Low-temperature 9Be spin relaxation in superconducting UBe13

Journal of Magnetism and Magnetic Matermls 63 & 64 (1987) 455-457 North-Holland, A m s t e r d a m

LOW-TEMPERATURE

9Be SPIN R E L A X A T I O N

455

IN S U P E R C O N D U C T I N G

DE MacLAUGHLIN,*MD LAN,+C TIEN,*JM MOORE,+WG J L SMITH* and H R O T T II Department o[ Physics, Umversttyof Cah[orma, Rwerstde, CA 92521, USA

UBela

CLARK,+Z

FISK,*

The dependence of the 9Be spin-lattice relaxation rate 1/T~ on magnetic field has been measured m the heavy-ferm~on superconductor UBet~ at temperatures well below T~ A crossover between relaxation vm spin d~ffus~on to m~xed-state v o r t e x cores (H > 6 kOe) and to paramagnetlc ~mpunhes (H < 6 kOe) ~s referred

1. Introduction

2. Results

Nuclear spin-lattice relaxation studies of the heavy-fermton superconductors UBe~3 [1,2] and CeCu2S12 [3] have ytelded evidence for unconvennonal C o o p e r p a m n g 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 v a n e s as T below ~ 150 m K [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 m a g n e n c 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

The field d e p e n d e n c e of 1/TI between 20 Oe and 16 kOe ts gtven m fig l at temperatures of 67 and 1 4 7 m K For high fields ( H > 6 k O e ) 1/7"1 approaches a lmear variation in H, whereas at low fields the relation 1/T1 ~ H -1/z is an approximate fit to the data over more than two decades of field vartatlon Here tt can also be seen that, at least for these two temperatures, I/T~ varies essentially hnearly wtth temperature at constant field We now consider the origins of these features

i

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UBeaa 10-2 Z

* Supported by US NSF grant no DMR-8413730 and the UC Rwerslde Academic Senate Committee on R e s e a r c h Department of Physics and Sohd Science Center, Umvers~ty of Cahfornm, Los Angeles, CA 90024, USA Supported by US NSF grant no ,DMR-8409390 and the UCLA Academic Senate Commlltee on R e s e a r c h Matermls Soence and Technology Dzvlslon, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Work performed under the auspices of the U S D e p a r t m e n t of Energy II Laboratormm fur Festkorperphyslk, ETH-Honggerberg, CH-8093 Zurich, Switzerland Supported by the Schwelzensche Nauonalfonds zur Forderung der Wlssenschafthchen Forschung

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F~g 1 Field dependence of 9Be spin-lattice relaxation rate 1/T~ at temperatures of 67 mK (x) and 147mK (D) A rough v a l u e for the field a b o v e which saturation of paramagnetlc lmpuntles would be expected (p-BH = kB T) IS indicated by the arrow T h e straight hnes m&cate p o w e r laws H ~/2 and H ~ as labeled

0304-8853/87/$03 50 O Elsevier Science Publishers B V ( N o r t h - H o l l a n d P h y s t c s P u b h s h m g Division)

456

D E MacLaughhn et al / Low-temperature 9Be spin relaxation m superconducting UBe;

2 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 T h e excess relaxation rate varied linearly with both temperature and applied field, as m the present case T h e 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]

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,

(2)

after angular dependences, R K K Y sinusmdal variations (cos 2kvr), e t c , have been a v e r a g e d over M c H e n r y et al [1 1] have reviewed these coupling mechamsms, which Involve rather longitudinal or transverse fluctuations of the impurity electron spin T h e impurity spin polarization Bj(x) and the transverse and longitudinal correlation tLmes r~ r, *~L of the fluctuations enter m the form [11] K ~ [B, Ix)/x]

~-~

1 + ('DrcT)ZH 2 (transverse flucts )

(3a)

or 'rcL

l / T . =(H/dPo),~e/Tt.+[1-(H/dP,,),~2]/TI~,

(1)

K ~ (dBj/dx) 1 + ( T f r c L ) 2 H 2 (longitudinal flucts ) ,

where T~, is the relaxation time due to superconducting excitations, l e far from cores At low temperatures T ~ b e c o m e s very long, and the first term dominates This picture accounts for the low-temperature relaxation behavior in UBe~3 at high fields (fig 1) T h e 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~= 3 5 0 / ~ at T / T c = O 1 This is in satisfactory a g r e e m e n t 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

2 2 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 T h e lnpuntms will, however, couple to nuclei via dipolar or redirect hyperfine

(3b)

d e p e n d m g 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 m o m e n t It is likely that longitudinal fluctuations wdl d o m m a t e the relaxation, since yj >> y~ According to this model several relaxation regimes can be distinguished, d e p e n d m g 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 (1/W,)dt = ( 4 " I r / 3 ) N c D 3 / 4 K ' / 4 ,

(4)

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

2 3 Temperature dependence T h e observed temperature dependence m the high-field regime follows naturally from the

D E MacLaughhn et al / Low-temperature 9Be spin relaxaaon m superconducting UBeI~ n o r m a l - h k e q u a s l p a r t l c l e e x o t a t l o n s in v o r t e x c o r e s which, as m t h e n o r m a l state, g i v e rise to a l i n e a r t e m p e r a t u r e d e p e n d e n c e of t h e r e l a x a t i o n rate ( l / T 1 ) . ~ T T h e t e m p e r a t u r e d e p e n d e n c e m the l o w - f i e l d r e g i m e , o n the o t h e r h a n d , m u s t arise f r o m a t e m p e r a t u r e d e p e n d e n c e of the l o n g i t u d i n a l Imp u r i t y - s p i n f l u c t u a t i o n r a t e 1/TcL, O a n d all o t h e r f a c t o r s in K a r e t e m p e r a t u r e i n d e p e n d e n t for low fields If 1/%L lS d u e to r e l a x a t i o n b y b u l k s u p e r c o n d u c t i n g q u a s l p a r t l c l e e x c i t a t i o n s , then ~t m i g h t o b e y t h e s a m e p o w e r law as the n u c l e a r r e l a x a t i o n r a t e 1/Tt at h i g h e r t e m p e r a t u r e I / Z c L ~ T ~ ( W e n o t e , h o w e v e r , that E S R m e a s u r e m e n t s in the n o r m a l state of U B e l 3 d o p e d with 4f p a r a m a g n e t l c l m p u r l t l e s [12] d o n o t yield the h n e w l d t h e n h a n c e m e n t e x p e c t e d f r o m r e l a x a t i o n b y h e a v y e l e c t r o n s In the slowf l u c t u a t i o n limit K oc 1/%L, a n d t h e r e f o r e (1/T1)dl oc T 3/4 T h i s w o u l d n o t b e d i s t i n g u i s h a b l e f r o m a l i n e a r t e m p e r a t u r e d e p e n d e n c e m the d a t a of fig 1

2 4 Crossover from low to htgh field The observed relaxation rate should then be the s u m of eq (1) [with n e g l i g i b l e l/T1s] a n d eq (4) T h i s is of the f o r m

1/Tt = A H -1/2 + B H ,

(5)

if t h e r e is no field d e p e n d e n c e o t h e r t h a n t h a t d i s c u s s e d a b o v e If m a t c h e d to the l o w - a n d h i g h - f i e l d d a t a of fig 1, e q (5) lies a b o v e the d a t a m t h e c r o s s o v e r r e g i o n T h e d e p e n d e n c e of eqs (3) on B j ( x ) c a n n o t b e n e g l e c t e d , h o w e v e r , at the low t e m p e r a t u r e s of t h e s e m e a s u r e m e n t s / z a H a n d k~ T a r e r o u g h l y e q u a l in the v i c i n i t y of the field i n d i c a t e d by the a r r o w in fig 1 A b o v e this field the i m p u r i t y spins a r e s a t u r a t e d , a n d b o t h B j ( x ) / x a n d d B j [ d x d e c r e a s e [as l / x a n d exp(-2x), respectively] Such a decrease would rapzdly r e m o v e the dlffUSlOn-hmlted c o m p o n e n t of the o b s e r v e d r e l a x a t i o n

457

3. Conclusion W e h a v e f o u n d an u n e x p e c t e d n o n m o n o t o n l c d e p e n d e n c e of the 9Be s p i n - l a t t i c e r e l a x a t i o n r a t e on a p p h e d field in UBe13 well b e l o w the s u p e r conducting transition temperature The most c o n v e n t i o n a l e x p l a n a t i o n a s c r i b e s the h i g h - f i e l d r e g i m e to r e l a x a t i o n by spin diffusion to v o r t e x cores, a n d the low-field r e l a x a t i o n ~s a t t r i b u t e d to spin dlffus~on to p a r a m a g n e t ~ c I m p u r i t i e s in a p a r t i c u l a r (dlffUSlOn-hmlted) r e l a x a t i o n r e g i m e O t h e r s p e c u l a t w e f e a t u r e s , s u c h as a s e c o n d b a n d of (hght) n o n s u p e r c o n d u c t m g e l e c t r o n s , an excess of l o w - l y i n g q u a s l p a r t l c l e e x o t a t l o n s , o r a h n e of p h a s e t r a n s m o n s at ~-6 k O e , d o n o t s e e m to b e r e q m r e d T h e a u t h o r s a r e g r a t e f u l to C T M u r a y a m a for h e l p with the l o w - t e m p e r a t u r e m e a s u r e m e n t s

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