Radiofrequency size-effect measurements of the electron scattering frequency in cadmium

Abstract

Precise parallel- and tilted-field radiofrequency size-effect measurements of the temperature dependence of the electron scattering frequency v(T) have been made on symmetric orbits on the first-, second-, and third-band Fermi surface sheets in samples with normals 〈11\-20〉 and 〈10\-10〉. The limiting point measurements on the third-band lens near 〈0001〉 provide the clearest evidence for a T 2 contribution to v(T) that is the right order of magnitude for electron-electron scattering in cadmium. In parallel field measurements on orbits on the first and second bands (including a “broken” orbit) we find v(T) ≃ αT 2 + βT 3. On these orbits the values for α are 5–20 times larger than for the limiting point and other orbits on the third band. The temperature dependence of v(T\> 2 K) on extremal, limiting point, and open orbits on the second- and third-band Fermi surface sheets can be well accounted for by a simple plane wave model for electron-phonon intersheet scattering. This contribution to v(T) “turns on” approximately as exp (−T t /T) above T t /10, where T t is the minimum “gap” temperature on the orbit for intersheet scattering by quasi-transversely polarized phonons. The fitted gap temperatures as well as the other parameters of the plane wave model agree well with the known dimensions of the Fermi surface of cadmium. While clear evidence is lacking, we note that this intersheet scattering model can also be used to explain the large T 2 coefficients obtained for the first- and second-band orbits, where, in fact, one has gap temperatures T t smaller than 1 K.