Ultrasonic Attenuation in Thallium

We have observed both geometric and open-orbit resonances in the ultrasonic attenuation in thallium at frequencies up to 460 Mc/sec. Sound was propagated in the [0001], [11{}20], and [10{}10] directions and extremal k vectors in the planes perpendicular to these propagation directions were measured. The measured k vectors agree well with the calculated values of Soven for the major pieces of the Fermi surface. We also observed an open-orbit resonance and several subharmonics for ^q parallel to [0001] and ^H parallel to [11{}20]. This results from magnetic breakdown between zones 3 and 4 in the vicinity of the AL line. No open orbits along the c axis were observed, probably indicating that the fourth-zone electron surface does not contact the ALH plane.