- Email: [email protected]
Period doubling and magnetic chaos in superconducting YBa2Cu3O7
Physica C 153 155 (1988) 332 333 North-Holland, Amsterdam
PERIOD DOUBLING AND MAGNETIC CHAOS IN SUPERCONDUCTING YBa2Cu307 T. DATTA* , Carmen ALMASANm, D.U. GUBSER+, S.A. WOLF+ and L.E. TOTH+ ~Physics Department, U n i v e r s i t y of South C a r o l i n a , Columbia, SC 29208, USA Naval Research L a b o r a t o r y , Washington, DC 20375, USA
The time dependence of the f i e l d - c o o l e d cool down and f i e l d - c o o l e d warm up remnant magnetic moments, M ( t ) , were s t u d i e d as f u n c t i o n s of temperature. For T<70K both the cool down and warm up M(t) were r e g u l a r and showed a slow decay. For 700 in the " c h a o t i c " temperature region and ~<0 in o t h e r regions. 1.
INTRODUCTION The o b s e r v a t i o n (1) of the i r r e v e r s i b i l i t y between the z e r o - f i e l d cooled (ZFC) and f i e l d cooled (FC) magnetic moments in copper oxide superconductors has s t i m u l a t e d a l o t of i n t e r e s t in the time dependent behaviors of t h i s system ( 2 , 4 ) , because i t is associated w i t h the n o n e r g o d i c i t y or glassy p r o p e r t i e s . An i r r e v e r s i b i l i t y between the f i e l d - c o o l e d , cool down (FCC) and warm up (FCW) moments in YBaCuO has also r e c e n t l y been r e p o r t e d (5). Here we r e p o r t on the time dependence of the remnant magnetic moment in th~se samples. B r i e f l y , we observed an enhanced diamagnetism in the FCW data. This increase is most prominent around 75K and gives r i s e to an irreversibility between the FCC and FCW responses The i r r e v e r s i b i l i t y between ZFC and FC behaviors mentioned a t the beginning may be d i s t i n c t from t h a t between FCC and FCW. The increased diamagnetism in FCW may be due to the m e l t i n g of the f l u x - l a t t i c e and v o r t e x d e t r a p p i n g . EXPERIMENTAL The p r e p a r a t i o n procedure f o r our ceramic samples has been r e p o r t e d (6) e a r l i e r . The measurements were performed w i t h a computerc o n t r o l l e d v a r i a b l e temperature SQUID susceptometer. For the time dependence measurements, two p r o t o c o l s were f o l l o w e d : ( i ) In the FCC procedure the specimens were cooled from 150 K down to the d e s i r e d experimental temperature in a f i e l d B=O.2 mT, p a r a l l e l to the samples long a x i s . ( i i ) In the FCW procedure, from 150 K the temperature was lowered f i r s t to 10 K in presence of B. The temperature was held at 10 K f o r a w a i t i n g time (~600 s) and then increased to T w i t h B s t i l l on. For both ( i ) and ( i i ) , a f t e r T was reached, the specimen was allowed to t h e r m a l ~ze f o r several minutes. Then the f i e l d was
turned o f f and about 300 seconds were allowed f o r the e l e c t r o n i c t r a n s i e n t s to s e t t l e . At t h i s time the sample response or remnant moment, M, was observed to change sign to a p o s i t i v e value c o n f i r m i n g f l u x t r a p p i n g . The values of M(t) were recorded every 20 seconds by the computer. These measurements were 40.0
~-~ ~ ~'~
39.5
39.0
o 38.5
ooO~ •
N <
38.0
•
• I
;,,°
O~o0•
Z
•eO
2.
0921-4534/88/$03.50 ©ElsevierSciencePublishers B.V. (North-Holland Physics Publishing Division)
37.5
37.0
, 0
i 500
_ ,
l
1000
1500
2000
TIME ( s e e ) FIGURE 1 Chaotic FCW remnant magnetic moment vs time a t 74 K. The f l u c t u a t i o n s are several orders of magnitude l a r g e r than the i n s t r u mental r e s o l u t i o n • made under isothermal c o n d i t i o n s w i t h the specimen v e r t i c a l l y o s c i l l a t i n g a t .05 Hz in the background f i e l d (~O.01mT).
T. Datta et al. / Period doubling and magnetic chaos
3.
RESULTSAND DISCUSSION Several specimens with d i f f e r e n t Meissner fractions and sharpness of t r a n s i t i o n s were studied. To be s p e c i f i c , presently, we w i l l focus on the results from one sample. Qualit a t i v e l y , three types of time dependent M(t) were observed in three temperature regions. (a) High temperature T~9_OK, in t h i s region M(t) was very small (~10 s emu) and decayed rapidly. (b) low temperature, T<7OK; in t h i s case M(t) was large (~10 - 3 emu) %and decayed very slowly in a non-exponential rate. (c) In the intermediate region, 70
lO
~
'--
i
333
~
~ -~1 ~ t
t-
-i
h"
~q v
0.1
1 2
~Q
0.01
; rj
3
o.ool
0.0001 50
100
150
200
250
300
350
OMEGA (mHz) ~
"-~
iI'
'
'
'
....
. , . , .
FIGURE 3 Spectral density of FCW at 74 K. The positions of the 1st, 2nd and 3rd order b i f u r c a t i o n s are shown. Notice the larger broad spectrum response at 74 K compared with 70 K.
0,1
4. Z ~
CONCLUSIONS We believe that the b i f u r c a t i o n and the Liapunov exponent values are evidence for d e t e r m i n i s t i c chaos in these granular superconductors, perhaps a r i s i n g from the nonlinear dynamics of the trapped f l u x - l a t t i c e melting. Other non-linear and chaotic superconducting effects may also be operative.
0.01
o.ool G~
0.0001
,K
0
1
50
,
I
l ~ t
,
100
150
,
200
I
250
,
J
300
5. 350
OMEGA (rnHz)
ACKNOWLEDGEMENTS This work was p a r t i a l l y supported at USC by a NRL Grant # 1070K101. L.E. Toth was on a leave of absence from NSF. Carmen Almasan acknowledges a graduate fellowship from ZONTA International.
FIGURE 2 Spectral density of FCW at 70 K peak in the spectral density corresponds to the measurement frequency and is present ]n both figures. The spectra of 70 K shown in Figure 2 do not e x h i b i t any other structure. In contrast, the 74 K spectra, Figure 3, c l e a r l y shows up to the t h i r d order period doubling. The spectra from other data sets taken in t h i s "chaotic" temperature region also exhibited s i m i l a r subharmonic b i f u r cations. The Liapunov exponent, e, was also calculated from M(t) and we observed e>O in the chaotic region and e
6. REFERENCES (1) K.A. MUller et al. Phys. Rev. Lett. 58 (1987) 1143. (2) K.W. Blaze et al. Phys. Rev. B36 (1987) 7241. (3) G. Deutscher and K.A. MUller, Phys. Rev. Lett. 59 (1987) 1745. (4) C. Giovannella et al. Euro. Phys. Lett. 4 (1987) 109. (5) T. Datta et al. in: Novel Superconductivit y, eds. S.A. Wolf and V.Z. Kresin, (Plenum, NY 1987) p. 817. (6) S.B. Qadri et al. Phys. Rev. B35 (1987) 7235.
PERIOD DOUBLING AND MAGNETIC CHAOS IN SUPERCONDUCTING YBa2Cu307 T. DATTA* , Carmen ALMASANm, D.U. GUBSER+, S.A. WOLF+ and L.E. TOTH+ ~Physics Department, U n i v e r s i t y of South C a r o l i n a , Columbia, SC 29208, USA Naval Research L a b o r a t o r y , Washington, DC 20375, USA
The time dependence of the f i e l d - c o o l e d cool down and f i e l d - c o o l e d warm up remnant magnetic moments, M ( t ) , were s t u d i e d as f u n c t i o n s of temperature. For T<70K both the cool down and warm up M(t) were r e g u l a r and showed a slow decay. For 70
INTRODUCTION The o b s e r v a t i o n (1) of the i r r e v e r s i b i l i t y between the z e r o - f i e l d cooled (ZFC) and f i e l d cooled (FC) magnetic moments in copper oxide superconductors has s t i m u l a t e d a l o t of i n t e r e s t in the time dependent behaviors of t h i s system ( 2 , 4 ) , because i t is associated w i t h the n o n e r g o d i c i t y or glassy p r o p e r t i e s . An i r r e v e r s i b i l i t y between the f i e l d - c o o l e d , cool down (FCC) and warm up (FCW) moments in YBaCuO has also r e c e n t l y been r e p o r t e d (5). Here we r e p o r t on the time dependence of the remnant magnetic moment in th~se samples. B r i e f l y , we observed an enhanced diamagnetism in the FCW data. This increase is most prominent around 75K and gives r i s e to an irreversibility between the FCC and FCW responses The i r r e v e r s i b i l i t y between ZFC and FC behaviors mentioned a t the beginning may be d i s t i n c t from t h a t between FCC and FCW. The increased diamagnetism in FCW may be due to the m e l t i n g of the f l u x - l a t t i c e and v o r t e x d e t r a p p i n g . EXPERIMENTAL The p r e p a r a t i o n procedure f o r our ceramic samples has been r e p o r t e d (6) e a r l i e r . The measurements were performed w i t h a computerc o n t r o l l e d v a r i a b l e temperature SQUID susceptometer. For the time dependence measurements, two p r o t o c o l s were f o l l o w e d : ( i ) In the FCC procedure the specimens were cooled from 150 K down to the d e s i r e d experimental temperature in a f i e l d B=O.2 mT, p a r a l l e l to the samples long a x i s . ( i i ) In the FCW procedure, from 150 K the temperature was lowered f i r s t to 10 K in presence of B. The temperature was held at 10 K f o r a w a i t i n g time (~600 s) and then increased to T w i t h B s t i l l on. For both ( i ) and ( i i ) , a f t e r T was reached, the specimen was allowed to t h e r m a l ~ze f o r several minutes. Then the f i e l d was
turned o f f and about 300 seconds were allowed f o r the e l e c t r o n i c t r a n s i e n t s to s e t t l e . At t h i s time the sample response or remnant moment, M, was observed to change sign to a p o s i t i v e value c o n f i r m i n g f l u x t r a p p i n g . The values of M(t) were recorded every 20 seconds by the computer. These measurements were 40.0
~-~ ~ ~'~
39.5
39.0
o 38.5
ooO~ •
N <
38.0
•
• I
;,,°
O~o0•
Z
•eO
2.
0921-4534/88/$03.50 ©ElsevierSciencePublishers B.V. (North-Holland Physics Publishing Division)
37.5
37.0
, 0
i 500
_ ,
l
1000
1500
2000
TIME ( s e e ) FIGURE 1 Chaotic FCW remnant magnetic moment vs time a t 74 K. The f l u c t u a t i o n s are several orders of magnitude l a r g e r than the i n s t r u mental r e s o l u t i o n • made under isothermal c o n d i t i o n s w i t h the specimen v e r t i c a l l y o s c i l l a t i n g a t .05 Hz in the background f i e l d (~O.01mT).
T. Datta et al. / Period doubling and magnetic chaos
3.
RESULTSAND DISCUSSION Several specimens with d i f f e r e n t Meissner fractions and sharpness of t r a n s i t i o n s were studied. To be s p e c i f i c , presently, we w i l l focus on the results from one sample. Qualit a t i v e l y , three types of time dependent M(t) were observed in three temperature regions. (a) High temperature T~9_OK, in t h i s region M(t) was very small (~10 s emu) and decayed rapidly. (b) low temperature, T<7OK; in t h i s case M(t) was large (~10 - 3 emu) %and decayed very slowly in a non-exponential rate. (c) In the intermediate region, 70
lO
~
'--
i
333
~
~ -~1 ~ t
t-
-i
h"
~q v
0.1
1 2
~Q
0.01
; rj
3
o.ool
0.0001 50
100
150
200
250
300
350
OMEGA (mHz) ~
"-~
iI'
'
'
'
....
. , . , .
FIGURE 3 Spectral density of FCW at 74 K. The positions of the 1st, 2nd and 3rd order b i f u r c a t i o n s are shown. Notice the larger broad spectrum response at 74 K compared with 70 K.
0,1
4. Z ~
CONCLUSIONS We believe that the b i f u r c a t i o n and the Liapunov exponent values are evidence for d e t e r m i n i s t i c chaos in these granular superconductors, perhaps a r i s i n g from the nonlinear dynamics of the trapped f l u x - l a t t i c e melting. Other non-linear and chaotic superconducting effects may also be operative.
0.01
o.ool G~
0.0001
,K
0
1
50
,
I
l ~ t
,
100
150
,
200
I
250
,
J
300
5. 350
OMEGA (rnHz)
ACKNOWLEDGEMENTS This work was p a r t i a l l y supported at USC by a NRL Grant # 1070K101. L.E. Toth was on a leave of absence from NSF. Carmen Almasan acknowledges a graduate fellowship from ZONTA International.
FIGURE 2 Spectral density of FCW at 70 K peak in the spectral density corresponds to the measurement frequency and is present ]n both figures. The spectra of 70 K shown in Figure 2 do not e x h i b i t any other structure. In contrast, the 74 K spectra, Figure 3, c l e a r l y shows up to the t h i r d order period doubling. The spectra from other data sets taken in t h i s "chaotic" temperature region also exhibited s i m i l a r subharmonic b i f u r cations. The Liapunov exponent, e, was also calculated from M(t) and we observed e>O in the chaotic region and e
6. REFERENCES (1) K.A. MUller et al. Phys. Rev. Lett. 58 (1987) 1143. (2) K.W. Blaze et al. Phys. Rev. B36 (1987) 7241. (3) G. Deutscher and K.A. MUller, Phys. Rev. Lett. 59 (1987) 1745. (4) C. Giovannella et al. Euro. Phys. Lett. 4 (1987) 109. (5) T. Datta et al. in: Novel Superconductivit y, eds. S.A. Wolf and V.Z. Kresin, (Plenum, NY 1987) p. 817. (6) S.B. Qadri et al. Phys. Rev. B35 (1987) 7235.