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Effects of lattice disorder on the heavy-fermion-systems CeCu2Si2, CeCu6, and UPt3
P h y s i c a C 153 North-Holland,
155 ( 1 9 8 8 ) 4 3 5 - 4 3 6 Amsterdam
EFFECTS OF LATTICE DISORDER ON THE HEAVY-FERMION-SYSTEMS C e C u z S i 2 , CeCum, a n d UPt3
G. ADRIAN a n d H. ADRIAN Physikalisches Institut,
Universitiit Eriangen-Ntirnberg,
E r w i n - R o m m e l - S t r a l 3 e 1) 8520 E r l a n g e n , FRG
W e r e p o r t t h e i n f l u e n c e of l a t t i c e d e f e c t s o n r e s i s t i v i t y p(T) a n d H a l l - e f f e c t RH(T) of t h e h e a v y f e r m i o n s y s t e m s CeCu2Si2, CeCu6, a n d U P t s ) i n t r o d u c e d b y h e a v y ion i r r a d i a t i o n of t h i n f i l m s . I n all c a s e s t h e r e s u l t i n g d r a s t i c v a r i a t i o n s of t h e low t e m p e r a t u r e p r o p e r t i e s r e v e a l a c o m p l e t e s u p p r e s s i o n o f t h e c o h e r e n t s t a t e a t d e f e c t c o n c e n t r a t i o n s a s low a s 0 . 1 d p a . C o n t r a r y to t h i s t h e b e havior at high defect concentrations is different for the Ce-systemy and for UPts, indicating that in the l a t t e r c o m p o u n d f - d - h y b r i s a t i o n is not as i m p o r t a n t .
1. INTRODUCTION AND EXPERIMENTAL Among t h e Heavy Fermion S y s t e m s UPt s o c c u p i e s a s p e c i a l p o s i t i o n : i t s r e s i s t i v i t y p(T) shows a posistive temperature coefficient over the measured temperature range and the specific h e a t c l e a r l y p r o v e s t h e p r e s e n c e of s p i n f l u c t a t i o n s (1). T h e o r i g i n of t h e d e v e l o p m e n t of a l a r g e e l e c t r o n i c s p e c i f i c h e a t a t low t e m p e r a tures might be different for U-systems comp a r e d t o C e - s y s t e m s , w h e r e t h e e n h a n c e m e n t of t h e d e n s i t y o f s t a t e s a t t h e F e r m i l e v e l N(EF) i s e v i d e n t l y d u e to t h e K o n d o r e s o n a n c e a r i s i n g f r o m t h e h y b r i d i s a t i o n of t h e C e - 4 f - e l e c t r o n s w i t h t h e c o n d u c t i o n e l e c t r o n s . I n U - s y s t e m s it could be p a r t l y d e t e r m i n e d by b a n d s t r u c t u r e e f f e c t s , a s t h e 5 f - s t a t e s a r e c l o s e to E F. I n t h i s r e s p e c t it i s i n t e r e s s t i n g to s t u d y t h e v a r i a t i o n of transport properties, which reflect the c h a n g e o f N(EF), b y d e v i a t i o n s f r o m l a t t i c e p e riodicity. The irradiation experiments were carried out w i t h t h i n s p u t t e r e d f i l m s (d < l # m ) u s i n g 25MeV a 6 0 - i o n s . As t h e i r m e a n r a n g e 1 i n t h e e x a m i n e d c o m p o u n d s i s l a r g e r t h a n d (1 ~ 7/~m) n o i m plantation occurs and the radiation damage cons i s t s in d i s p l a c e m e n t s o f a t o m s d u e to t h e C o u lomb i n t e r a c t i o n b e t w e e n t h e p r o j e c t i l e s a n d t h e s a m p l e n u c l e i . Within a s i m p l e d e f e c t model, t h e a p p l i e d f l u e n c e s c a n b e r e l a t e d to t h e r e l a t i v e c o n c e n t r a t i o n C of d i s p l a c e d a t o m s , l e a d i n g to: C : 1.8"10-a~cm2"~ f o r CeCu2Si 2 C : 2 . 1 " 1 0 - t ~ c m 2 . ~ f o r CeCu 6 C : 4.3'10-~7cm2'~ for UPts
34
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FIG. 1: p(T) of v a r i o u s CeCu2Si 2 f i l m s ( s h a d e d #(T) r a n g e ) a n d a f t e r i r r a d i a t i o n
T (K)
before
T h e H a l l - e f f e c t IRH(T) I of t h e f i l m s b e f o r e irradiation increases with decreasing temperat u r e , e x h i b i t s a m a x i m u m a t 2K (CeCu2Si2), 4K (CeCu6), a n d 15K (UPt3), r e s p e c t i v e l y a n d r e a c h e s v e r y low v a l u e s f o r T -~ 0. T h e s i g n o f R H i s p o s i t i v e f o r t h e two C e - s y s t e m s a n d n e g a t i v e for UPts, consistent with published data for b u l k s a m p l e s (2-4). T h e CeCu2Si 2 f i l m s a r e s u perconducting w i t h T c = 0.4K ( m i d p o i n t ) . F o r U P t 3 - f i l m s T e - v a l u e s of o n l y = 0.15K w e r e a chieved. As o n e c a n s e e i n Fig. 1 t h e s t r u c t u r e s o f i
2. RESULTS AND DISCUSSION T h e p(T) b e h a v i o r o f CeCu2Si 2 a n d CeCu 6 films before irradiation shows the typical struct u r e s a s k n o w n f o r b u l k s a m p l e s (2,3) e s p e c i a l ly a m a x i m u m a t T* = 10K a n d a F e r m i - l i q u i d r e g i m e (Ap : A.T 2) below TFL : 1.8K (CeCu~Si2) a n d TFL : 0.2K (GeCu6) , r e s p e c t i v e l y . U P t 3 f i l m s exhibit a positive temperature c o e f f i c i e n t of p(T) w i t h p(280K)/Pres = 7.0) i n c l u d i n g a s t r o n g 9 r e d u c t i o n a t low t e m p e r a t u r e s T < 10K w h i c h i s s u p p o s e d to i n d i c a t e t h e f o r m a t i o n of a c o h e r e n t s t a t e of h e a v y f e r m i o n s .
0921-4534/88/$03.50 ©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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FIG. 2: p(T) of UPt 3 films before and after irradiation
436
G. Adrian and H. Adrian / Hea~y-fermion-systems CeCu2Si 2, CeCum, and UPt 3
p(T) o f C e C u 2 S i 2 a r e g r a d u a l l y s h i f t e d to l o w e r temperature and become less pronounced with i n c r e a s i n g d i s o r d e r till a f t e r ~ ~ 1 0 ' 6 c m - = , o n l y a m o n o t o n o u s i n c r e a s e o f p t o low t e m p e r a t u r e s is observed. The influence of irradiation on CeCu 6 films is qualitatively the same. In order to classify the defect sensitivity more quantitat i v e l y we c o m p a r e l o o k a t t h e e s t i m a t e d c o n c e n trations of displaced atoms necessary to reduce the characteristic temperatures T c , TFL, a n d T* to h a l f o f t h e i r i n i t i a l v a l u e s : C c = 0.005, CFL = 0.025, T* = 0.022 f o r C e C u 2 S i 2 a n d CFL = 0.011, C* = 0.013 f o r CeCum. T h e r e a r e t w o i n d i c a t i o n s t h a t N(EF), i s s e n sitively reduced by disorder: The slope of the upper critical field Bc2', which is in the dirty l i m i t g i v e n b y B e 2 ' = ?f'Pres, i s i n d e p e n d e n t of the defect concentration, although Pres is strongly enhanced. The coefficient A of the T 2behavior, which reflects excitations of quasiparticles out of the Fermi-liquid ground state, A = [N(EF)] 2 (5) i s d i m i n i s h e d d u e t o d i s o r d e r i n b o t h s y s t e m s b y a b o u t a f a c t o r o f 2. For UPt 3 films also a strong resistivity inc r e a s e is o b s e r v e d with disorder, as shown in F i g . 2. H o w e v e r , c o n t r a r y to t h e b e h a v i o r of t h e C e - s y s t e m s t h e d e c r e a s e o f p(T) to low t e m peratures i s no__~t r e d u c e d , but even intensified f o r ~ ~ 10XScm - ~ . A s f o r f l u e n e e s ~ ~ 101ecru - ~ the p(T)-curves remain nearly unchanged by further irradiation, the topmost curve in Fig. 2 e s s e n t i a l l y r e f l e c t s t h e b e h a v i o r f o r ~ -~ - . That lattice defects act strongly on the electronic structure of heavy fermion systems is obvious from the variation of the RH(T)-behavior of the 3 systems. Exemplarily R H(T) o f CeCu~ films is shown before and after irradiation with different fluences i n F i g . 3. T h e r e d u c t i o n o f RH(T) a t low t e m p e r a t u r e d u e to t h e f o r m a t i o n o f a c o h e r e n t s t a t e (6), i s a l r e a d y suppressed at ¢ ~ 4"10~cm -~. Introducing further lattice defects a strong enhancement of RH a t low t e m p e r a t u r e is observed in the two Cesystems. The continous decrease of R H with T after high fluenees may indicate that then the properties of the systems are dominated by incoherent scattering of conduction electrons by
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as in diluted Kondo the 4f-electrons just systems. T h e Hall e f f e c t o f U P t 3 f i l m s d i s p l a y e d in Fig. 4 changes sign at fluences a s low a s 1014cm - 2 . I n t h e c r o s s - o v e r region dUH/dB is negative f o r low f i e l d s (B ~ 2T) a n d p o s i t i v e f o r h i g h f i e l d s (B ~ 4T) c o r r e s p o n d i n g to t h e t w o i n d i c a t e d s y m b o l s . At ¢ ~ 5 ' 1 0 1 4 c m - 2 a s o l e l y p o s i t i v e RH(T ) r e s u l t s which, however, still exhibits a maximum structure. Contrary to t h e Ce-systems RH(T) d e c r e a s e s upon further irradiation. The observed behavior of UPt 3 films may be explained by a disorder induced variat i o n o f N(E) w h i c h c a u s e s a c h a n g e o f t h e d o m i n a t i n g c a r r i e r s f r o m e l e c t r o n - l i k e to h o l e - l i k e . The strong temperature dependence o f RH(T) a t --5"10t4cm -2 indicates the existence of sharp structures in the band density of states. The irradiation induced variation of the magnetoresistivty in CeCu2Si 2 and C e C u ~ (7) agrees with the observations of the RH(¢)-behariot; whereas in UPt~ the main effect at high defect concentrations is a reduction o f ap(B), which can be understood by the reduced mean free path of the conduction electrons. Concluding we obtain drastic alternations of the transport properties of the heavy fermion s y s t e m s C e C u 2 S i 2 , C e C u 6 , a n d U P t 3 e v e n a t low defect concentrations, from which we deduce the existence of sharp structures i n N(E) n e a r E F. F r o m t h e d i f f e r e n t behavior at high defect concentrations we conclude that the hybridisation of conduction electrons with f-electrons, which determines the properties of the Ce-syst e m s i s n o t a s d o m i n a n t i n U P t 3.
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J.J.M. F r a n s e , P.H. F r i n g s , A. d e V i s s e r , A. M e n o v s k y , T.T.M. P a l s t r a , P.H. K e s , a n d J.A. M y d o s h , P h y s i c a 126B, 116 (1984) N.B. B r a n d t a n d V.V. M o s h c h a l k o v , A d v . P h y s . 3 3 , 374 (1984) Y. O n u k i a n d T. K o m a t s u b a r a , J. M a g n . M a g n . M a t 63&64, 527 (1987) W.R. D a t a r s , K. K a d o w a k i , hi. All, a n d S.B. W o o d s , J. P h y s . F 16, L63 (1986) D.W. H e s s , J. L o w T e m p . P h y s . 6 8 , 3 1 1 ( 1 9 8 7 ) A. F e r t a n d P.M. L e v y , P h y s . H e y . B36, 1907 (1987) G.Adrian and H.Adrian, Physica148B,26(1987)
155 ( 1 9 8 8 ) 4 3 5 - 4 3 6 Amsterdam
EFFECTS OF LATTICE DISORDER ON THE HEAVY-FERMION-SYSTEMS C e C u z S i 2 , CeCum, a n d UPt3
G. ADRIAN a n d H. ADRIAN Physikalisches Institut,
Universitiit Eriangen-Ntirnberg,
E r w i n - R o m m e l - S t r a l 3 e 1) 8520 E r l a n g e n , FRG
W e r e p o r t t h e i n f l u e n c e of l a t t i c e d e f e c t s o n r e s i s t i v i t y p(T) a n d H a l l - e f f e c t RH(T) of t h e h e a v y f e r m i o n s y s t e m s CeCu2Si2, CeCu6, a n d U P t s ) i n t r o d u c e d b y h e a v y ion i r r a d i a t i o n of t h i n f i l m s . I n all c a s e s t h e r e s u l t i n g d r a s t i c v a r i a t i o n s of t h e low t e m p e r a t u r e p r o p e r t i e s r e v e a l a c o m p l e t e s u p p r e s s i o n o f t h e c o h e r e n t s t a t e a t d e f e c t c o n c e n t r a t i o n s a s low a s 0 . 1 d p a . C o n t r a r y to t h i s t h e b e havior at high defect concentrations is different for the Ce-systemy and for UPts, indicating that in the l a t t e r c o m p o u n d f - d - h y b r i s a t i o n is not as i m p o r t a n t .
1. INTRODUCTION AND EXPERIMENTAL Among t h e Heavy Fermion S y s t e m s UPt s o c c u p i e s a s p e c i a l p o s i t i o n : i t s r e s i s t i v i t y p(T) shows a posistive temperature coefficient over the measured temperature range and the specific h e a t c l e a r l y p r o v e s t h e p r e s e n c e of s p i n f l u c t a t i o n s (1). T h e o r i g i n of t h e d e v e l o p m e n t of a l a r g e e l e c t r o n i c s p e c i f i c h e a t a t low t e m p e r a tures might be different for U-systems comp a r e d t o C e - s y s t e m s , w h e r e t h e e n h a n c e m e n t of t h e d e n s i t y o f s t a t e s a t t h e F e r m i l e v e l N(EF) i s e v i d e n t l y d u e to t h e K o n d o r e s o n a n c e a r i s i n g f r o m t h e h y b r i d i s a t i o n of t h e C e - 4 f - e l e c t r o n s w i t h t h e c o n d u c t i o n e l e c t r o n s . I n U - s y s t e m s it could be p a r t l y d e t e r m i n e d by b a n d s t r u c t u r e e f f e c t s , a s t h e 5 f - s t a t e s a r e c l o s e to E F. I n t h i s r e s p e c t it i s i n t e r e s s t i n g to s t u d y t h e v a r i a t i o n of transport properties, which reflect the c h a n g e o f N(EF), b y d e v i a t i o n s f r o m l a t t i c e p e riodicity. The irradiation experiments were carried out w i t h t h i n s p u t t e r e d f i l m s (d < l # m ) u s i n g 25MeV a 6 0 - i o n s . As t h e i r m e a n r a n g e 1 i n t h e e x a m i n e d c o m p o u n d s i s l a r g e r t h a n d (1 ~ 7/~m) n o i m plantation occurs and the radiation damage cons i s t s in d i s p l a c e m e n t s o f a t o m s d u e to t h e C o u lomb i n t e r a c t i o n b e t w e e n t h e p r o j e c t i l e s a n d t h e s a m p l e n u c l e i . Within a s i m p l e d e f e c t model, t h e a p p l i e d f l u e n c e s c a n b e r e l a t e d to t h e r e l a t i v e c o n c e n t r a t i o n C of d i s p l a c e d a t o m s , l e a d i n g to: C : 1.8"10-a~cm2"~ f o r CeCu2Si 2 C : 2 . 1 " 1 0 - t ~ c m 2 . ~ f o r CeCu 6 C : 4.3'10-~7cm2'~ for UPts
34
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FIG. 1: p(T) of v a r i o u s CeCu2Si 2 f i l m s ( s h a d e d #(T) r a n g e ) a n d a f t e r i r r a d i a t i o n
T (K)
before
T h e H a l l - e f f e c t IRH(T) I of t h e f i l m s b e f o r e irradiation increases with decreasing temperat u r e , e x h i b i t s a m a x i m u m a t 2K (CeCu2Si2), 4K (CeCu6), a n d 15K (UPt3), r e s p e c t i v e l y a n d r e a c h e s v e r y low v a l u e s f o r T -~ 0. T h e s i g n o f R H i s p o s i t i v e f o r t h e two C e - s y s t e m s a n d n e g a t i v e for UPts, consistent with published data for b u l k s a m p l e s (2-4). T h e CeCu2Si 2 f i l m s a r e s u perconducting w i t h T c = 0.4K ( m i d p o i n t ) . F o r U P t 3 - f i l m s T e - v a l u e s of o n l y = 0.15K w e r e a chieved. As o n e c a n s e e i n Fig. 1 t h e s t r u c t u r e s o f i
2. RESULTS AND DISCUSSION T h e p(T) b e h a v i o r o f CeCu2Si 2 a n d CeCu 6 films before irradiation shows the typical struct u r e s a s k n o w n f o r b u l k s a m p l e s (2,3) e s p e c i a l ly a m a x i m u m a t T* = 10K a n d a F e r m i - l i q u i d r e g i m e (Ap : A.T 2) below TFL : 1.8K (CeCu~Si2) a n d TFL : 0.2K (GeCu6) , r e s p e c t i v e l y . U P t 3 f i l m s exhibit a positive temperature c o e f f i c i e n t of p(T) w i t h p(280K)/Pres = 7.0) i n c l u d i n g a s t r o n g 9 r e d u c t i o n a t low t e m p e r a t u r e s T < 10K w h i c h i s s u p p o s e d to i n d i c a t e t h e f o r m a t i o n of a c o h e r e n t s t a t e of h e a v y f e r m i o n s .
0921-4534/88/$03.50 ©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
o
UPt3
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6 50 10 I~.
.~ .
~23 10 ~
FIG. 2: p(T) of UPt 3 films before and after irradiation
436
G. Adrian and H. Adrian / Hea~y-fermion-systems CeCu2Si 2, CeCum, and UPt 3
p(T) o f C e C u 2 S i 2 a r e g r a d u a l l y s h i f t e d to l o w e r temperature and become less pronounced with i n c r e a s i n g d i s o r d e r till a f t e r ~ ~ 1 0 ' 6 c m - = , o n l y a m o n o t o n o u s i n c r e a s e o f p t o low t e m p e r a t u r e s is observed. The influence of irradiation on CeCu 6 films is qualitatively the same. In order to classify the defect sensitivity more quantitat i v e l y we c o m p a r e l o o k a t t h e e s t i m a t e d c o n c e n trations of displaced atoms necessary to reduce the characteristic temperatures T c , TFL, a n d T* to h a l f o f t h e i r i n i t i a l v a l u e s : C c = 0.005, CFL = 0.025, T* = 0.022 f o r C e C u 2 S i 2 a n d CFL = 0.011, C* = 0.013 f o r CeCum. T h e r e a r e t w o i n d i c a t i o n s t h a t N(EF), i s s e n sitively reduced by disorder: The slope of the upper critical field Bc2', which is in the dirty l i m i t g i v e n b y B e 2 ' = ?f'Pres, i s i n d e p e n d e n t of the defect concentration, although Pres is strongly enhanced. The coefficient A of the T 2behavior, which reflects excitations of quasiparticles out of the Fermi-liquid ground state, A = [N(EF)] 2 (5) i s d i m i n i s h e d d u e t o d i s o r d e r i n b o t h s y s t e m s b y a b o u t a f a c t o r o f 2. For UPt 3 films also a strong resistivity inc r e a s e is o b s e r v e d with disorder, as shown in F i g . 2. H o w e v e r , c o n t r a r y to t h e b e h a v i o r of t h e C e - s y s t e m s t h e d e c r e a s e o f p(T) to low t e m peratures i s no__~t r e d u c e d , but even intensified f o r ~ ~ 10XScm - ~ . A s f o r f l u e n e e s ~ ~ 101ecru - ~ the p(T)-curves remain nearly unchanged by further irradiation, the topmost curve in Fig. 2 e s s e n t i a l l y r e f l e c t s t h e b e h a v i o r f o r ~ -~ - . That lattice defects act strongly on the electronic structure of heavy fermion systems is obvious from the variation of the RH(T)-behavior of the 3 systems. Exemplarily R H(T) o f CeCu~ films is shown before and after irradiation with different fluences i n F i g . 3. T h e r e d u c t i o n o f RH(T) a t low t e m p e r a t u r e d u e to t h e f o r m a t i o n o f a c o h e r e n t s t a t e (6), i s a l r e a d y suppressed at ¢ ~ 4"10~cm -~. Introducing further lattice defects a strong enhancement of RH a t low t e m p e r a t u r e is observed in the two Cesystems. The continous decrease of R H with T after high fluenees may indicate that then the properties of the systems are dominated by incoherent scattering of conduction electrons by
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as in diluted Kondo the 4f-electrons just systems. T h e Hall e f f e c t o f U P t 3 f i l m s d i s p l a y e d in Fig. 4 changes sign at fluences a s low a s 1014cm - 2 . I n t h e c r o s s - o v e r region dUH/dB is negative f o r low f i e l d s (B ~ 2T) a n d p o s i t i v e f o r h i g h f i e l d s (B ~ 4T) c o r r e s p o n d i n g to t h e t w o i n d i c a t e d s y m b o l s . At ¢ ~ 5 ' 1 0 1 4 c m - 2 a s o l e l y p o s i t i v e RH(T ) r e s u l t s which, however, still exhibits a maximum structure. Contrary to t h e Ce-systems RH(T) d e c r e a s e s upon further irradiation. The observed behavior of UPt 3 films may be explained by a disorder induced variat i o n o f N(E) w h i c h c a u s e s a c h a n g e o f t h e d o m i n a t i n g c a r r i e r s f r o m e l e c t r o n - l i k e to h o l e - l i k e . The strong temperature dependence o f RH(T) a t --5"10t4cm -2 indicates the existence of sharp structures in the band density of states. The irradiation induced variation of the magnetoresistivty in CeCu2Si 2 and C e C u ~ (7) agrees with the observations of the RH(¢)-behariot; whereas in UPt~ the main effect at high defect concentrations is a reduction o f ap(B), which can be understood by the reduced mean free path of the conduction electrons. Concluding we obtain drastic alternations of the transport properties of the heavy fermion s y s t e m s C e C u 2 S i 2 , C e C u 6 , a n d U P t 3 e v e n a t low defect concentrations, from which we deduce the existence of sharp structures i n N(E) n e a r E F. F r o m t h e d i f f e r e n t behavior at high defect concentrations we conclude that the hybridisation of conduction electrons with f-electrons, which determines the properties of the Ce-syst e m s i s n o t a s d o m i n a n t i n U P t 3.
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J.J.M. F r a n s e , P.H. F r i n g s , A. d e V i s s e r , A. M e n o v s k y , T.T.M. P a l s t r a , P.H. K e s , a n d J.A. M y d o s h , P h y s i c a 126B, 116 (1984) N.B. B r a n d t a n d V.V. M o s h c h a l k o v , A d v . P h y s . 3 3 , 374 (1984) Y. O n u k i a n d T. K o m a t s u b a r a , J. M a g n . M a g n . M a t 63&64, 527 (1987) W.R. D a t a r s , K. K a d o w a k i , hi. All, a n d S.B. W o o d s , J. P h y s . F 16, L63 (1986) D.W. H e s s , J. L o w T e m p . P h y s . 6 8 , 3 1 1 ( 1 9 8 7 ) A. F e r t a n d P.M. L e v y , P h y s . H e y . B36, 1907 (1987) G.Adrian and H.Adrian, Physica148B,26(1987)