PHYSICAL REVIEW LETTERS VOLUME 56, NUMBER 23 Depth in the Heavy-Electron Magnetic Field Penetration D. Einzel, P. J. Hirschfeld, 'i F. Gross, Walther Meissner Institut fur Tieftemperaturforschung, 9 JUNE 1986 Snyerconductor UBet3 B. S. Chandrasekhar, t ' and K. Andres D8046 Garchi ng bei Munchen, Federal Republic of Germany H. R. Ott Laboratorium fiir Festkorperphysik, Eidgenossische Technische Hochschule Honggerberg, CH8093 Ziirich, Switzerland J. Beuers Max Plane-k Institu-t fur Metallforschung, D7000 Stuttgart 80, Federal Republic of Germany and Z. Fisk and J. L. Smith Los AIamos Nationa/ Laboratory, Los Alamos, New Mexico 87545 (Received 4 February 1986) %e report the observation of a T temperature dependence of the magnetic field penetration %'e show that this behavior is consistent with an anisotropic depth in UBel3 at low temperatures. gap function for an axial p-wave state. Our results further show that the Landau parameter F'l ap- pears to be small. PACS numbers: 74. 30. Ci, 74.70. Rv The heavy-electron superconductor UBe~3 shows anomalous, i.e. , non-BCS, behavior in several proper- ties like the electronic specific heat, ultrasonic at- tenuation, 2 and spin-lattice relaxation. s These proper- ties are directly related to the spectrum of quasiparticle states that can be excited from the superconducting ground state, and it has been argued that they are more consistent with the spectrum expected for a spin-triplet, or odd-parity, paired state. Among exper- iments yielding more direct information about such an unconventional superconducting state are ground those which investigate the supercurrent properties, such as Josephson effects and magnetic field penetra- tion. The former are particularly sensitive to the sym- metry properties of the ground-state wave function. Partly as a result of material preparation difficulties, however, they have not yet yielded clear-cut answers in the case of UBei3. This Letter describes principal results on the latter experiments in which we have ob- served and calculated the magnetic field penetration depth in UBei3 as a function of temperature. The de- tails of this work will be published elsewhere. 5 By inspecting the basic London equation j'= — (c/4m)X 'A, z'= (m c'/4me')m/p', which relates the supercurrent density j' to the mag- netic vector potential A and defines a field penetration depth X, one sees that by measuring X(T) one can get information about the following quantities and proper- ties of the superconductor: (i) the value of the effec- tive mass m', (ii) the temperature dependence of the superfluid mass density p', and (iii) (as will be shown below) the possible importance of Fermi-liquid effects and the value of the Landau parameter F'i. In what follows, we show that our measurements yield infor- mation on each of these points. We obtained internally consistent data on four sam- ples of UBei3, and present here the results for one of them. Its characteristics were as follows: density T, = 0. 86 K, 10'l0-900/0 transition p = 4. 3 glcm, width 0. 06 K, Meissner effect (in H = 0. 3 Oe) =3. 5olo. The experiment consisted of observation of the reversible changes in magnetization with tempera- ture of the superconducting sample which was located inside one coil of a sensitive SQUID bridge circuit. These reversible changes, which must be due to the field penetration effect only (for a more detailed dis- cussion of this point see Ref. 5), were nearly indepen- dent of whether the measuring field (always less than 0. 3 Oe) was switched on either above or below T, . From them the changes in the penetration depth ii. A. (T) — with the lowest measuring tem- can be calculated in a straightforward perature, manner. In Fig. 1 we show these observed changes, plotted versus ( T/T, )2 for both the UBe» sample as well as for a reference sample of Sn. The most striking feature of Fig. 1 is that the tem- perature variation of A. (T) for UBe, 3 is quite unlike In fact, that of Sn, a well-known BCS superconductor. UBe, 3 shows a T variation of X(T) — X(0), with a 2 (see below), inconsistent temperature exponent K behavior the with exponential (l3o/kT) 'i' x exp( b, o/'kT) expected for an isotropic London su- perconductor. The tin data are, over a significant well represented range of temperature, by X(T) — X(0) = P (0) { [I — (T/T, ) ] 'i — 1 j, as would be expected for a nonlocal BCS superconductor with near- (T;„), 1986 The American Physical Society T;,