Volume 118, number 4 PHYSICS LETTERS A 13 October 1986 TEMPERATURE DEPENDENCE OF NUCLEAR, SPIN-LATTICE RELAXATION IN THE HEAVY-FERMION SUPERCONDUCIING STA’tE H. BAHLOULI Department of Physics, University of Illinois at Urbana-Champaign, Loomis Laboratory, 1110 West Green Street, Urbana, IL 61801, USA Received 30 June 1986; revised manuscript received 1 August 1986; accepted for publication 5 August 1986 Some features of the experimental data on nuclear spin relaxation time T, in the heavy-fermion superconducting state can be explained by taking into account the effect of the electron Zeeman energy. It is found that at intermediate temperatures the usual quasiparticle spin-flip scattering dominates, while at very low temperatures a new process, pair creation (annihilation), dominates and gives T; ' a T. The nuclear spin-lattice relaxation time Tl has always been used to study the nature of the super- conducting state because it gives information about low-energy excitations and the so-called coherence factor. In the new class of heavy-fermion super- conductors [l], Tl has been measured by Mac- Laughhn et al. m UBe,, and Kitaoka et al. in CeCu,Siz [2]. The data in UBe,, in fairly high fields *l seem to follow a T3 power law for T/5 5 T Q T,, while below - T/5 they follow a Kor- ringa law with a reduction factor - l/30. For the present calculation we will neglect the few percent of flux expulsion [3] and assume penetration of the magnetic field in the whole sample. Also it is assumed everywhere that ** GI-=:d,, I@ -X k,T, 0) where pLnis the nuclear magnetic moment and p the effective electronic magnetic moment at low temperatures [4]. *l Such high fields are possible for UBe,, since Hc2 = 80 kG at low temperatures whereas Hc2 LJ 2 kG for CeCu,Si s. Thus even though I will be concentrating on the data in UBe,, the results of my study should be valid for CeCu 2 Si a with the only difference that a Korringa law should occur at a much lower temperature than in UBe,,. ** With A/k,T,= 2.02 for ABM and A,/k,T, = 2.45 for polar and d-wave states, unpublished. The phenomenon we will be concentrating on occurs only when the gap has nodes. Neglecting spin-orbit coupling for the present purposes $3, we find out that nodes inm the gap can be ob- tained in three different situations: (1) Even-parity state with L # 0 and S = 0; (2) Odd-parity state with S = 1 and d ]I H ]] z; (3) Odd-parity state with S = 1 and d I H 11 z. Here L and S are the intrinsic orbital angular momentum and spin of the Cooper pair. We will be confined soon to cases L = 1,2 only. The order parameter is assumed to be of the form *4 d(n) = df(n), n=k/lk/. The first case needs no comment while the third one corresponds to fl and J,J spin pairing along the magnetic field H. This case is of no interest to us since all the electron Zeeman energy does is to shift the, up and down Fermi surfaces independently so that diagonalization of the qua- siparticle hamiltonian gives the 2 x 2 diagonal ma- trix ck = [(c, + r~,pH)~ + IAk I *]l’*, c-9 G *3 $4 The inclusion of spin-orbit coupling will be the subject of another investigation. In ref. [5] U, and Vk have been shown to be unaffected by the magnetic field to order H* for case (2). 0375-9601/86/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) 209