Attenuation of ultrasonic shear waves in copper at low temperatures

Jericho, M. H.; Simpson, A. M.

doi:10.1080/14786436808226162

Cited by 8 publications

(2 citation statements)

References 14 publications

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“…Detailed magnetoacoustic attenuation experiments on copper single crystals have been reported. 6,7 Their results are comparable to those from our helicon measurements.…”

Section: Introductionsupporting

confidence: 92%

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Doppler-Shifted Cyclotron Resonances with Helicons in Copper

Hui

1969

Phys. Rev.

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The nonlocal propagation of helicons in a mixed electron and hole plasma is discussed. The conditions under which the Doppler-shifted cyclotron resonance (DSCR) of either type of carrier are effective are specified. The nonlocal magnetoconductivity, the dispersion relation for helicons, and the consequent surface impedance are evaluated for the case where the helicon wave vector is parallel to B and to the [001] axis of copper, assuming Roaf's model of the Fermi surface. The low-rf surface impedance of a copper single crystal of the above orientation is measured at 4.2°K. The standing-wave pattern is damped out before the nonlocal region is reached. The damping effect is interpreted to be the DSCR from the sections of the Fermi surface at &[ooii =0.96 and 0.60 A -1 . Large surface-impedance anomalies are observed at low field. The field-frequency relation for the surface-impedance anomalies indicates that the electron orbits near the region k [oon = 0.45 A -1 are responsible. Detailed computation verifies this argument. The result is comparable to that of the magnetoacoustic attenuation measurements. INTRODUCTIONR ECENTLY there were several reports on the measurement of Fermi surfaces by the Dopplershifted cyclotron resonance (DSCR) with helicons. 1-3 This theory was first suggested, and later developed, by Stern and co-workers. 4 -5 In this paper, we present our result and interpretation of helicon measurements in a copper single crystal, with the magnetic field B parallel to the [001"] axis.In theory, the DSCR with helicons is very similar to that with ultrasonic shear waves. Both methods draw the same information about the Fermi surface. Detailed magnetoacoustic attenuation experiments on copper single crystals have been reported. 6,7 Their results are comparable to those from our helicon measurements. THEORYFor helicon waves propagating along the magnetic field direction (taken as the z axis of the Cartesian coordinates), the dispersion equation may be written (in mks units), with displacement current neglected, as tivity ).(1)Here q and w are the wave number and angular frequency of the waves, and o-± is the conductivity related to the propagation of the circularly polarized waves. The ± sign indicates left-and right-handed circular polarizations of the waves. In general, l/r^>co, the real and imaginary parts of (2) may be separated as 5(4)The nonlocal region is defined by ql> 1, where I is the carrier mean free path. DSCR occurs when u approaches unity and e<

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“…Detailed magnetoacoustic attenuation experiments on copper single crystals have been reported. 6,7 Their results are comparable to those from our helicon measurements.…”

Section: Introductionsupporting

confidence: 92%

“…The observed, but yet unexplained, ultrasonic absorption peaks between 3 and 10 kG at 100 MHz may also be caused by these regions. 7 uable discussions. The communication with Professor E. A. Stern is appreciated.…”

Section: Discussionmentioning

confidence: 98%

Doppler-Shifted Cyclotron Resonances with Helicons in Copper

Hui

1969

Phys. Rev.

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Theory of Electromagnetic Waves in Metals and Their Interaction with Ultrasonic Waves (III)

Mertsching¹

1970

Physica Status Solidi (b)

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Ultrasonic Absorption in the Intermediate State of Gallium and Indium

Singh¹

1977

Physica Status Solidi (b)

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BY SINGH~)The absorption is stndicd of longitudinal ultrasound in the intermediate state of indium and gallium single crystal cylinders a t 1.17 and 0.39 K, respectively, for frequencies ranging between 10 and 70 MHz. The results are analysed with a theory developed by Andreev which is extended to allow for the arbitrary values of ql. The width of the normal regions calculated from the results is in reasonable agreement with that calculated using Landau's unbranched model with surface energy parameters equal t o 3.5 :.cm for indium and gallium, respectively. The nonlinear variation of the high-frequency-limit attenuation is perhaps due t o the curvature of thc N-S interfaces near the surface of the specimen. and 8 :.:Es wird die Absorption longitudinaler Ultraschallwellen in zylindrischen In-und Ga-Einkristallcn im Zwischenzustand gemessen, und zwar bei T = 1,17 bzw. 0.39 K im Frequenzbereich 10 bis 70 MHz. Die Ergebnisse werden mit der Theorie yon Andreev verglichen, die auf beliebige ql erweitert wird. Die aus den MeBergebnissen ormittelte Ausdehnung der nornialleitenden Bereiche stimnit mit derjenigen aus dem ,,unverzweigten Modell" (nach Landau) errechneten gut iiberein. Dabei wird fur die Breite des ubergangsbereiches 81, = 3,5 i:cm gewahlt. Die nichtlineare Ahhangigkeit der Grenze, bei der die HF-Danipfung einsetzt, wird mijglicherweise durch die Kriimniung der N-S-Grenzflachcn an der Probenoberflache verursacht.

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Attenuation of ultrasonic shear waves in copper at low temperatures

Cited by 8 publications

References 14 publications

Doppler-Shifted Cyclotron Resonances with Helicons in Copper

Doppler-Shifted Cyclotron Resonances with Helicons in Copper

Theory of Electromagnetic Waves in Metals and Their Interaction with Ultrasonic Waves (III)

Ultrasonic Absorption in the Intermediate State of Gallium and Indium

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