2368 C.C. Lam et al./Physica C 282-287 (1997) 2367-2368

pm. The critical temperature T, of the W-doped Hg-based superconductor is about 133 K.

3. Results and discussion

From a set of experimental results of ac susceptibility measurements, the current density dependence of U.s and bff can be obtained through the plot of lnv versus g(t)/T for various current densities by making use of Eq. (1) [5-6]. Fig. 1 shows the current density dependence of t+e for our specimen. In within the range of current densities, the order of &lies within the interval from lug to lo-” s. From the relation of I&a and J, the glassy exponent p can be found, i.e. p = 1.6.

3. 2.

lo-9 : s

3 3 / /I

50 55 60 65 70 75 80 J (1 0’A/cm2)

Figure 1. The relationship between the macroscopic time scale for creep &s and the driving current density J under the applied field of 40 mT for our specimen.

:. 2-

102:

:. 2-

- 116K - 118K - 12OK - 122K t 124K

1 lo’ 50 I

55 60 65 70 75 80 J (1 O’A/cmz)

Figure 2. The plot of v& vs J for different temperature under the applied field of 40 mT.

Based on Eq. (4) and using the results obtained above, we are able to evaluate the quantity v& for

various current densities at different temperatures. Fig. 2 shows the current density dependence of v& at different temperatures under dc field of 40 mT. As compared our results of v& to that of McHemy et a1.[4] obtained from dc magnetic relaxation method, the order of v& obtained by McHenry et al. lies within the range of our results. Finally, by making use of Eq. (5), we obtain the plot of vm against J at different temperatures, as shown in Fig. 3. The results of the flux creep velocity vm, within the range of our experimental temperature and current density, lie in the range from 1.61x lo4 to 558x10~ cm/s under an applied field of 40 mT for the Pbdoped Hg-1223 sample. The relevant physical mechanism for the varying of the flux creep velocity with the temperature, the current density, and even the H field, is certainly obvious, because the thermally activated flux creep velocity should depend on the thermal fluctuation and the gradient of the magnetic field inside the sample.

10-l

1w

lo-3

lo-(

10-S

10-6

lo-7

1W

B: - 120K - 122K + 124K

50 55 60 65 70 75 80 J (1 O’Akm’)

Figure 3. The relationship between the thermally activated flux creep velocity vm and driving current density J for different temperature under dc field of 40 mT in our Hgo.~&,,,BaL&Cu,o8M specimen.

References

1. 2. 3.

4.

5. 6.

P.W. Anderson, Phys. Rev. Lett. 9,309 (1962). P. Bak et al., Phys. Rev. A 38, 364 (1988). G. Blat& et al., Rev. Mod. Phys. 66, 1125 (1994). M.E. McHemy et al., Phys. Rev. B 44, 7614 (1991). K.C. Hung et al., Physica C (to be published). S.Y. Ding et al., Phys. Rev. B 53, 900 (1996).

PHYSICA lI:i Physica C 282-287 (1997) 2367-2368

Thermally activated flux creep velocity in Hgo.a~Pbo.~IBa2Ca2CuJO~~

C.C. Lam’, X. Jin2, K.C. Hung’, and H.M. Shao’

‘Department of Physics and Materials Science, City University of Hong Kong, Hong Kong ‘National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing, 2 10008, China

The thermally activated flux creep velocity, vFL, is determined by the product of the hopping frequency vh and the average hopping distance L, thus we have vn = v&. At a temperature which is below or close to T,, the flux creep velocity plays an important role in the magnetic behaviour of the superconductor. In this paper, the thermally activated flux creep velocity in superconductor of Hgo.&~.31Ba2CazCusC)8+6 was studied by means of ac susceptibility response based on the theory of self organized criticality (SOC) given by Blatter et al. The measurement was carried out with various driving frequencies, current densities, and under a fixed dc magnetic field of 40 mT. Results obtained from measurement indicate that the thermal flux creep velocity is current density dependence and sensitive to the temperature at which it was measured. As the temperature approaches the critical temperature, the flux creep velocity will drastically increase.

1. Theory

The giant magnetic flux creep is one of the most prominent characters of high temperature superconductors in the presence of an applied magnetic field at high temperature regime. In the flux creep theory proposed by Anderson[l], the thermally activated flux creep velocity plays important role in the vortex dynamics theory. Based on the theory of nonlinear response of the SOC[2], Blatter et al. [3] proposed that the peak of the out-of- phase x” of the ac susceptibility can be described by

1 U,(T,H,J)=kTln-

2nvt, ’ (1)

where U,n is the effective pinning potential, T is the temperature at the peak in x”. fdff, is a macroscopic time scale for creep, which can be written as

t, = kTd’

au ’ Sv,LH, 2

I I f3J

(2)

where vo and L are the attempt frequency and the average hopping distance of flux bundles respectively, and 6 is the applied dc field; J is the driving current density which can be calculated by using Bean critical state model, J = h&d/2) where d is the thickness of the slab sample. On the other hand, the effective pinning potential U,,a(T,H,J) is expressible in the form ofl4-61

0921-4534/97/$17.00 0 Elsevier Science B.V. All rights reserved PI1 SO921-4534@7)01323-3

A,g(t)J-' U,(TKJ)= H” 7

where p is the glassy exponent, n is a constant dependent on different sample and g(t) = (1-t)q in which t = T/T,. In view of Eq. (3) Eq. (2) becomes

kTd’J t, =8v,LH,uU,(T,H,J) ’

Based on the Arrhenius law, see Ref. [l], the flux creep velocity v~ is determined by

v, =v,L=v,Lexp[-U,(T,H,J)/kT] . (5)

In order to evaluate the flux creep velocity, first of all we should know the effective pinning potential U,E and the value of v&. Then, by making use of Eq. (5), vn. can be evaluated.

2. Experimental

The complex ac susceptibility measurements were performed under a dc magnetic field of 40 mT and combined with ac field of different amplitudes of &, = 0.64, 0.96, 1.28, 1.44, 1.60, 1.76 and 1.92 mT. The driving frequencies used in this study were in the range from 1 kHz to 10 kHz. The size of the Hgo,&$,s,Ba2Ca2Cu&+6 sample is of 2x2x8 mm3. This sample is almost consisted of Hg-1223 single phase. The average grain size of this sample was observed by SEM analysis, and its value is about 4