)

[c2] M. D. Sturge, in Solid State Physics, edited by F. Seitz, D. Turnbull, and H. Ehrenreich (Academic Press Inc., New York, 1967), Vol. 20

[c3] J. H. Van Vleck, J. Chem. Phys. 7, 72 (1939)

[c4] F. S. Ham, Phys. Rev. 138, A1727 (1965)

[c5] M. Caner and R. Englman, J. Chem. Phys. 44, 4054 (1966)

[c6] U. Öpik and M. H. L. Pryce, Proc. Roy. Soc. (London), A238, 425 (1957)

[c7] A. F. Devonshire, Proc. Roy. Soc. (London) 153, 601 (1936) P. Sauer, Z. Physik 194, 360 (1966)

[c8] G. F. Koster, J. O. Dimmock, R. G. Wheeler, and H. Statz, Properties of the 32 Point Groups (MIT Press, Inc., Cambridge, Mass. 1966)

[c9] A. Abragam and M. H. L. Pryce, Proc. Roy. Soc. (London) A205, 135 (1951)

[c10] F. S. Ham. Phys. Rev. 166, 307 (1968)

[c11] F. I. B. Williams, D. C. Krupka, and D. P. Breen, Phys. Rev. 179, 255 (1969)

[c12] J. C. Kemp, W. M. Ziniker, J. A. Glaze, and J. C. Cheng, Phys. Rev. 171, 1024 (1968)

[c13] R. G. Bessent, B. C. Cavenett, and I. C. Hunter, J. Phys. Chem. Solids 29, 1523 (1968)

[c14] A. E. Hughes and W. A. Runciman, J. Phys. C2, 37 (1969)

[c15] M. D. Sturge, Phys. Rev. 140, A880 (1965)

[c16] F. S. Ham, in Optical Properties of Ions in Crystals, edited by H. M. Crosswhite and H. W. Moos (Wiley-Interscience, Inc., New York, 1967), p. 357

[c17] G. D. Watkins, J. Phys. Soc. Japan 18, Suppl. II, 22 (1963)

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Dynamic Jahn-Teller Effect in an Orbital Triplet State Coupled to Both $E_{g}$ and $T_{2 σ}$ Vibrations

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Dynamic Jahn-Teller Effect in an Orbital Triplet State Coupled to Both Eg and T2σ Vibrations

Abstract

References (17)

Dynamic Jahn-Teller Effect in an Orbital Triplet State Coupled to Both $E_{g}$ and $T_{2 σ}$ Vibrations