Low-temperature 9Be spin relaxation in superconducting UBe13

Abstract The dependence of the 9 Be spin-lattice relaxation rate 1/ T 1 on magnetic field has been measured in the heavy-fermion superconductor UBe 13 at temperatures well below T c . A crossover between relaxation via spin diffusion to mixed-state vortex cores ( H > 6 kOe) and to paramagnetic impurities ( H


Nuclear spin-lattice relaxation studies of the heavy-fermton superconductors UBe~3 [1,2] and
CeCu2S12 [3] have ytelded evidence for unconvennonal Cooper pamng m these exotic matertals In both systems the spin-lattice relaxation rate 1/T~ varies as T 3 over a considerable range of temperatures In the case of UBe~3, however, the spm-latnce relaxation rate 1/Tt dewates from the T ~ law at lower temperatures, and vanes as T below ~ 150 mK [2] It is obvtously destrable to determine whether this devmtlon ts extrmstc, e g due to paramagnetlc tmpurltles, or is an intrinsic feature of the superconducting state We report m th~s paper field-cychng 9Be spin-lattice relaxanon measurements in superconducting UBel3 over a wide magnenc field range (20 Oe < H < 15 kOe) at two temperatures (67 and 147 mK), which were undertaken to clarify further the anomalous relaxation behavtor descrtbed above

1 H~gh-field regime
Previous nuclear spin-lattice studies of conventional superconductors in the mixed state [4] revealed a breakdown of the actwated behavior [5] expected for relaxation by quaslpamcle excitations over the BCS energy gap The excess relaxation rate varied linearly with both temperature and applied field, as m the present case The mechanism suggested [4] for this breakdown invokes low-lying exmtatlons [6] in Abrlkosov vortex cores (of radms ~ the superconducting coherence length ~j), with energies similar to normal-state excitations, together with transfer of spin energy by spin diffusion between core and bulk nuclei If spin diffusion is fast (DH/~o>> 1/TI, where D is the spin diffusion constant and ~o is the flux quantum), the order of magnitude of the observed spin-lattme rate IS given by [7] where T~, is the relaxation time due to superconducting excitations, l e far from cores At low temperatures T~ becomes very long, and the first term dominates This picture accounts for the low-temperature relaxation behavior in UBe~3 at high fields ( fig  1) The temperature and field dependences (1/T~ oc HT) are consistent with the first term of eq (1), and the observed ratio (1/T1),,b,/(1/Tl)n 25 at 15 kOe ymlds s ~= 350/~ at T/Tc=O 1 This is in satisfactory agreement with the value of 140 ~ derived from critical field measurements [8], consldenng the approximate nature of eq (1) and the unusual behavior of the crmcal field

Low-field reg:me
Here the relaxation is clearly dominated by a different mechanism We consider as a candidate for thts mechanism relaxation vm nuclear spin dlffus~on to dilute paramagnetlc impurities These are postulated to be present at some low concentration, too low to cause appreciable pair breaking [9] or other perturbation of the superconductwlty The lnpuntms will, however, couple to nuclei via dipolar or redirect hyperfine interactions [ 10,1 I] All these mechanisms yield a direct relaxation rate l/T~(r) of a nucleus a distance r from an impurity at the origin which is given, in the absence of spin diffusion, by l/Tl(r) = K/r 6, dependmg on the mechanism Here y, and y~ are the impurity and nuclear gyromagnetlc ratios, respectively, and B1(x), x = gatxuH/kuT, is the Brillomn function appropriate to the impurity moment It is likely that longitudinal fluctuations wdl dommate the relaxation, since yj >> y~ According to this model several relaxation regimes can be distinguished, dependmg on the relatwe strengths of K and the nuclear spin diffusion constant D [10] One of these, the so-called diffusion-limited regime, ymlds a relaxation rate where N is the density of impurity s~tes per unit volume and c is the impurity concentration We can therefore account for the low-field relaxation field dependence 1/T1 oc H -1/2 if (a) the Impurity relaxation is m the dlffUsion-hmlted regime, and (b) the longitudinal impurity correlation time %L Ls long, so that yircLH > 1

3 Temperature dependence
The observed temperature dependence m the high-field regime follows naturally from the normal-hke quaslpartlcle exotatlons in vortex cores which, as m the normal state, give rise to a linear temperature dependence of the relaxation rate (l/T1). ~ T The temperature dependence m the low-field regime, on the other hand, must arise from a temperature dependence of the longitudinal Impurity-spin fluctuation rate 1/TcL, O and all other factors in K are temperature independent for low fields If 1/%L lS due to relaxation by bulk superconducting quaslpartlcle excitations, then ~t might obey the same power law as the nuclear relaxation rate 1/Tt at higher temperature I/ZcL~ T ~ (We note, however, that ESR measurements in the normal state of UBel3 doped with 4f paramagnetlc lmpurltles [12] do not yield the hnewldth enhancement expected from relaxation by heavy electrons In the slowfluctuation limit K oc 1/%L, and therefore (1/T1)dl oc T 3/4 This would not be distinguishable from a linear temperature dependence m the data of fig 1   2

Crossover from low to htgh field
The observed relaxation rate should then be the sum of eq (1) [with negligible l/T1s] and eq (4) This is of the form 1/Tt = AH -1/2 + BH, (5) if there is no field dependence other than that discussed above If matched to the low-and high-field data of fig 1, eq (5) lies above the data m the crossover region The dependence of eqs (3) on Bj(x) cannot be neglected, however, at the low temperatures of these measurements /zaH and k~ T are roughly equal in the vicinity of the

Conclusion
We have found an unexpected nonmonotonlc dependence of the 9Be spin-lattice relaxation rate on apphed field in UBe13 well below the superconducting transition temperature The most conventional explanation ascribes the high-field regime to relaxation by spin diffusion to vortex cores, and the low-field relaxation ~s attributed to spin dlffus~on to paramagnet~c Impurities in a particular (dlffUSlOn-hmlted) relaxation regime Other speculatwe features, such as a second band of (hght) nonsuperconductmg electrons, an excess of low-lying quaslpartlcle exotatlons, or a hne of phase transmons at ~-6 kOe, do not seem to be reqmred