Theory of the Galvanomagnetic Properties of Magnesium and Zinc

L. M. Falicov; A. B. Pippard; Paul R. Sievert

doi:10.1103/PhysRev.151.498

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Theory of the Galvanomagnetic Properties of Magnesium and Zinc

L. M. Falicov^*,†

A. B. Pippard

Paul R. Sievert^‡

Cavendish Laboratory, University of Cambridge, Cambridge, England
Department of Physics and Institute for the Study of Metals, University of Chicago, Chicago, Illinois

Cavendish Laboratory, University of Cambridge, Cambridge, England

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

^*Alfred P. Sloan Research Fellow.
^†Work supported in part by the National Science Foundation and the U. S. Office of Naval Research.
^‡Advanced Research Projects Agency Research Assistant.

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Phys. Rev. 151, 498 – Published 11 November, 1966

DOI: https://doi.org/10.1103/PhysRev.151.498

Abstract

A theory of the galvanomagnetic properties of magnesium and zinc is developed. It is restricted to magnetic fields parallel to the hexad axis and takes into account the effects of magnetic breakdown. The transverse magnetoresistance shows the expected transition from electron-hole compensation at low fields to a noncompensated state at high fields, i.e., a transition from quadratic behavior to saturation. The Hall resistance shows the corresponding behavior. In addition, all transverse components of both conductivity and resistivity tensors show strong oscillations of the de Haas-van Alphen type due to coherent effects in the tunneling probability through small pieces of the Fermi surface. Theoretical curves are shown for various components of the galvanomagnetic tensors and compared with experimental measurements. Most parameters involved in the comparison are provided, or at least checked, by other experiments; only the breakdown field strength $H_{0}$ is unknown. It is found that a single $H_{0}$ suffices for Zn, but that for Mg, $H_{0}$ varies along the hexad axis. With this limited degree of adjustability, good agreement may be obtained between theory and experiment, though minor discrepancies remain unexplained.

References (34)

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R. W. Stark (private communication)
W. A. Reed, Bull. Am. Phys. Soc. 9, 633 (1964) private communication
R. G. Chambers, in The Fermi Surface, edited by W. A. Harrison and M. B. Webb (John Wiley & Sons, Inc., New York, 1962), p. 100 E. Fawcett, Advan. Phys. 13, 139 (1964)
I. M. Lifshitz, M. Ya. Azbel, and M. I. Kaganov, Zh. Eksperim. i Teor. Fiz. 30, 220 (1955) ibid.31, 63 (1956) English transls.: Soviet Phys.—JETP; 3, 143 (1956) Soviet Phys.—JETP4, 41 (1957) I. M. Lifshitz and V. G. Peschanskii, Zh. Eksperim. i Teor. Fiz. 35, 1251 (1958) ibid.38, 188 (1960) English transls.: Soviet Phys.—JETP 8, 875 (1959) Soviet Phys.—JETP11, 137 (1960)
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[15]
A. B. Pippard, Rept. Progr. Phys. 23, 176 (1960)
Omitted endnote
E. Fawcett, J. Phys. Chem. Solids 18, 320 (1961)
J. S. Dhillon and D. Shoenberg, Phil. Trans. Roy. Soc. (London) A248, 1 (1955)
L. M. Falicov and H. Stachowiak, Phys. Rev. 147, 505 (1966)
Omitted endnote
A. Myers and J. R. Bosnell, Phys. Letters 17, 9 (1965)
R. W. Stark (private communication)
C. G. Grenier, J. M. Reynolds, and N. H. Zebouni, Phys. Rev. 129, 1088 (1963)

[c1] R. W. Stark, Phys. Rev. Letters 9, 482 (1962) Phys. Rev. 135, A1698 (1964)

[c2] N. E. Alekseevskii and Y0323;. P. Gaidukov, Zh. Eksperim. i Teor. Fiz. 43, 2094 (1962) [English transl.: Soviet Phys.—JETP 16, 1481 (1963)]

[c3] W. A. Reed and G. F. Brennert, Phys. Rev. 130, 565 (1963)

[c4] R. W. Stark, T. G. Eck, and W. L. Gordon, Phys. Rev. 133, A443 (1964)

[c5] R. W. Stark, in Proceedings of the IXth International Conference on Low Temperature Physics, Columbus, Ohio 1964 (Plenum Press, Inc., New York, 1965), p. 712

[c6] R. W. Stark (private communication)

[c7] W. A. Reed, Bull. Am. Phys. Soc. 9, 633 (1964) private communication

[c8] R. G. Chambers, in The Fermi Surface, edited by W. A. Harrison and M. B. Webb (John Wiley & Sons, Inc., New York, 1962), p. 100 E. Fawcett, Advan. Phys. 13, 139 (1964)

[c9] I. M. Lifshitz, M. Ya. Azbel, and M. I. Kaganov, Zh. Eksperim. i Teor. Fiz. 30, 220 (1955) ibid.31, 63 (1956) English transls.: Soviet Phys.—JETP; 3, 143 (1956) Soviet Phys.—JETP4, 41 (1957) I. M. Lifshitz and V. G. Peschanskii, Zh. Eksperim. i Teor. Fiz. 35, 1251 (1958) ibid.38, 188 (1960) English transls.: Soviet Phys.—JETP 8, 875 (1959) Soviet Phys.—JETP11, 137 (1960)

[c10] M. H. Cohen and L. M. Falicov, Phys. Rev. Letters 7, 231 (1961)

[c11] E. I. Blount, Phys. Rev. 126, 1636 (1962)

[c12] M. G. Priestley, L. M. Falicov, and G. Weisz, Phys. Rev. 131, 617 (1963)

[c13] A. B. Pippard, Proc. Roy. Soc. (London) A270, 1 (1962)

[c14] A. B. Pippard, Phil. Trans. Roy. Soc. London A256, 317 (1964)

[c15] A. B. Pippard, Proc. Roy. Soc. (London) A287, 165 (1965)

[c16] L. M. Falicov and P. R. Sievert, Phys. Rev. Letters 12, 550 (1964) Phys. Rev. 138, A88 (1965)

[c17] W. G. Chambers, Phys. Rev. 140, A135 (1965)

[c18] L. M. Falicov, Phil. Trans. Roy. Soc. (London) A255, 55 (1962)

[c19] W. A. Harrison, Phys. Rev. 126, 497 (1962)

[c20] M. G. Priestley, Proc. Roy. Soc. (London) A276, 258 (1963)

[c21] A. S. Joseph and W. L. Gordon, Phys. Rev. 126, 489 (1962)

[c22] D. F. Gibbons and L. M. Falicov, Phil. Mag. 8, 177 (1963)

[c23] A. J. Bennett and L. M. Falicov, Phys. Rev. 136, A998 (1964)

[c24] A. B. Pippard, Proc. Roy. Soc. (London) A282, 464 (1964)

[c25] [15]

[c26] A. B. Pippard, Rept. Progr. Phys. 23, 176 (1960)

[c27] Omitted endnote

[c28] E. Fawcett, J. Phys. Chem. Solids 18, 320 (1961)

[c29] J. S. Dhillon and D. Shoenberg, Phil. Trans. Roy. Soc. (London) A248, 1 (1955)

[c30] L. M. Falicov and H. Stachowiak, Phys. Rev. 147, 505 (1966)

[c31] Omitted endnote

[c32] A. Myers and J. R. Bosnell, Phys. Letters 17, 9 (1965)

[c33] R. W. Stark (private communication)

[c34] C. G. Grenier, J. M. Reynolds, and N. H. Zebouni, Phys. Rev. 129, 1088 (1963)

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Theory of the Galvanomagnetic Properties of Magnesium and Zinc

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