Relaxation of the magnetization in high-Tc superconductors

PhysicaC 153-155 (1988) 6 7 - 7 0 North-Holland, Amsterdam

RELAXATION OF THE MAGNETIZATION IN HIGH-T c SUPERCONDUCTORS A.C. MOTA, A. POLLINI, P. VlSANI, K.A. MUELLER*, and J.G. BEDNORZ* Laboratorium f~r Festk6rperphysik, ETH-H6nggerberg, CH-8093 Z~rich, Switzerland; * IBM Laboratories ZUrich, CH-8803 RUschlikon, Switzerland. Logarithmic time decays of the magnetization M have been observed in Sr-La-Cu-O and Ba-La-Cu-O specimens. I f a small f i e l d Hi < Hcz is applied to a v i r g i n specimen, the isothermal dc magn e t i z a t i o n M is unstable and decays in time following the law M-M0 ~ T H i n l n ( t / t 0 ) with n : 3 over an observation period of i0 ~ sec. I f the f i e l d Hi is removed, the same law is followed at H = 0 with a logarithmic rate ~M/~Int about a f a c t o r of three smaller. This indicates that these substances have a strong "memory" of the f i e l d Hi applied previously. The f i r s t observation of metastable states in the magnetization of Ba-La-Cu-O was reported by M~ller, Takashige and Bednorz ( I ) . In t h e i r experiment, when a f i e l d of 300 Oe was switched off on a f i e l d - c o o l e d specimen, the magnetization M decayed following an exponent i a l law for short times and a f t e r some few minutes, a much weaker time dependence. Similar decays were observed on a z e r o - f i e l d cooled specimen a f t e r a f i e l d of 300 Oe was switched on and at a l a t e r time switched o f f . The correct form of the r e l a x a t i o n was not determined from t h e i r data. Here we discuss some recent experimental r e s u l t s (2) on time e f f e c t s in the isothermal magnetization M on a scale of 1 sec to 105 sec

÷ 4 ÷**

Sr0 2LOlsCU04 T=0.8

(powder)

S÷ +

at T << Tc and H < 400 Oe. From these measurements we have obtained the exact form of the time dependence of M in the given time i n t e r val as well as the e f f e c t of temperature and applied f i e l d in the r e l a x a t i o n . Time-decay measurements were made on three d i f f e r e n t specimens: BaozsLa185Cu04 in powdered form and Sro2La18CuO # in s'intered and powdered form. The dc magnetization measurements were done with non-commercial SQUID magnetometers in the following way: a f t e r z e r o - f i e l d cooling of the specimens to below Tc in the residual f i e l d of the cryostat (Hre s = 2 mOe), a constant magnetic f i e l d Hi was app l i e d . The dc magnetization M corresponding to the f i e l d Hi was theo recorded as a function of time for about one day at constant temperat u r e . Later on, the f i e l d Hi was removed and again, the change in the magnetization at H = 0 was recorded for about one day. This procedure was repeated with a d i f f e r e n t Hi

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FIGURE 1 Change in the magnetization of Sr-La-Cu-O at H : 0 as a function of the logarithm of time.

0921-4534/88/$03.50 ©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

FIGURE 2 Same data as in f i g u r e 1 plotted scale.

in a log-log

68

A.C. Mota et al. / Relaxation of magnetization in high-T~ superconductors

a f t e r the specimen had been warmed up above Tc and cooled down again at zero f i e l d . In f i g u r e 1 we show the remanent magnetizat i o n in a r b i t r a r y u n i t s and a r b i t r a r y o r i g i n f o r powdered Sr-La-Cu-O at T = 0.8 K as a f u n c t i o n of the l o g a r i t h m of time a f t e r a f i e l d Hi = 120 Oe has been switched o f f . In f i g u r e 2 we show the same p o i n t s p l o t t e d in a l o g - l o g s c a l e . Indeed, in a time scale extending from 2 sec to 105 sec, the m a g n e t i z a t i o n a c c u r a t e l y f o l l o w s the law:

I0

SrLaCuO (powder) H=O

(Hi = 4 0 0 e )

cIM cllnt

M(t) - M(t0) ~ A l n ( t / t 0 ) The same l o g a r i t h m i c law is f o l l o w e d at H = Hi with the p r e f a c t o r A about t h r e e times b i g g e r than at H = O. At H = Hi the magnetiz a t i o n decreases in absolute value as a funct i o n of t i m e , w h i l e at H = 0 the s m a l l , p o s i t i v e remanent m a g n e t i z a t i o n r e l a x e s toward zero. I t is important to p o i n t out t h a t , c o n t r a r y to the behaviour of glassy m a t e r i a l s , we have not observed w a i t i n g time e f f e c t s . A f t e r c o o l ing the specimens in about one hour to temperat u r e s T << Tc, the f i e l d was r a i s e d up to Hi, subsequently turned o f f , and then a t i m e decay measurement was done. We obtained the same decay r a t e s at H = 0 w i t h i n our accuracy, whether the f i e l d Hi was on f o r few seconds or f o r several hours. The r e l a x a t i o n r a t e is also independent of the time taken to reduce the f i e l d from Hi to zero in the range of seconds to hours. The time e v o l u t i o n of the m a g n e t i z a t i o n in the high Tc copper oxides f o l l o w a law d i f f e r e n t from t h a t in s p i n - g l a s s e s . Very accur a t e measurements of the thermal remanent magn e t i z a t i o n as a f u n c t i o n of time in Cu:Mn and Ag:Mn by Chamberlin, Mozurkewich and Orbach (3) showed t h a t in glassy m a t e r i a l s n e i t h e r an a l g e b r a i c law nor a l o g a r i t h m i c f u n c t i o n of time described the data c o r r e c t l y . In t h e i r case, the remanent m a g n e t i z a t i o n was charact e r i z e d a c c u r a t e l y at a l l temperatures w i t h i n the spin glass region by a " s t r e t c h e d " expon e n t i a l of the form: ~ ( t ) = Go e x p [ - ( t / ~ ) l - n ] w i t h 0 < n < 1. In f i g u r e 3 we show the l o g a r i t h m i c r a t e ~M/~Int at H = 0 f o r Sr-La-Cu-O powder a f t e r a f i e l d Hi = 40 Oe has been switched o f f , as a f u n c t i o n of the temperature T. We n o t i c e t h a t , f o r 2 K < T < i0 K, the l o g a r i t h m i c r a t e is a p p r o x i m a t e l y l i n e a r w i t h t e m p e r a t u r e , w h i l e f o r T < 1 K, the l o g a r i t h mic r a t e tends to a much weaker temperature dependence i n d i c a t i n g t h a t the r e l a x a t i o n is less t h e r m a l l y a c t i v a t e d . In Fig. 4 we show precise measurements of the m a g n e t i z a t i o n f o r the same powdered s p e c i men as in Fig. 3. At these low f i e l d s , M has a

O.L

l O.L

l

I t

i

i

T[K]

I LO

FIGURE 3 Log-log graph of the slope aM/alnt as a funct i o n of the temperature. The data was taken at H = 0 a f t e r a f i e l d of 40 Oe was turned o f f . constant slope and i t is r e v e r s i b l e to b e t t e r than 1%. From t h i s o b s e r v a t i o n , we cannot expect t h a t some small remanent f l u x could b u i l d up a c o n s i d e r a b l e f l u x d e n s i t y g r a d i e n t at H = O. This conclusion is not v a l i d f o r the s i n t e r e d specimen. In t h i s case, s h i e l d i n g c u r r e n t s across d i f f e r e n t grains gave almost a f a c t o r of two increase of the slope of M vs H f o r f i e l d s H < 3 0 e (4) with i r r e v e r s i b l e behaviour below 3 0 e . In the three specimens studied here, the r e l a x a t i o n of M does not show any f l u x jumps as is commonly the case in conventional type I I superconductors in the Shubnikov phase. On the c o n t r a r y , the time e v o l u t i o n of M at H = Hi or at H = 0 is very smooth on a scale of one f l u x quantum, as can be seen in Fig. 5. The dependence of the l o g a r i t h m i c r a t e ~M/~Int at H = 0 and T = 4 K on the f i e l d Hi is d i s played in Fig. 6 in a l o g - l o g graph f o r the t h r e e specimens studied in t h i s work. Here Hi is the maximum f i e l d at which a v i r g i n specimen was exposed before the H = 0 decay was measured. We observe t h a t f o r Hi
69

A.C. Mota et al. / Relaxation of magnetization in high-TC superconductors

I

I

I

L

with 3 < n < 4. The s i n t e r e d Sr-La-Cu-O s p e c i men (open square symbols) shows a d e v i a t i o n from t h i s law f o r Hi < 50 Oe. This is due to the g r a n u l a r behaviour of s i n t e r e d specimens. In s i n t e r e d samples when the f i e l d Hi is r e duced, f l u x is trapped in the voids formed by d i f f e r e n t grains j o i n e d by weak Josephson j u n c t i o n s w i t h the r e s u l t of some a d d i t i o n a l c o n t r i b u t i o n to the r e l a x a t i o n of M described here.

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FIGURE 5 O i r e c t r e c o r d i n g of the time decay of M at H = 0 f o r Ba-La-Cu-O powder at T = 4 K a f t e r a f i e l d Hi = 140 Oe has been switched o f f . One f l u x quantum ¢0 at the sample is i n d i c a t e d .

FIGURE 6 L o g a r i t h m i c r a t e at H = 0 and T = 4.2 K as a f u n c t i o n of the f i e l d Hi at which the s p e c i mens have been exposed. S i m i l a r f l u x motion at H = O, also independent of Hi , was observed by us (5) in s p e c i mens of g r a n u l a r niobium a f t e r applying f i e l d s as high as 200 Oe. In Fig. 6 we observe t h a t f o r the highest f i e l d s the l o g a r i t h m i c r a t e ~M/~Int tends to a weaker f i e l d dependence than Hi 4, At those f i e l d s , some v o r t i c e s s t a r t p e n e t r a t i n g i n t o the specimen as we observe in the corresponding m a g n e t i z a t i o n curves.

70

A.C. Mota et a L / Relaxation of magnetization in high-T, superconductors

A comparison of r e l a x a t i o n rates at d i f f e rent temperatures and d i f f e r e n t f i e l d s showed t h a t , f o r each specimen, l~M/~Int| is in a l l cases only about a f a c t o r of thre~ to four smaller when the f i e l d Hi is o f f than when the f i e l d Hi is on. At a given temperature, the absolute value of ~M/~Int at H = Hi and at H = 0 are determined o n l y by the f i e l d Hi to which the specimen is or has been exposed during or before the measurement. This f a c t seems to i n d i c a t e some kind of memory e f f e c t , since the f l u x density c o n f i g u r a t i o n s are so very d i f f e r e n t f o r the case Hi on from the case Hi o f f . Q u a n t i t a t i v e l y , the r e l a x a t i o n r a t e in Ba-La-Cu-O at T = 4 K and H = 70 Oe f o r example, is : AM/M = 1.5 % per decade of time in seconds. In powdered Sr-La-Cu-O at the same temperature and f i e l d 4M/M is about one order of magnitude smaller. In summary, we have observed some novel rel a x a t i o n e f f e c t s in the magnetization of Ba-La-Cu-O and Sr-La-Cu-O at H < Hcl and T<
gradients. Recently, some of us have found two very d i f f e r e n t superconductors where s i m i l a r e f f e c t s to those reported here, were observed. They are the heavy fermion CeCu2Si 2 (6) in bulk p o l y c r y s t a l l i n e form, and the quasitwodimensional organic superconductor p-(BEDTTTF)213 in the form of a s i n g l e c r y s t a l (7). REFERENCES 1. K.A. MUller, M. Takashige and J.G. Bednorz Phys. Rev. L e t t . 58, 1143 (1987) 2. A.C. Mota, A. P o l l i n i , P. V i s a n i , K.A. MUller and J.G. Bednorz, Phys. Rev. B36, 4011 (1987) 3. R.V. Chamberlin, G. Mozurkewich and R. Orbach, Phys. Rev. Lett 52, 867 (1984) 4. A.C. Mota, A. P o l l i n i , P. Visani, K.A. MUller and J.G. Bednorz, I n t . J. of Mod. Phys. B 3&4, 903 (1987) 5. A.C. Mota, P. V i s a n i , A. P o l l i n i , G. J u r i , J. Rosenblatt and P. Peyral, to be published. 6. A.C. Mota, P. Visani and A. P o l l i n i ( t h i s Conference) 7. A.C. Mota, P. Visani, A. P o l l i n i , G. J u r i , and D. Jerome ( t h i s Conference)