de Haas-van Alphen Effect and Fermi Surface in Antimony

Lee R. Windmiller

doi:10.1103/PhysRev.149.472

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de Haas-van Alphen Effect and Fermi Surface in Antimony

Lee R. Windmiller^*,†

Institute for the Study of Metals and Department of Physics, The University of Chicago, Chicago, Illinois

^*National Science Foundation Predoctoral Fellow.
^†Present Address: Argonne National Laboratory, Lemont, Illinois.

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Phys. Rev. 149, 472 – Published 16 September, 1966

DOI: https://doi.org/10.1103/PhysRev.149.472

Abstract

The Fermi surface of antimony has been completely determined by the de Haas-van Alphen (dHvA) effect using the field-modulation measuring technique, modified to give strong dHvA period spectrometer action. The Fermi surface is found to consist of two sets of warped ellipsoids, the $α$ set having a tilt angle of 53.0°±0.1° defined by the period maximum in the mirror plane, and the $β$ set having a tilt angle of 87.7°±0.1° (angles are measured from $Γ T$ in the sense toward $Γ X$ ). Carrier compensation has been established with the $α$ set of carriers consisting of 6 pockets and the $β$ set of 3 pockets. When the present results are compared with the recent band-structure calculations it is clear that the $α$ carriers are the holes and the $β$ carriers the electrons. This is the reverse of the conventional assumption for the signs of the carriers in antimony. The deviation of each set of pockets from ellipsoids has been accurately determined From the ellipsoidal approximation, the carrier concentration was found to be $n_{e} = (5.54 \pm 0.05) \times 10^{19}$ electrons/ ${cm}^{3}$ and $n_{h} = (5.49 \pm 0.03) \times 10^{19}$ holes/ ${cm}^{3}$ . This new model removes the necessity for postulating a third band of carriers and is in agreement with all the previous experimental data. Comparison of the observed spin splitting with the electron-spin-resonance data of Datars gives new information on the angular variation of the $g$ factor. Extra period branches have been observed along almost every field direction, but these have all been shown to arise from nonlinear mixing of strong dHvA period components.

References (40)

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M. H. Cohen, L. M. Falicov, and S. Golin, IBM J. Res. Develop. 8, 215 (1964)
L. M. Falicov and S. Golin, Phys. Rev. 137, A871 (1965)
P. J. Lin and L. M. Falicov, Phys. Rev. 142, 441 (1966)
L. M. Falicov and P. J. Lin, Phys. Rev. 141, 562 (1966)
L. R. Windmiller and M. G. Priestley, Solid State Commun. 3, 199 (1965)
M. G. Priestley, L. R. Windmiller, J. Ketterson, and Y. Eckstein (to be published)
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L. S. Lerner and P. C. Eastman, Can. J. Phys. 41, 1523 (1963)
G. N. Rao, N. H. Zebouni, C. G. Grenier, and J. M. Reynolds, Phys. Rev. 133, A141 (1964)
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[11,13]
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[3]
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Omitted endnote
[13,19,20]
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[c1] the proceedings of the Topical Conference on Semimetals, New York, published in IBM J. Res. Develop. 8, 215 (1964)

[c2] M. H. Cohen, L. M. Falicov, and S. Golin, IBM J. Res. Develop. 8, 215 (1964)

[c3] L. M. Falicov and S. Golin, Phys. Rev. 137, A871 (1965)

[c4] P. J. Lin and L. M. Falicov, Phys. Rev. 142, 441 (1966)

[c5] L. M. Falicov and P. J. Lin, Phys. Rev. 141, 562 (1966)

[c6] L. R. Windmiller and M. G. Priestley, Solid State Commun. 3, 199 (1965)

[c7] M. G. Priestley, L. R. Windmiller, J. Ketterson, and Y. Eckstein (to be published)

[c8] S. Golin, Phys. Rev. 140, A993 (1965)

[c9] D. Shoenberg, Phil. Trans. Roy. Soc. London A245, 1 (1952)

[c10] Y. Saito, J. Phys. Soc. Japan 18, 452 (1963)

[c11] J. Ketterson and Y. Eckstein, Phys. Rev. 132, 1885 (1963)

[c12] L. S. Lerner and P. C. Eastman, Can. J. Phys. 41, 1523 (1963)

[c13] G. N. Rao, N. H. Zebouni, C. G. Grenier, and J. M. Reynolds, Phys. Rev. 133, A141 (1964)

[c14] W. R. Datars and J. Vanderkooy, IBM J. Res. Develop. 8, 247 (1964)

[c15] Y. Eckstein, Phys. Rev. 129, 12 (1963)

[c16] J. B. Ketterson, Phys. Rev. 129, 18 (1963)

[c17] L. Erikson, O. Beckman, and S. Hörnfeldt, J. Phys. Chem. Solids 25, 1339 (1964)

[c18] C. Nanney, Phys. Rev. 129, 109 (1963)

[c19] S. J. Freedman and H. J. Juretschke, Phys. Rev. 124, 1379 (1961)

[c20] S. Epstein and H. J. Juretschke, Phys. Rev. 129, 1148 (1963)

[c21] M. S. Dresselhaus and J. G. Mavroides, Solid State Commun. 2, 297 (1964)

[c22] [11,13]

[c23] J. J. Hall and S. H. Koenig, IBM J. Res. Develop. 8, 241 (1964)

[c24] R. Stark, L. R. Windmiller, and M. G. Priestley (to be published)

[c25] [3]

[c26] A. A. Abrikosov and L. A. Falkovskii, Zh. Eksperim. i Teor. Fiz. 43, 1089 (1962) [English transl.: Soviet Phys.—JETP 16, 769 (1963)]

[c27] M. H. Cohen, Phys. Rev. 121, 387 (1961)

[c28] D. Shoenberg and P. J. Stiles, Proc. Roy. Soc. (London) A281, 62 (1964)

[c29] D. Shoenberg, in Progress in Low Temperature Physics, edited by C. J. Gorter (North-Holland Publishing Company, Amsterdam, 1957), Vol. II, p. 226

[c30] M. Cohen and E. I. Blount, Phil. Mag. 5, 115 (1960)

[c31] G. E. Smith, J. K. Galt, and F. R. Merritt, Phys. Rev. Letters 4, 276 (1960)

[c32] Omitted endnote

[c33] [13,19,20]

[c34] D. Shoenberg, Phil. Trans. Roy. Soc. London A255, 85 (1962)

[c35] A. B. Pippard, Proc. Roy. Soc._(London) A272, 192 (1963)

[c36] N. B. Brandt, T. F. Dolgolenko, and N. N. Stupochenko, Zh. Eksperim. i Teor. Fiz. 45, 1319 (1963) [English transl.: Soviet Phys.—JETP 18, 908 (1964)]

[c37] G. E. Smith, G. A. Baraff, and J. M. Rowell, Phys. Rev. 135, A1118 (1964)

[c38] Y. Ishizawa and S. Tanuma, J. Phys. Soc. Japan 20, 1279 (1965)

[c39] M. S. Dresselhaus and J. G. Mavroides, Phys. Rev. Letters 14, 259 (1965)

[c40] W. R. Datars, Phys. Rev. 126, 975 (1962)

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de Haas-van Alphen Effect and Fermi Surface in Antimony

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