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NMR in high-Tc oxide superconductors
Physlea C 185-189 (1991) 98-103 North-Holland
NMR
IN HIOH-T c OXIDE
Y o s h i o KITAOKA,
Kenji
SUPERCONDUCTORS
ISHIDA,
Shigeki OHSUGI,
D e p a r t m e n t of M a t e r i a l Physics, Toyonaka, Osaka 560, Japan
Kenji
F u j i w a r a and K u n i s u k e A S A Y A M A
F a c u l t y of E n g i n e e r i n g
Science,
O s a k a University,
63Cu NQR and NMR studies are e x t e n s i v e l y reported in L a 2 _ x S r x C u O 4 ( L S C O ) , heavilydoped TI2Ba2CuO6+y(TBCO) and Z n - d o p e d Y B a 2 C u 3 0 7 ( Y B C O y ) . The n u c l e a r s p i n - l a t t i c e r e l a x a t i o n (T 1) study extracts that the a n t i f e r r o m a E n e t i c (AF) s p i n c o r r e l a t i o n b e c o m e s less d i s t i n c t w i t h d e c r e a s i n g T c in h e a v i l y - d o p e d T B C O over an o p t i m u m hole content. In n o n - s u p e r c o n d u c t i n g TBCO, the A F s p i n c o r r e l a t i o n d i s a p p e a r s , s u g E e s t i n g an i n t i m a t e i n t e r r e l a t i o n between the o c c u r r e n c e of the s u p e r c o n d u c t i v i t y and the p r e s e n c e of the AF spin correlation. In s u p e r c o n d u c t i n g state, both the T 1 and Knight shift results in undoped- and Z n - d o p e d Y B C O 7 are c o n s i s t e n t l y u n d e r s t o o d w i t h i n a simple model combining both e f f e c t s of the gap zeros of lines at the Fermi s u r f a c e a r i s i n g f r o m d - w a v e p a i r i n g a n d of the s m a l l but f i n i t e r e s i d u a l d e n s i t y of s t a t e s at the Fermi level i n d u c e d by some i m p u r i t y and some imperfection.
1. I n t r o d u c t i o n To e l u c i d a t e the mechanism of t h e high-T c superconductivity, many exp e r i m e n t a l and t h e o r e t i c a l i n v e s t i g a t i o n s h a v e been c u r r e n t l y carried out. Among the extensive e x p e r i m e n t a l efforts, NMR and NQR are playing an important role in c l a r i f y i n g s e p a r a t e l y t h e e l e c t r o n i c state of the oxygen and copper sites in the CuO 2 plane,the p r e s e n c e of w h i c h is c r u c i a l for the o c c u r r e n c e of the s u p e r c o n d u c t i v i t y . So far, there are numerous NMR and NQR works on YBa?Cu306+x(YBCO6+x). The o u t s t a n d i n g feature is that the n u c l e a r spin lattice r e l a x a t i o n rate, 1/T 1 of 63Cu and 1 7 0 revealed a totally different Td e p e n d e n c e in normal state [I], a l t h o u g h both are strongly coupled through the c o v a l e n c y . This d i f f e r e n c e w a s u n d e r stood as due to the g e o m e t r i c a l c a n c e l lation of the a D t i f e r r o m a g n e t i c (AF) spin fluctuation among Cu s p i n s a t oxygen sites[l,2,3,4,5], demonstrating that there survives the coherent AF spin f l u c t u a t i o n between n e a r e s t n e i g h b o r Cu s p i n s in Y B C O 7. In f a c t , the n e u t r o n s c a t t e r i n g e x p e r i m e n t s in LSCO [6] a n d the d e p l e t e d YBCO6+ x [7] except in Y B C O 7
have d e t e c t e d the i n e l a s t i c s c a t t e r i n g o r i g i n a t i n g from the AF spin c o r r e l a t i o n a m o n g Cu s p i n s and e x t r a c t e d the m a g netic c o h e r e n c e length, (~ M/a) (a: distance b e t w e e n Cu s i t e s ) to b e ~ 3 f o r L a l . 8 5 S r 0 . 1 5 C u 0 4 (Tc=38 K) a n d ~ 1.5 f o r Y B C O 6 . 6 5 ( T o = 6 0 K). A p p a r e n t l y , the AF spin c o r r e l a t i o n remains in normal state of the s u p e r c o n d u c t i n g compounds. Now, it is a c o n t r o v e r s i a l issue whether the spin correlation mediates effectively the f o r m a t i o n of the C o p p e r paring. In t h i s c o n t e x t , it s h o u l d be n o t e d t h a t T c s t a r t s to d e c r e a s e u p o n f u r t h e r d o p i n g h o l e s o v e r an o p t i m u m v a l u e a n d t h a t the s u p e r c o n d u c t i v i t y disappears when the system becomes rather usual m e t a l [ 8 , 9 ] . T h u s far, s t u d i e s a r e c o n c e n t r a t e d on the system n e a r an o p t i m u m hole content as in L a l . 8 5 S r 0 . 1 5 C u O 4 and YBCO 7. In order to i n s p e c t the c o r r e l a t i o n b e t w e e n the T c and the AF spin f l u c t u a t i o n from a wide view, we h a v e e x t e n d e d the NQR and N M R works from the l i g h t l y - d o p e d region near the m a g n e t i c insulator-superconductor t r a n s i t i o n in LSCO [i0] to the heavilydoped region in T l 2 B a 2 C u O 6 + y (TBCO) [ii] where T c is ranging from 85K to OK.
0921-4534/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved.
/ NMR
Y. lOtaoka et at.
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63Cu NQR
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300 ,
,,, ,
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•
FIG
1. T - d e p e n d e n c e
xSrxCuO4
of 6 3 ( I / T I T )
in La2-
-100
0
A s for the s u p e r c o n d u c t i n g properties, a n s - w a v e m o d e l s e e m s to be s u p p o r t e d by many experiments. For instance, the r e s u l t s of 6 3 C u [12] and 170 [13] K n i g h t s h i f t in Y B C O 7 a n d T B C O [14] w e r e close to the BCS prediction if t h e r e s i d u a l s h i f t at l o w - T w a s a s c r i b e d o n l y to the T-independent orbital shift. On the other hand, t h e r e s u l t of I/T1, w h i c h decreases markedly without a coherence p e a k just b e l o w Tc, w a s quite s i m i l a r to t h a t in h e a v y f e r m i o n superconductors, which were interpreted in t e r m s of a n anisotropic energy gap model ( s a y dw a v e ) w i t h the g a p z e r o s of l i n e s at t h e F e r m i s u r f a c e [15]. T h u s the d i s c r e p a n c y between the Knight shift and the T 1 r e s u l t s still r e m a i n s to be r e s o l v e d . Quite recently, Ishida et al h a v e p r o p o s e d [16] t h a t b o t h K n i g h t s h i f t and T 1 results are consio~n~: explalned within a d-wave model with a gapless feature as A = ~ o s i n ~ at the c y l i n d r i cal Fermi surface [17] and in a d d i t i o n the finite density of states at the F e r m i surface b r o u g h t by the p a i r b r e a k ing effect. In t h i s p a p e r , we p r o v i d e n e w N M R i n s i g h t s i n t o the n o r m a l and superconducting states in t h e h i g h - T c cuprates.
100
200
300
T (K)
and Y B a 2 C u 3 O T . FIG.
2.
T-dependence
of
63(TIT ) in
La 2-
xSrxCuO4 • EXPERIMENT S i n g l e phase L S C O [I0], TBCO [9] a n d Zn-doped YBCO 7 [16] were prepared by solid state reaction described elsewhere . The T 1 of 63Cu in L S C O was measured in z e r o field by N Q R . T h e K n i g h t s h i f t and T 1 of 6 3 C u in T B C O a n d YBCO 7 were measured in a h i g h m a g n e t i c f i e l d o f 11.5 T b y N M R . The oriented powder was employed for NMR measurements. 2.
3. R E S U L T S (3.1) Normal S t a t e First of a l l , in Fig. I, t h e T d e p e n d e n c e s of 6 3 ( I / T I T ) in L a 2 - x S r x C u O 4 are shown for x=0.075(A ), 0.I ( O ) , w i t h Y B C O T ( N )[I0]. C o r r e s p o n d i n g to the development of the AF s p i n c o r r e l a t i o n brought by the reduction of holes, 6 3 ( I / T I T ) is s t r o n g l y enhanced, b e h a v i n g as the C u r i e - W e i s s law. In case that two dimensional s y s t e m is l a r g e l y d o m i n a t e d by the A F spin c o r r e l a t i o n , (I/TIT) is r e l a t e d to the s t a g g e r e d s u s c e p t i b i l i t y X Q(T) at the zone b o u n d a r y , Q = ( x /a,
I00
Y. Kitaoka et aL / I~MR in high-To o__'_n:4e__superconductors
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v
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o T¢-72 K •
TC - tA) K
o •
0.1 0.2 5r content X ,
FIG. 3. Sr content d e p e n d e n c e T¢(@ ) and 0 (O). A solid g u i d e to the eyes.
and hence
(IITIT)=ACI(T+@)
(2)
X Q(T)~
(3)
CI(T+0
)
in h i g h e r T-region t h a n T c [i0]. T h e remarkable feature is t h a t t h e W e i s s temperature, 0 , is l i n e a r l y extrapol a t e d to 0 K for x = 0 . 0 5 w i t h d e c r e a s i n g Sr c o n t e n t as i n d i c a t e d in Fig. 3, in w h i c h T c and the N ~ e l t e m p e r a t u r e , T N are also shown, while the slope, C, i n c r e a s e s slightly. T h u s the l i g h t l y - d o p e d system is c h a r a c t e r i z e d by the p r e s e n c e of t h e l a r g e AF s p i n f l u c t u a t i o n among Cu spins, which causes the Curie-Weiss law of X @(T). It s h o u l d be noted that X Q(T) is d e p r e s s e d by the increase of h o l e s and at the same time, the T - r e g i o n w h e r e (I/TIT) b e c o m ~ almost the con-
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(i)
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o ,
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of T N ( B ), l i n e is a
/~). As a m a t t e r of f a c t , as s e e n in Fig. 2 w h e r e (TIT) is p l o t t e d a g a i n s t t h e temperature, we h a v e e x p e r i m e n t a l relat i o n s of TIT=
.
o
4.
T-dependence
Tl2Ba2CuO6+y and O K ( ~ ).
with
of
Tc=72K(O
63(I/TI) ),
40K(O
in )
stant is w i d e r near T c [i0]. In T l ~ B a 2 C u O 6 + y , T c is g o i n g up from O K to 85 K b y r e d u c i n g o x y g e n s in the interstitial sites between double TIC 2 layers [9]. F r o m K n i g h t s h i f t m e a s u r e ments of 63Cu [14], the samples with Tc e x c e e d i n g 40K were confirmed to be homogeneous, showing bulk superconductivity. F i g u r e 4 shows the T - d e p e n d e n c e of 6 3 ( I / T I) i n T B C O w i t h Tc=72K(O ), 40K(R ) and 0K(~ )[ii]. The absolute value of 63(I/T 1 ) above T c does not depend on the compounds appreciably. This is b e c a u s e the isotropic supertransferred hyperfine field from four n e a r e s t n e i g h b o r Cu s p i n s is e n h a n c e d by the increase of h o l e s in T B C O [II]. Therefore, the d y n a m i c a l s u s c e p t i b i l i t y e n h a n c e d by t h e AF s p i n c o r r e l a t i o n is considered to be s u p p r e s s e d with inc r e a s i n g h o l e s . As s e e n in t h e f i g u r e , the notable feature is that the TiT=const.law are o b s e r v e d in a wide Trange of 8 5 - 1 4 0 K and 4 0 - 1 5 0 K for 72K-and 40K-superconductors, respectively [11] as compared with those in LSCO [i0].
/
Y. Kitaoka et al.
N M R in high-Tc oxide superconductors
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YBa2Cu307
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. . . .
.,,I
10
T (K)
FIG. 5. T - d e p e n d e n c e of 6 3 ( I / T I T ) a b in La2-xSrxCuO 4 with x=0.075(~ ) and 0.15 (A), YBa2Cu3OT( O ) and TI2Ba2CuO6+y(D ) with Tc=40K. In o r d e r to c o m p a r e an o v e r a l l v a r i a tion of (I/TIT) over a whole doping region, we present in Fig. 5 the Tdependence of 6 3 ( I / T I T ) a b p e r p e n d i c u l a r to c - a x i s in L S C O w i t h x = 0 . 0 7 5 and 0.15, Y B C O 7 and T B C O w i t h T c = 4 0 K [ I I ] . As s e e n in the figure,63(I/TiT)ab, which is l a r g e l y e n h a n c e d by t h e A F spin c o r r e l a tion and obeys the Curie-Weiss l a w in LSCO, is s i g n i f i c a n t l y depressed by inc r e a s i n g holes. T h e r e s u l t that the m a g nitude of 6 3 ( I / T I T ) in T B C O w i t h T c = 4 0 K is c o m p a r a b l e to t h a t in Y B C O 7 m a y be related to t h e f a c t t h a t the i s o t r o p i c supertransferred h y p e r f i n e field in T B C O are l a r g e r t h a n t h a t in Y B C O 7 [Ii]. Accordingly, the enhancement of the dynamical susceptibility X (q,~ ) is reduced in 4 0 K - T B C O as compared with t h a t in Y B C O 7. T h e r e c e n t n e u t r o n e x p e r i m e n t on the YBCO6+ x has shown that the m a g n e t i c c o h e r e n c e length, (~ M/a) is as small as 1.5 e v e n in Y B C 0 6 . 6 9 w i t h T c = 5 9 K [7],
FIG. 6. 6 3 ( I / T I) n o r m a l i z e d by the v a l u e at T c is plotted against T/T for Lal.85Sr0.15CuO4(O 1, YBa2Cu307(~) ) a n d Bi-Pb-Sr-Ca-Cu-O (x). but d o e s n o t s u c c e e d in o b s e r v i n g the inelastic magnetic scattering in Y B C O 7. This r e s u l t seems to s u g g e s t that ~ M in Y B C O 7 Is c o n s i d e r a b i y short, being presumably (~ M / a ) ~ I. A c c o r d i n g l y , from above argument, (~ M / a ) in 4 0 K - T B C O is s u p p o s e d to be r e d u c e d less than ~ I. Furthermore, an analysis of the anisotropy of t h e relaxation rate, 6 3 R = ( I / T I ) a b / ( I / T l ) c has e x t r a c t e d t h a t the A F s p i n f l u c t u a t i o n among nearest n e i g h b o r Cu sites, w h i c h s u r v i v e still in 7 2 K - T B C O , become less distinct in 40K-TBCO and disappear in n o n superconducting T B C O [ 11 ] . T h u s t h e r e appears an i n t i m a t e interre!8%i~n between the presence of t h e AF spin correlation a n d the o c c u r r e n c e of the superconductivity: a l t h o u g h ~ M is s p e c u lated to be as small as (~ M/a)~_ ~ I. (3.2) S u p e r c o n d u c t i n g State The rapid decrease of I/T 1 just below Tc shown in Figs. 6 and 4 was commonly o b s e r v e d being i n d e p e n d e n t of the
Y. lOtaoka et a L / NMR in high-To oxide superconductors
102
1.5
i
I
Y Ba2(Cul-x Zn.)30~
TllBa;.CuO6.y(Tc=72 K) o YBa2Cu307 Tc .
,t ,,,/~'
•, 0.00
:0%
1.0 C
• •
0.5
0,5
@9 @ l 0
0
A
I I
TI Tc
I
i
1.5
FIG.7. T-dependence of (Ks/Kn)ab est i m a t e d by a s s u m i n g t h e r e s i d u a l s h i f t to c o n s i s t o n l y of t h e o r b i t a l s h i f t , K a b ( o r b ) = 0 . 2 8 and 0 . 2 6 % in Y B C O 7 [ 1 2 ] a n d TBCO[14], respectively. Dashed and solid l i n e s c o r r e s p o n d to t h e B C S p r e d i c t i o n w i t h 2 A =3.5 and 4.5 kBTc, r e s p e c t i v e l y . materials, the a t o m i c sites, the magn e t i c field, t h e e n h a n c e m e n t of t h e A F spin fluctuation a n d e v e n of t h e Z n impurity doping into the CuO 2 plane which causes the gapless superconductivity [16]. So fsr, there have been several efforts to explain the r e m a r k able relaxation behavior below T c by c o n s i d e r i n g the g a p l e s s n a t u r e o n l y n e a r T c based on an s-wave model [ 18 ] . However, the u n i v e r s a l f e a t u r e of t h e T 1 b e h a v i o r just b e l o w T c was d i f f i c u l t to be understood consistently. D i f f e r e n t f r o m t h i s , the r e s u l t s o f K n i g h t s h i f t in Y B C O 7 [12] and T B C O [14] w e r e i m p l i e d to be c o n s i s t e n t w i t h a n sw a v e m o d e l w i t h a l a r g e r e n e r g y gap t h a n the B C S v a l u e as s h o w n in Fig. 7. H e r e the r e s i d u a l s h i f t at l o w - T was a s s u m e d to be dominated only by t h e o r b i t a l shift. Surprisingly, it was, h o w e v e r , reported that the small Zn-doping ( x = 0 . 0 1 ~- 0 . 0 2 ) into the CuO 2 in YBCO 7 left the s i g n i f i c a n t spin K n i g h t s h i f t of 63Cu at low-T. C o r r e s p o n d i n g l y ,
0
@ •
--
O
0
O0
A
&A
, I
0.5
1.0
1.5
TITc
FIG.8. T-dependence timated by assuming
of (Ks/Kn)ab Kab(orb)=0.21%
esin
YBa2(CUl_xZnx)307 with x=O.0(~ ), 0.01 (O) a n d 0 . 0 2 ( 0 ). S o l i d l i n e s are c a l c u l a t e d b y a d - w a v e m o d e l w i t h the d e n s i t y of s t a t e s as N s ( E ) = = r N 0 / 2, (E< r A ) N s(E)= ~ N 0E/ 2A , (r A < E < A ) N s(E) = N 0 E s i n - l ( A / E ) / A , (A < E) w i t h 2 A = g k B T c and r = O . 0 5 , 0.2, 0 . 3 , f o r x = 0 . 0 , 0 . O l a n d 0.02, r e s p e c t i v e l y . T i T = c o n s t . law was f o u n d to h o l d at l o w T far b e l o w T c = 7 9 K a n d 68 K for x = 0 . 0 1 and 0 . 0 2 , r e s p e c t i v e l y , providing a clear sign of the gapless superconductivity w i t h the f i n i t e d e n s i t y of s t a t e s at t h e Fermi level [16]. T h e n t h e N M R r e s u l t s in Z n - d o p e d YBCO 7 were well interpreted by a c o m b i n e d e f f e c t of t h e gap z e r o s of lines at the Fermi surface originating from a d-wave pairing a n d the r e s i d u a l d e n s i t y o f s t a t e s at the Fermi level induced by non-magnetic Zn-impurities. From t h e s e results, it w a s d e d u c e d t h a t some imperfection existing inevitably even in u n d o p e d Y B C O 7 m a y p o s s e s s a g a p less f e a t u r e w h i c h l e a v e s t h e r e s i d u a l spin shift in a d d i t i o n to t h e o r b i t a l shift at l o w - T [16]. A c t u a l l y , our m o d e l has well reproduced t h e e x p e r i m e n t s of the K n i g h t shift in Z n - d o p e d and u n d o p e d Y B C O 7 as s h o w n by s o l i d l i n e s in Fig. 8
Y. Kitaoka et ol
/ NMR
in h~gh-Tc ox/de superconductors
[16]. D i f f e r e n t f r o m the a r g u m e n t s s u p p o r t ing a simple s - w a v e model, we h a v e sugg e s t e d that a d - w a v e m o d e l is o n e of a promising superconducting model for the high-T c superconductors. It s h o u l d be stressed that this model has explained a universal feature of I/T 1 j u s t b e l o w T c in a q u i t e s i m p l e way, a l t h o u g h we cannot exclude t h a t t h e r e m a y be other w a y to u n d e r s t a n d the NMR results. The different approaches are highly required. 5. C o n c l u s i o n The spin dynamics in t h e high-T c oxide superconductors has b e e n i n v e s tigated over a wide doping region by 63Cu nuclear spin lattice relaxation study. T h e AF s p i n c o r r e l a t i o n still survives in t h e v i c i n i t y of t h e h o l e content w h e r e T c h a s a peak, a l t h o u g h the magnetic coherence length, ~ M is considerably short being presumably ( ~ M / a ) ~ i. H o w e v e r , the f u r t h e r d o p i n g destroys progressively the A F s p i n c o r r e l a t i o n , w h i c h is no longer p r e s e n t in non-superconductitng compound. This NMR evidence s i g n i f i e s that there is an int e r r e l a t i o n b e t w e e n the p r e s e n c e of the A F s p i n c o r r e l a t i o n and the o n s e t of the superconductivity. Furthermore, it is worth noting that the disappearance of the AF spin correlation r e s u l t s in the progressive change of t h e p o w e r l a w Tdependence, T n of t h e r e s i s t i v i t y from n ~ 1 to 2 [19]. In s u p e r c o n d u c t i n g state, a d-wave m o d e l is a p p l i c a b l e in i n t e r p r e t i n g consistently both results of K n i g h t shift a n d T 1 if the f i n i t e d e n s i t y of s t a t e s at t h e F e r m i l e v e l w a s taken into consideration depending on t h e e x t e n t of the pair breaking i n d u c e d by s o m e imp u r i t y and i m p e r f e c t i o n of the c r y s t a l . When considering t h a t there is no v a l i d experiments proving an e x p o n e n t i a l decrease of the p h y s i c a l q u a n t i t i e s , we conclude that indeed a d - w a v e c o u l d be one of possible superconducting models f o r the h i g h - T c s u p e r c o n d u c t o r .
in c o l l a b o r a t i o x l with Y.Shimakawa, T. M a n a k o and Y.Kubo. T h i s works were supported by a G r a n t - i n - A i d for the M i n i s try of Education, S c i e n c e , and C u l t u r e of J a p a n .
References [I] P.C. Hamme], M. Takigawa, R.H. H e f f n e r , Z. F i s k a n d Z.C.Ott, Phys. Rev. Lett. 63 (1989) 1992. [2] F . M i l a and T.M. Rice, Phys. Rev. B40 (1989} 11382. [3] A.J. Millis, H. M o n i e n and D. Pines, P h y s . R e v . B42 ( 1 9 9 0 ) . [ 4 ] B . S . S h a s t r y , P h y s . Rev. L e t t . 63 (1989) 1288. [ 5 ] N. B u l u t e , D. Hone, D . J . S c a l a p i n o a n d N.E. Bickers, Phys. Rev. B41 (1990) 1797. [6] G. S h i r a n e et el., Phys. Rev. Lett. 63 (1989) 330. [7] J. R o s s a t - M i g n o d et al., P h y s i c a B 169 (1991) 58. [8] J.B. Torrance et at., Phys. Rev. Left. 61 ( 1 9 8 8 ) 1 1 2 7 . [ 9 ] Y. S h i m a k a w a , Y. K u b o , T. M a , a k o a n d H. I g a r a s h i , Phys. Rev. B40, (1989) 11400. [ i 0 ] Y. K i t a o k a , S. O h s u g i , K. I s h i d a a n d K. A s a y a m a , P h y s i c a C 170 ( 1 9 9 0 ) 1 8 9 ; S. O h s u g i e t a l . , J . P h y s . S o c . J p n . 60 ( 1 9 9 1 ) 2 3 5 1 . [ii] Y. K i t a o k a et al., to be p u b l i s h e d in P h y s i c a C (1991). [12] S.E. B a r r e t t et al., Phys. Rev. B41 (1990) 6238. [ 1 3 ] M. T a k i g a w a e t a l . , Phys. Rev. Lett. 63 ( 1 9 8 9 ) 1 8 6 5 . [14] K. F u j i w a r a et el., J. Phys. Soc. Jpn. 59 [1990) 3459. [15] Y. K i t a o k a et al., J. Magn. Magn. Mater. 52 (1985) 341. [16] K. Ishida et el., to be p u b l i s h e d in P h y s i c a C (1991). [17] H. Monien and D. Pines, Phys. Rex. B41 (1990} 6297. [18] T . K o y a m a and T. Tachiki, Phys. Key. B39 (1989) 2279 ; L. Coffey, Phys. Ray. Let,. 64 (1990) 1071; Y . K u r o d a a n d C.H. Varma, Phys. Rev. B42 [19]
Acknowledgement The work on T l 2 B a 2 C u O 6 + y
has
beer,
done
103
(1990) 8619. Y. Kubo, Y. S h i m a k a w a , and H. Igarashi, Phys. (1991)
7875.
T. H a n a k o Rex. B43
NMR
IN HIOH-T c OXIDE
Y o s h i o KITAOKA,
Kenji
SUPERCONDUCTORS
ISHIDA,
Shigeki OHSUGI,
D e p a r t m e n t of M a t e r i a l Physics, Toyonaka, Osaka 560, Japan
Kenji
F u j i w a r a and K u n i s u k e A S A Y A M A
F a c u l t y of E n g i n e e r i n g
Science,
O s a k a University,
63Cu NQR and NMR studies are e x t e n s i v e l y reported in L a 2 _ x S r x C u O 4 ( L S C O ) , heavilydoped TI2Ba2CuO6+y(TBCO) and Z n - d o p e d Y B a 2 C u 3 0 7 ( Y B C O y ) . The n u c l e a r s p i n - l a t t i c e r e l a x a t i o n (T 1) study extracts that the a n t i f e r r o m a E n e t i c (AF) s p i n c o r r e l a t i o n b e c o m e s less d i s t i n c t w i t h d e c r e a s i n g T c in h e a v i l y - d o p e d T B C O over an o p t i m u m hole content. In n o n - s u p e r c o n d u c t i n g TBCO, the A F s p i n c o r r e l a t i o n d i s a p p e a r s , s u g E e s t i n g an i n t i m a t e i n t e r r e l a t i o n between the o c c u r r e n c e of the s u p e r c o n d u c t i v i t y and the p r e s e n c e of the AF spin correlation. In s u p e r c o n d u c t i n g state, both the T 1 and Knight shift results in undoped- and Z n - d o p e d Y B C O 7 are c o n s i s t e n t l y u n d e r s t o o d w i t h i n a simple model combining both e f f e c t s of the gap zeros of lines at the Fermi s u r f a c e a r i s i n g f r o m d - w a v e p a i r i n g a n d of the s m a l l but f i n i t e r e s i d u a l d e n s i t y of s t a t e s at the Fermi level i n d u c e d by some i m p u r i t y and some imperfection.
1. I n t r o d u c t i o n To e l u c i d a t e the mechanism of t h e high-T c superconductivity, many exp e r i m e n t a l and t h e o r e t i c a l i n v e s t i g a t i o n s h a v e been c u r r e n t l y carried out. Among the extensive e x p e r i m e n t a l efforts, NMR and NQR are playing an important role in c l a r i f y i n g s e p a r a t e l y t h e e l e c t r o n i c state of the oxygen and copper sites in the CuO 2 plane,the p r e s e n c e of w h i c h is c r u c i a l for the o c c u r r e n c e of the s u p e r c o n d u c t i v i t y . So far, there are numerous NMR and NQR works on YBa?Cu306+x(YBCO6+x). The o u t s t a n d i n g feature is that the n u c l e a r spin lattice r e l a x a t i o n rate, 1/T 1 of 63Cu and 1 7 0 revealed a totally different Td e p e n d e n c e in normal state [I], a l t h o u g h both are strongly coupled through the c o v a l e n c y . This d i f f e r e n c e w a s u n d e r stood as due to the g e o m e t r i c a l c a n c e l lation of the a D t i f e r r o m a g n e t i c (AF) spin fluctuation among Cu s p i n s a t oxygen sites[l,2,3,4,5], demonstrating that there survives the coherent AF spin f l u c t u a t i o n between n e a r e s t n e i g h b o r Cu s p i n s in Y B C O 7. In f a c t , the n e u t r o n s c a t t e r i n g e x p e r i m e n t s in LSCO [6] a n d the d e p l e t e d YBCO6+ x [7] except in Y B C O 7
have d e t e c t e d the i n e l a s t i c s c a t t e r i n g o r i g i n a t i n g from the AF spin c o r r e l a t i o n a m o n g Cu s p i n s and e x t r a c t e d the m a g netic c o h e r e n c e length, (~ M/a) (a: distance b e t w e e n Cu s i t e s ) to b e ~ 3 f o r L a l . 8 5 S r 0 . 1 5 C u 0 4 (Tc=38 K) a n d ~ 1.5 f o r Y B C O 6 . 6 5 ( T o = 6 0 K). A p p a r e n t l y , the AF spin c o r r e l a t i o n remains in normal state of the s u p e r c o n d u c t i n g compounds. Now, it is a c o n t r o v e r s i a l issue whether the spin correlation mediates effectively the f o r m a t i o n of the C o p p e r paring. In t h i s c o n t e x t , it s h o u l d be n o t e d t h a t T c s t a r t s to d e c r e a s e u p o n f u r t h e r d o p i n g h o l e s o v e r an o p t i m u m v a l u e a n d t h a t the s u p e r c o n d u c t i v i t y disappears when the system becomes rather usual m e t a l [ 8 , 9 ] . T h u s far, s t u d i e s a r e c o n c e n t r a t e d on the system n e a r an o p t i m u m hole content as in L a l . 8 5 S r 0 . 1 5 C u O 4 and YBCO 7. In order to i n s p e c t the c o r r e l a t i o n b e t w e e n the T c and the AF spin f l u c t u a t i o n from a wide view, we h a v e e x t e n d e d the NQR and N M R works from the l i g h t l y - d o p e d region near the m a g n e t i c insulator-superconductor t r a n s i t i o n in LSCO [i0] to the heavilydoped region in T l 2 B a 2 C u O 6 + y (TBCO) [ii] where T c is ranging from 85K to OK.
0921-4534/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved.
/ NMR
Y. lOtaoka et at.
,
!
'
I
,
•
I
40
o:
:0.10
x,
=0.13
0000
0:
=0.15
a:
:020
o
Tu
~30
e,~°,,..xlx 0 %
~
,
I
x: o zo
63Cu NQR
• : X "0.075
•
Tc
•
Lo~-xSrxCuO~
Lae xSrxCu04 63Cu NOR
50
99
in high-Tc oxide ~perconductorx
=o.,s
100 / o
=0,13 ': 0 . 1 0
x
q,
" : Y Ba2Cu307
: 0.07S
-
o
bI-=
q,
~20
o,~.
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•
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•
a
ee.- x ",V,° .. °- ~o a
o
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el
• o X
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•
•
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100
•
•
i
I.-
~.
•
I
T (K)
so
AA
I
200
,"i
I
300 ,
,,, ,
t Tc
•
FIG
1. T - d e p e n d e n c e
xSrxCuO4
of 6 3 ( I / T I T )
in La2-
-100
0
A s for the s u p e r c o n d u c t i n g properties, a n s - w a v e m o d e l s e e m s to be s u p p o r t e d by many experiments. For instance, the r e s u l t s of 6 3 C u [12] and 170 [13] K n i g h t s h i f t in Y B C O 7 a n d T B C O [14] w e r e close to the BCS prediction if t h e r e s i d u a l s h i f t at l o w - T w a s a s c r i b e d o n l y to the T-independent orbital shift. On the other hand, t h e r e s u l t of I/T1, w h i c h decreases markedly without a coherence p e a k just b e l o w Tc, w a s quite s i m i l a r to t h a t in h e a v y f e r m i o n superconductors, which were interpreted in t e r m s of a n anisotropic energy gap model ( s a y dw a v e ) w i t h the g a p z e r o s of l i n e s at t h e F e r m i s u r f a c e [15]. T h u s the d i s c r e p a n c y between the Knight shift and the T 1 r e s u l t s still r e m a i n s to be r e s o l v e d . Quite recently, Ishida et al h a v e p r o p o s e d [16] t h a t b o t h K n i g h t s h i f t and T 1 results are consio~n~: explalned within a d-wave model with a gapless feature as A = ~ o s i n ~ at the c y l i n d r i cal Fermi surface [17] and in a d d i t i o n the finite density of states at the F e r m i surface b r o u g h t by the p a i r b r e a k ing effect. In t h i s p a p e r , we p r o v i d e n e w N M R i n s i g h t s i n t o the n o r m a l and superconducting states in t h e h i g h - T c cuprates.
100
200
300
T (K)
and Y B a 2 C u 3 O T . FIG.
2.
T-dependence
of
63(TIT ) in
La 2-
xSrxCuO4 • EXPERIMENT S i n g l e phase L S C O [I0], TBCO [9] a n d Zn-doped YBCO 7 [16] were prepared by solid state reaction described elsewhere . The T 1 of 63Cu in L S C O was measured in z e r o field by N Q R . T h e K n i g h t s h i f t and T 1 of 6 3 C u in T B C O a n d YBCO 7 were measured in a h i g h m a g n e t i c f i e l d o f 11.5 T b y N M R . The oriented powder was employed for NMR measurements. 2.
3. R E S U L T S (3.1) Normal S t a t e First of a l l , in Fig. I, t h e T d e p e n d e n c e s of 6 3 ( I / T I T ) in L a 2 - x S r x C u O 4 are shown for x=0.075(A ), 0.I ( O ) , w i t h Y B C O T ( N )[I0]. C o r r e s p o n d i n g to the development of the AF s p i n c o r r e l a t i o n brought by the reduction of holes, 6 3 ( I / T I T ) is s t r o n g l y enhanced, b e h a v i n g as the C u r i e - W e i s s law. In case that two dimensional s y s t e m is l a r g e l y d o m i n a t e d by the A F spin c o r r e l a t i o n , (I/TIT) is r e l a t e d to the s t a g g e r e d s u s c e p t i b i l i t y X Q(T) at the zone b o u n d a r y , Q = ( x /a,
I00
Y. Kitaoka et aL / I~MR in high-To o__'_n:4e__superconductors
I
.
!
,
.,,,.[
,
,
./
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, ....
Lo2-xSrxCuO4
f.-i"
NM
100 TN
/:.
i
,
.
o o
o
3D
~
AF
v
50
V
o
~0
Tc
o
10
o •m
%%
5C
o T¢-72 K •
TC - tA) K
o •
0.1 0.2 5r content X ,
FIG. 3. Sr content d e p e n d e n c e T¢(@ ) and 0 (O). A solid g u i d e to the eyes.
and hence
(IITIT)=ACI(T+@)
(2)
X Q(T)~
(3)
CI(T+0
)
in h i g h e r T-region t h a n T c [i0]. T h e remarkable feature is t h a t t h e W e i s s temperature, 0 , is l i n e a r l y extrapol a t e d to 0 K for x = 0 . 0 5 w i t h d e c r e a s i n g Sr c o n t e n t as i n d i c a t e d in Fig. 3, in w h i c h T c and the N ~ e l t e m p e r a t u r e , T N are also shown, while the slope, C, i n c r e a s e s slightly. T h u s the l i g h t l y - d o p e d system is c h a r a c t e r i z e d by the p r e s e n c e of t h e l a r g e AF s p i n f l u c t u a t i o n among Cu spins, which causes the Curie-Weiss law of X @(T). It s h o u l d be noted that X Q(T) is d e p r e s s e d by the increase of h o l e s and at the same time, the T - r e g i o n w h e r e (I/TIT) b e c o m ~ almost the con-
,,.,,I
,
.
,
,c*U~
,,+,,I
10o T (K)
FIG.
(i)
(T+0)/AC
o ,
•
1o
of T N ( B ), l i n e is a
/~). As a m a t t e r of f a c t , as s e e n in Fig. 2 w h e r e (TIT) is p l o t t e d a g a i n s t t h e temperature, we h a v e e x p e r i m e n t a l relat i o n s of TIT=
.
o
4.
T-dependence
Tl2Ba2CuO6+y and O K ( ~ ).
with
of
Tc=72K(O
63(I/TI) ),
40K(O
in )
stant is w i d e r near T c [i0]. In T l ~ B a 2 C u O 6 + y , T c is g o i n g up from O K to 85 K b y r e d u c i n g o x y g e n s in the interstitial sites between double TIC 2 layers [9]. F r o m K n i g h t s h i f t m e a s u r e ments of 63Cu [14], the samples with Tc e x c e e d i n g 40K were confirmed to be homogeneous, showing bulk superconductivity. F i g u r e 4 shows the T - d e p e n d e n c e of 6 3 ( I / T I) i n T B C O w i t h Tc=72K(O ), 40K(R ) and 0K(~ )[ii]. The absolute value of 63(I/T 1 ) above T c does not depend on the compounds appreciably. This is b e c a u s e the isotropic supertransferred hyperfine field from four n e a r e s t n e i g h b o r Cu s p i n s is e n h a n c e d by the increase of h o l e s in T B C O [II]. Therefore, the d y n a m i c a l s u s c e p t i b i l i t y e n h a n c e d by t h e AF s p i n c o r r e l a t i o n is considered to be s u p p r e s s e d with inc r e a s i n g h o l e s . As s e e n in t h e f i g u r e , the notable feature is that the TiT=const.law are o b s e r v e d in a wide Trange of 8 5 - 1 4 0 K and 4 0 - 1 5 0 K for 72K-and 40K-superconductors, respectively [11] as compared with those in LSCO [i0].
/
Y. Kitaoka et al.
N M R in high-Tc oxide superconductors
....
|
'
200
150
'
' ' ....
YBa2Cu307
o
T 2Ba2CuO6,y T¢=~OK
'
'
' '''"1
o ° o ° oo o
C
.x:0.15
•
]
, 8iPt>~,CoCuO o O.o~.%)zcuo,. • YSo.2Cu3~
La2.xSrxCuO,.,.:o~m •
!OI
16 | "T oe
"r~.
100
o
10.2
o~
zero field
~A
&
le
50 •A&A&
Ie
A 6
• &
•
A
,
16 3 •
S
n o
0
el
°
e9
, • :,:1 °
•
I'
I 100
e
I
20O
0.1
300
l
0
.....
|
I TI Tc
•
. . . .
.,,I
10
T (K)
FIG. 5. T - d e p e n d e n c e of 6 3 ( I / T I T ) a b in La2-xSrxCuO 4 with x=0.075(~ ) and 0.15 (A), YBa2Cu3OT( O ) and TI2Ba2CuO6+y(D ) with Tc=40K. In o r d e r to c o m p a r e an o v e r a l l v a r i a tion of (I/TIT) over a whole doping region, we present in Fig. 5 the Tdependence of 6 3 ( I / T I T ) a b p e r p e n d i c u l a r to c - a x i s in L S C O w i t h x = 0 . 0 7 5 and 0.15, Y B C O 7 and T B C O w i t h T c = 4 0 K [ I I ] . As s e e n in the figure,63(I/TiT)ab, which is l a r g e l y e n h a n c e d by t h e A F spin c o r r e l a tion and obeys the Curie-Weiss l a w in LSCO, is s i g n i f i c a n t l y depressed by inc r e a s i n g holes. T h e r e s u l t that the m a g nitude of 6 3 ( I / T I T ) in T B C O w i t h T c = 4 0 K is c o m p a r a b l e to t h a t in Y B C O 7 m a y be related to t h e f a c t t h a t the i s o t r o p i c supertransferred h y p e r f i n e field in T B C O are l a r g e r t h a n t h a t in Y B C O 7 [Ii]. Accordingly, the enhancement of the dynamical susceptibility X (q,~ ) is reduced in 4 0 K - T B C O as compared with t h a t in Y B C O 7. T h e r e c e n t n e u t r o n e x p e r i m e n t on the YBCO6+ x has shown that the m a g n e t i c c o h e r e n c e length, (~ M/a) is as small as 1.5 e v e n in Y B C 0 6 . 6 9 w i t h T c = 5 9 K [7],
FIG. 6. 6 3 ( I / T I) n o r m a l i z e d by the v a l u e at T c is plotted against T/T for Lal.85Sr0.15CuO4(O 1, YBa2Cu307(~) ) a n d Bi-Pb-Sr-Ca-Cu-O (x). but d o e s n o t s u c c e e d in o b s e r v i n g the inelastic magnetic scattering in Y B C O 7. This r e s u l t seems to s u g g e s t that ~ M in Y B C O 7 Is c o n s i d e r a b i y short, being presumably (~ M / a ) ~ I. A c c o r d i n g l y , from above argument, (~ M / a ) in 4 0 K - T B C O is s u p p o s e d to be r e d u c e d less than ~ I. Furthermore, an analysis of the anisotropy of t h e relaxation rate, 6 3 R = ( I / T I ) a b / ( I / T l ) c has e x t r a c t e d t h a t the A F s p i n f l u c t u a t i o n among nearest n e i g h b o r Cu sites, w h i c h s u r v i v e still in 7 2 K - T B C O , become less distinct in 40K-TBCO and disappear in n o n superconducting T B C O [ 11 ] . T h u s t h e r e appears an i n t i m a t e interre!8%i~n between the presence of t h e AF spin correlation a n d the o c c u r r e n c e of the superconductivity: a l t h o u g h ~ M is s p e c u lated to be as small as (~ M/a)~_ ~ I. (3.2) S u p e r c o n d u c t i n g State The rapid decrease of I/T 1 just below Tc shown in Figs. 6 and 4 was commonly o b s e r v e d being i n d e p e n d e n t of the
Y. lOtaoka et a L / NMR in high-To oxide superconductors
102
1.5
i
I
Y Ba2(Cul-x Zn.)30~
TllBa;.CuO6.y(Tc=72 K) o YBa2Cu307 Tc .
,t ,,,/~'
•, 0.00
:0%
1.0 C
• •
0.5
0,5
@9 @ l 0
0
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I I
TI Tc
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i
1.5
FIG.7. T-dependence of (Ks/Kn)ab est i m a t e d by a s s u m i n g t h e r e s i d u a l s h i f t to c o n s i s t o n l y of t h e o r b i t a l s h i f t , K a b ( o r b ) = 0 . 2 8 and 0 . 2 6 % in Y B C O 7 [ 1 2 ] a n d TBCO[14], respectively. Dashed and solid l i n e s c o r r e s p o n d to t h e B C S p r e d i c t i o n w i t h 2 A =3.5 and 4.5 kBTc, r e s p e c t i v e l y . materials, the a t o m i c sites, the magn e t i c field, t h e e n h a n c e m e n t of t h e A F spin fluctuation a n d e v e n of t h e Z n impurity doping into the CuO 2 plane which causes the gapless superconductivity [16]. So fsr, there have been several efforts to explain the r e m a r k able relaxation behavior below T c by c o n s i d e r i n g the g a p l e s s n a t u r e o n l y n e a r T c based on an s-wave model [ 18 ] . However, the u n i v e r s a l f e a t u r e of t h e T 1 b e h a v i o r just b e l o w T c was d i f f i c u l t to be understood consistently. D i f f e r e n t f r o m t h i s , the r e s u l t s o f K n i g h t s h i f t in Y B C O 7 [12] and T B C O [14] w e r e i m p l i e d to be c o n s i s t e n t w i t h a n sw a v e m o d e l w i t h a l a r g e r e n e r g y gap t h a n the B C S v a l u e as s h o w n in Fig. 7. H e r e the r e s i d u a l s h i f t at l o w - T was a s s u m e d to be dominated only by t h e o r b i t a l shift. Surprisingly, it was, h o w e v e r , reported that the small Zn-doping ( x = 0 . 0 1 ~- 0 . 0 2 ) into the CuO 2 in YBCO 7 left the s i g n i f i c a n t spin K n i g h t s h i f t of 63Cu at low-T. C o r r e s p o n d i n g l y ,
0
@ •
--
O
0
O0
A
&A
, I
0.5
1.0
1.5
TITc
FIG.8. T-dependence timated by assuming
of (Ks/Kn)ab Kab(orb)=0.21%
esin
YBa2(CUl_xZnx)307 with x=O.0(~ ), 0.01 (O) a n d 0 . 0 2 ( 0 ). S o l i d l i n e s are c a l c u l a t e d b y a d - w a v e m o d e l w i t h the d e n s i t y of s t a t e s as N s ( E ) = = r N 0 / 2, (E< r A ) N s(E)= ~ N 0E/ 2A , (r A < E < A ) N s(E) = N 0 E s i n - l ( A / E ) / A , (A < E) w i t h 2 A = g k B T c and r = O . 0 5 , 0.2, 0 . 3 , f o r x = 0 . 0 , 0 . O l a n d 0.02, r e s p e c t i v e l y . T i T = c o n s t . law was f o u n d to h o l d at l o w T far b e l o w T c = 7 9 K a n d 68 K for x = 0 . 0 1 and 0 . 0 2 , r e s p e c t i v e l y , providing a clear sign of the gapless superconductivity w i t h the f i n i t e d e n s i t y of s t a t e s at t h e Fermi level [16]. T h e n t h e N M R r e s u l t s in Z n - d o p e d YBCO 7 were well interpreted by a c o m b i n e d e f f e c t of t h e gap z e r o s of lines at the Fermi surface originating from a d-wave pairing a n d the r e s i d u a l d e n s i t y o f s t a t e s at the Fermi level induced by non-magnetic Zn-impurities. From t h e s e results, it w a s d e d u c e d t h a t some imperfection existing inevitably even in u n d o p e d Y B C O 7 m a y p o s s e s s a g a p less f e a t u r e w h i c h l e a v e s t h e r e s i d u a l spin shift in a d d i t i o n to t h e o r b i t a l shift at l o w - T [16]. A c t u a l l y , our m o d e l has well reproduced t h e e x p e r i m e n t s of the K n i g h t shift in Z n - d o p e d and u n d o p e d Y B C O 7 as s h o w n by s o l i d l i n e s in Fig. 8
Y. Kitaoka et ol
/ NMR
in h~gh-Tc ox/de superconductors
[16]. D i f f e r e n t f r o m the a r g u m e n t s s u p p o r t ing a simple s - w a v e model, we h a v e sugg e s t e d that a d - w a v e m o d e l is o n e of a promising superconducting model for the high-T c superconductors. It s h o u l d be stressed that this model has explained a universal feature of I/T 1 j u s t b e l o w T c in a q u i t e s i m p l e way, a l t h o u g h we cannot exclude t h a t t h e r e m a y be other w a y to u n d e r s t a n d the NMR results. The different approaches are highly required. 5. C o n c l u s i o n The spin dynamics in t h e high-T c oxide superconductors has b e e n i n v e s tigated over a wide doping region by 63Cu nuclear spin lattice relaxation study. T h e AF s p i n c o r r e l a t i o n still survives in t h e v i c i n i t y of t h e h o l e content w h e r e T c h a s a peak, a l t h o u g h the magnetic coherence length, ~ M is considerably short being presumably ( ~ M / a ) ~ i. H o w e v e r , the f u r t h e r d o p i n g destroys progressively the A F s p i n c o r r e l a t i o n , w h i c h is no longer p r e s e n t in non-superconductitng compound. This NMR evidence s i g n i f i e s that there is an int e r r e l a t i o n b e t w e e n the p r e s e n c e of the A F s p i n c o r r e l a t i o n and the o n s e t of the superconductivity. Furthermore, it is worth noting that the disappearance of the AF spin correlation r e s u l t s in the progressive change of t h e p o w e r l a w Tdependence, T n of t h e r e s i s t i v i t y from n ~ 1 to 2 [19]. In s u p e r c o n d u c t i n g state, a d-wave m o d e l is a p p l i c a b l e in i n t e r p r e t i n g consistently both results of K n i g h t shift a n d T 1 if the f i n i t e d e n s i t y of s t a t e s at t h e F e r m i l e v e l w a s taken into consideration depending on t h e e x t e n t of the pair breaking i n d u c e d by s o m e imp u r i t y and i m p e r f e c t i o n of the c r y s t a l . When considering t h a t there is no v a l i d experiments proving an e x p o n e n t i a l decrease of the p h y s i c a l q u a n t i t i e s , we conclude that indeed a d - w a v e c o u l d be one of possible superconducting models f o r the h i g h - T c s u p e r c o n d u c t o r .
in c o l l a b o r a t i o x l with Y.Shimakawa, T. M a n a k o and Y.Kubo. T h i s works were supported by a G r a n t - i n - A i d for the M i n i s try of Education, S c i e n c e , and C u l t u r e of J a p a n .
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Acknowledgement The work on T l 2 B a 2 C u O 6 + y
has
beer,
done
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7875.
T. H a n a k o Rex. B43