Orbital Ordering in a Two-Dimensional Triangular Lattice

H. F. Pen; J. van den Brink; D. I. Khomskii; G. A. Sawatzky

doi:10.1103/PhysRevLett.78.1323

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Orbital Ordering in a Two-Dimensional Triangular Lattice

H. F. Pen, J. van den Brink, D. I. Khomskii, and G. A. Sawatzky

Laboratory of Applied and Solid State Physics, Materials Science Centre, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands

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Phys. Rev. Lett. 78, 1323 – Published 17 February, 1997

DOI: https://doi.org/10.1103/PhysRevLett.78.1323

Abstract

We discuss the role of orbital ordering in a two-dimensional triangular lattice. Usually, this lattice is considered as “frustrated.” We show that a peculiar type of orbital ordering can remove this frustration if we allow for orbital degeneracy. We pay special attention to the $d^{2}$ case, for which we present mean field calculations for possible orbital orderings and an exact diagonalization study of a three-site cluster within a degenerate Hubbard model. The results support the possibility of an orbitally ordered singlet ground state. In particular, it provides new insight to the magnetic phase transition and the low temperature phase of ${LiVO}_{2}$ .

References (21)

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[c1] S. Jin et al., Science 264, 413 (1994).

[c2] W. Bao et al., Phys. Rev. Lett. 71, 766 (1993).

[c3] G. A. Thomas et al., Phys. Rev. Lett. 73, 1529 (1994).

[c4] V. Sachan, D. J. Buttrey, J. M. Tranquada, and J. E. Lorenzo, Phys. Rev. B 51, 12 742 (1995).

[c5] H. A. Jahn and E. Teller, Proc. R. Soc. London Sect. A 276, 238 (1937).

[c6] K. I. Kugel and D. I. Khomskii, Sov. Phys. JETP 37, 725 (1973) Sov. Phys. Usp. 25, 231 (1982), and references therein.

[c7] P. W. Anderson, Mater. Res. Bull. 8, 153 (1973).

[c8] J. B. Goodenough, Magnetism and the Chemical Bond (Interscience Publishers, New York, 1963).

[c9] W. A. Harrison, Electronic Structure and the Properties of Solids (Freeman, San Fransisco, 1989).

[c10] L. P. Cardoso, D. E. Cox, T. A. Hewston, and B. L. Chamberland, J. Solid State Chem. 72, 234 (1988).

[c11] C. E. Moore, Atomic Energy Levels, NBS Circular No. 467 (United States Government Printing Office, Washington, DC, 1949).

[c12] J. Zaanen and G. A. Sawatzky, J. Solid State Chem. 88, 8 (1990).

[c13] A. E. Bocquet et al., Phys. Rev. B 53, 1161 (1996).

[c14] P. F. Bongers, Ph.D. thesis, University of Leiden, 1957.

[c15] K. Kobayashi, K. Kosuge, and S. Kachi, Mater. Res. Bull. 4, 95 (1969).

[c16] H. F. Pen et al. (unpublished).

[c17] J. B. Goodenough, G. Dutta, and A. Manthiram, Phys. Rev. B 43, 10 170 (1991).

[c18] K. Imai et al., J. Solid State Chem. 114, 184 (1995).

[c19] J. Kikuchi et al., J. Phys. Soc. Jpn. 60, 3620 (1991).

[c20] K. Takeda, K. Miyake, K. Takeda, and K. Hirakawa, J. Phys. Soc. Jpn. 61, 2156 (1992).

[c21] S. J. Clarke et al., Chem. Commun. 3, 409 (1996).

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Orbital Ordering in a Two-Dimensional Triangular Lattice

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