Physica C 235-240 (1994)2897-2898 PHVSlgA ® North-Holland

THERMALLY ACTIVATED FLUX CREEP STUDIES IN SUPERCONDUCTING LA2CUO4+5

Lu Zhang a J.Z. Liu b, M.D. Lan c, P. Klavins b and R.N. Shelton b

aDepartment of Physics, California State University, Stanislaus, Turlock, CA 95382, USA.

bDepartment of Physics, University of California, Davis, CA 95616, USA.

CDepartment of Physics, National Chung Hsing University, Taiwan, ROC.

The time-dependent magnetic relaxation was measured in a full field penetrated La2CuO4+5

crystal over a time period of 105 sec. The relaxation data exhibit a power-law time dependence over a wide range of temperatures. A theoretical model based on a logarithmic dependence of the effective creep activation barrier is employed to analyze the experimental data and to study the thermally activated flux creep behavior in the mixed state.

Some recent investigations have probed an unusual long time asymptotic relaxation behavior of the magnetization due to the thermally-activated flux creep below the critical state. In this paper, we present flux creep s tud ies in a superconduc t ing La2CuO4+5 crystal.

High qua l i ty s ingle c rys ta l s of L a 2 C u O 4 + 5 were grown by a self-flux method and post-annealed in oxygen under high pressure. The crystal used in the relaxation experiment had a dimension of 10 x 5 x 0.1 mm 3, a mass of about 15.4 mg, and a transition temperature of 24 IL

The s h i e l d i n g ef fec t m a g n e t i c relaxation experiments were performed on a commercial superconducting quantum i n t e r f e r e n c e d e v i c e ( S Q U I D ) m a g n e t o m e t e r 1 over a time period of 105 seconds. The magnetometer was operated with a scan of 3 cm and an iterative regression mode was used. The magnetic fields were carefully applied as to prevent any overshoot. In addit ion, all the experiments were operated at 2 kOe, which was sufficiently large to ensure that the ent ire specimen was well into a fully penetrated state.

Figure 1 gives a M versus t plot of a La2CuO4+5 single crystal for the field parallel to the c-axis at T = 5 K and H = 2

0921-4534/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved. SSDI 0921-4534(94)02014-0

kOe. The inset of the figure clearly exhibits a significant departure from linearity in a logarithmic scale where the solid line represents the logarithmic fit. This reflects that the classical flux creep models 2 based on the approx imat ion of l inea r J- dependence near the critical state is not applicable over this long time period. A result of giant flux creep in the high temperature superconductors is tha t the actual metastable state creeps away from critical state so that J << Jc. Hence, the traditional theory of thermally activated flux motion based on U(J) = Uo(1-J/Jc) near critical state is a poor approximation in this long time region.

I 0

=

L a z C u O 4÷b . . . . .

l t l lc ~ H = 2 k O e • T=SK

1 0 I I n

10 10 z 10 3 10 4 10 5 t i m e (see)

F i g u r e 1 M a g n e t i c t i m e r e l a x a t i o n a t 5K a n d 2kOe for f ield pa ra l l e l to c-axis of a La2CuO 4 .8 c r y s t a l

2898 L. Zhang et al./Physica C 235-240 (1994) 2897-2898

Generally, the magnetic properties of high temperature superconductors in the mixed state have to take into account the nonlinear current dependence of the creep activation energy. Zeldov et al., Maley et al. and McHerny et al. observed a logarithmic current dependence of the activation energy barrier, U(J) = Uoln(Jc/J), in both magnetic

and transport measurements 3. Vinokur et al. 4 proposed a model describing a self- organized critical state, assuming the creep ac t iva t ion grows logar i thmical ly with decreas ing current . The corresponding magnet iza t ion in the case of a fully- penetrated field, H > H*, can be described a s :

kBT t lnM(t) = const. - ~ l n ( ~ )

where 1/to is a characteris t ic a t tempt frequency for flux hopping over the pinning barrier, H* is the full penetration field and b = I dlnM/dlnt I = kBT/Uo is the relaxation rate. This model presumes that temperature is low so that b << 1. Recent experiments observed power- law magne t i c t ime relaxations over a long time period up to 5 x 105 seconds in a LuBa2Cu307_5 crystal and a YBa2Cu307_5 detwinned crystal 5. These exper imenta l data supported Vinokur's theoretical predictions.

0.25

m 0 .2

0 . 1 5

II 0.1

0 . 0 5 4

L a 2 C u O 4+~ crystal /

I I I I

6 8 10 12 14

T (K) Figure 2 Temperature dependence of the relaxation rate for H = 2 kOe

The power-law fit in the Fig. 1 is r emarkab ly accurate over almost four decades in time. The slope of the curve, dlnM/dlnt, gave a relaxation rate, which is shown in Fig. 2 plotted as a function of t e m p e r a t u r e . However , the f i t t i ng coefficient b was found not to vanish when T --~ 0 K. This indicates the existence of a tempera ture- independent , non- thermal ly activated creep 6. The parameter b was also found to have a quadratic t empera tu re dependence term while kBT/Uo << 1. This indicates that Uo is temperature dependent.

In conclusion, we m e a s u r e d the magnetic relaxation on a La2CuO4+5 single crystal over a long time period of 105 sec. The power-law time dependence of the magnetizat ion was obtained at various temperatures, which can be well interpreted by Vinokur's model.

This work is supported by the U.S. Air Force Office of Scientific Research under grant number AFOSR-F49620-92-J-0514 and by the National Science Foundation under grant number DMR-90-21029.

REFERENCES

1Quantum Design, Inc. San Diego, CA.

2C.p. Bean, Phys. Rev. lett, 8, 250 (1962). P.W. Anderson, Phys. Rev. Lett. 9, 309 (1962). 3E. Zeldov et al., Appl. Phys. Lett. 56, 680 (1990). M.P. Maley et al., Phys. Rev. B 42, 2639 (1990). M E. McHenry et al, Phys. Rev. B, 44, 7614 (1991).

4V. M. Vinokur et al., Phys. Rev. Lett. 67, 915 (1991).

5J.Z. Liu, Lu Zhang, M.D. Lan, and R.N. Shelton, Phys. Rev. B 46, 9123 (1992). Lu Zhang, J.Z. Liu, M.D. Lan, and R.N. Shelton, submitted to Phys. Rev. B.

6Lu Zhang, J.Z. Liu, M.D. Lan, and R.N. Shelton, to be published.