Ultrasonic Attenuation in UPt3

We report measurements of the ultrasonic absorption in UPt3 through the superconducting transition. The attenuation varies as T at low temperature and is inconsistent with the iden-tification of UPt3 as a singlet superconductor. Our results can be well explained by assuming that UPt3 is an anisotropic (triplet) superconductor in a polarlike state, where the gap vanishes along a line on the Fermi surface.

Z. Fisk and J. L. Smith Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (Received 27 June 1984) We report measurements of the ultrasonic absorption in UPt3 through the superconducting transition. The attenuation varies as T at low temperature and is inconsistent with the identification of UPt3 as a singlet superconductor. Our results can be well explained by assuming that UPt3 is an anisotropic (triplet) superconductor in a polarlike state, where the gap vanishes along a line on the Fermi surface.
PACS numbers: 74.30.6n,74.20.z,74.70.Rv The discovery of superconductivity' in a class of materials which behave as Fermi liquids with large effective masses O(102-103) has raised important questions about the nature of the superconducting state and the interactions that are responsible for it.
One of us has suggested that conventional s-wave pairing through phonon-mediated interactions is unlikely in these materials and that S = 1 pairs must be involved. Anderson' has further argued this point of view while Tachiki and Maekawa4 and Razafimandimby, Fulde, and Keller5 favor the conventional form of superconductivity.
The measured anisotropy of the critical field in UPt3 has been used to show the existence of a polar-type S = 1 state, which has a line of zeros in the gap function on the Fermi surface. Also, the nonex-pOnential nature Of the Specific heat in UBe13 has been suggested as some indication for a nonsinglet superconducting State for UBe13 The specific heat' in CeCu2Si2 is also nonexponential but this has been taken as an indication for gapless behavior.
In this paper we report measurements of the temperature dependence of the ultrasonic attenuation in UPt3 to temperatures well below T, Our results are quite inconsistent with that expected for singlet pairing  LiNb03 and were fastened to the sample with epoxy resin. The sample was mounted in an ac susceptibility coil so that the susceptibility and the acoustical properties could be simultaneously measured. The superconducting transition occurred at about 480 mK with a width as measured by the susceptibility of -25 mK.
A pulse spectrometer of conventional design was used to measure the attenuation at frequencies from SO to 600 MHz. In Fig. 1 we show the ultrasonic attenuation and the ac susceptibility. Two points are readily apparent. At T, the attenuation does not drop off abruptly as it would for a singlet superconductor.
The data shown here (at 508 MHz) and shown later at 52 MHz are consistent with the attenuation approaching T, with zero or a very small slope. The second and the most impor-  We wiii concentrate on the calculation for quasiparticle scattering. In the limit ql « 1 but 1/( )) 1, " the longitudinal sound attenuation coefficient is given by' where A. is the electron-phonon matrix element, 6-" is the gap function, ' and E-" is the quasiparticle energy. This will in general yield nzeo, but its behavior as a function of temperature depends on the type of superconducting state. For singlet superconductors this yields the classic result' (2) where 5( T) is the singlet superconducting gap; this gives an attenuation which decreases exponentially at low temperatures and clearly disagrees with our results in Upt3.
For anisotropic superconductors ns/n~w111 depend on the type of state realized. These may be generally grouped into three classes: (a) States in which the gap exists over the entire Fermi surface (like the Balian-Werthamer or isotropic state in He). For these ns/nN has the temperature dependence given in Eq. This has a low-energy density of states -E2 and can be shown to have an attenuation proportional to T at low temperatures, in disagreement with our us/nN-(T/6)' for T « b, .
As was shown in Fig. 2 this temperature dependence is found experimentally.
To compare theory and experiment over the entire temperature range us/uz must be evaluated numerically. This is shown in Fig. 3. For 6 ( T) we have used the BCS expression with 5( T= 0) = -2.6T, chosen to obtain the best fit. Also shown in Fig. 3   For T -T, -Ifto/ks 7the ultrasonic attenuation in 'He is dominated by resonant absorption by collective' modes of the orbital angular momentum variables. In materials like UPt3, the crystal-field energies and the spin-orbit energies are considerably larger than even the effective heavy-electron bandwidth, Therefore, continuous symmetries for spin and orbit quantization axes do not exist. Propagating collective modes are therefore not expected. However, relaxational modes of the spin-orbit axes are still to be expected with significant amplitude near T, .
In conclusion, we have measured the ultrasonic attenuation and sound velocity in UPt3. Our results are unambiguous that superconductivity in this compound is not due to singlet pairing. We obtain good agreement with a model assuming anisotropic (triplet) pairing with a polarlike state.