Quantum Oscillations of the Velocity of Sound in Gallium

L. J. Neuringer; Y. Shapira

doi:10.1103/PhysRev.165.751

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Quantum Oscillations of the Velocity of Sound in Gallium

L. J. Neuringer^* and Y. Shapira^*

National Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts

^*Supported by the U. S. Air Force Office of Scientific Research.

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Phys. Rev. 165, 751 – Published 15 January, 1968

DOI: https://doi.org/10.1103/PhysRev.165.751

Abstract

Large-amplitude quantum oscillations of the ultrasonic velocity, $| \frac{Δ V}{V_{0}} | \sim 10^{- 3}$ , were measured in single-crystal gallium at $1.2 {}^{\circ}K < T < 1.6 {}^{\circ}K$ in magnetic fields up to 150 kG. The measurements were carried out using 11- and 28-Mc/sec longitudinal sound waves with $q ∥ H ∥$ ( $b$ crystallographic axis). The experimental results are compared with three different theories of this phenomenon. The most satisfactory account of the experimental observations, including the amplitude of the velocity oscillations, is given by the Blank-Kaner theory, although some features of the data remain unexplained.

References (15)

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[c1] V. L. Gurevich, V. G. Skobov, and Yu. A. Firsov, Zh. Eksperim. i Teor. Fiz. 40, 786 (1961) [English transl.: Soviet Phys.—JETP 13, 552 (1961)]

[c2] Y. Shapira and B. Lax, Phys. Rev. 138, A1191 (1965)

[c3] J. G. Mavroides, B. Lax, K. J. Button, and Y. Shapira, Phys. Rev. Letters 9, 451 (1962)

[c4] G. A. Alers and R. T. Swim, Phys. Rev. Letters 11, 72 (1963)

[c5] J. J. Quinn and S. Rodriguez, Phys. Rev. Letters 9, 145 (1962)

[c6] S. Rodriguez, Phys. Rev. 132, 535 (1963)

[c7] A. Ya. Blank and E. A. Kaner, Zh. Eksperim. i Teor. Fiz. 50, 1013 (1966) [English transl.: Soviet Phys.—JETP 23, 673 (1966)]

[c8] L. J. Neuringer and Y. Shapira, Phys. Rev. 148, 231 (1966)

[c9] T. W. Moore, Phys. Rev. (to be published)

[c10] D. Shoenberg, Phil. Trans. Roy. Soc. (London) A245, 1 (1952)

[c11] A. Goldstein and S. Foner, Phys. Rev. 146, 442 (1966)

[c12] J. H. Wood, Phys. Rev. 146, 432 (1966)

[c13] I. M. Lifshitz and A. M. Kosevich, Zh. Eksperim. i Teor. Fiz. 29, 730 (1955) [English transl.: Soviet Phys.—JETP 2, 636 (1956)]

[c14] L. Onsager, Phil. Mag. 43, 1006 (1952)

[c15] T. W. Moore, Phys. Rev. Letters 18, 310 (1967)

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Quantum Oscillations of the Velocity of Sound in Gallium

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