Attenuation and Rotation of Plane-Polarized Ultrasound in Copper in a Longitudinal Magnetic Field

Abstract

The rotation of the plane of polarization and attenuation of a shear sound wave at 4.2°K have been measured for the propagation vector q parallel to the magnetic field B in the [001] direction in copper. Frequencies from 30 to 110 Mc/sec were used. Both the attenuation and rotation are periodic in p/B, where v is the sound frequency. The period for the attenuation is 0.0201 ±0.0005 Mc/sec G, whereas the period for the rotation is 0.0402±0.001 Mc/sec G. A theory is presented which describes this effect. The oscillations in the attenuation are of the type predicted by Kaner, Peschanskii, and Privorotskii, with a peak in the attenuation preceding an absorption edge. An absorption edge is observed at about one-fourth the magnetic field value expected for the free-electron case. The results are interpreted in terms of the Fermi surface of copper as put forth by Roaf. A method is suggested for determining O> C T, where w c is the cyclotron frequency and r the relaxation time; a value of m c %=0.381 ±0.009X10~1 9 g cm/sec is assigned to electrons with orbits near the plane ^=0.45X10 8 cm -1 , where m c is the cyclotron effective mass, d z is the drift velocity, and k z is the [001] direction.

Attenuation of ultrasonic shear waves in copper at low temperatures

“…The variation of u and <D below about 2 kgauss has therefore been represented by dotted lines for the sake of clarity since in that range both u ( H ) and @ ( H ) had a strong oscillatory dependence on H . Near 3 kgauss the large attenuation peak reported by Boyd and Gavenda (1966) is visible and the magnitude-relative to the attenuation in zero field-as well as the general shape of the peak is in fair agreement with their results. As H was increased further three other peaks appeared.…”

“…I n the low field region our results are similar to those reported by Boyd and Gavenda (1966), but in the high field region several new features are apparent.…”

“…This should give best agreement in the high field range. As can be seen the overall quantitative agreement is reasonable but a t the higher frequencies the attenuation peak discussed by Boyd and Gavenda (1966) becomes visible and agreement with the free electron model is of course lost. I n fig.…”

“…If one measures the apparent attenuation for both positive and negative field one can obtain two simultaneous equations involving the rotation and the change in attenuation relative to the zero field value. These can be solved easily and Boyd and Gavenda (1966) have shown that the rotation angle is given by the expressions :…”

“…We have used this technique to obtain the electronic component of the attenuation of shear waves in copper and also information about the Fermi surface. Recently Boyd and Gavenda ( 1966) have reported attenuation measurements for shear waves in copper with this parallel field geometry for fields up to 10 kgauss. We have made similar measurements in fields up to 45 kgauss for the three principal symmetry directions in copper.…”