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cDepartment of Physics, Kyushu dDepartment of Applied Physics, Magnetic Relaxation in. 3 ... films in the mixed state and its time dependence is measu...

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Magnetic Relaxation in Ryuji Kondoa, Takeshi Fukamib, Fac. of Engineering, Oita Univ., b Department of Materials Science and a

Department of Physics, Kyushu d Department of Applied Physics, c

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Y-Ba-Cu-O Thin Films Kazumasa Makisec,Tsuyoshi Tamegaid 700 Dannoharu Oita, Japan Engineering, Himeji Institute of Technology,Himeji, Japan University, Fukuoka, Japan The University of Tokyo, Tokyo, Japan

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Abstract Distribution of a local field B(x) on the surface of YBCO thin films in the mixed state and its time dependence is measured using a micro Hall-probe array. Analizing these data based on the flux diffusion equation, the model-independent activation energy U is obtained. Since the local current density J is defind to reproduce the field profile B(x), U(B,J) can be plotted in a 3-dimensional space. This 3-dimensional mapping gives us information on U as a function of B and J.

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H

Experiments Sample : c-axis oriented YBCO epitaxial films Tc = 90K size 890x10000x0.27µm3. Micro Hall probe array* : Si doped GaAs : 6 elements,10x10 mm2 active area The sample is laid on the Hall probe array directly [Fig.1] and the surface field is measured.

Sample

Fig.1

*T. Tamegai et al, Phys. Rev. B, 45, 8201 (1992).

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Fig.2 Photo of a Hall probe array and the sample.

Hall Probe

154.4

µm

400

Hall probe YBCO Film

890 µm

B [gauss]

350

300

H = 400 Oe 250

200 Probe 1 Probe 4

150 1

10

Probe 2 Probe 5

100

1000

Probe 3 Probe 6

10000

t [s] Fig.3

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Measurements of the time dependence of local field B The sample is cooled to 20K at zero field and then a dc field is applied parallel to the c axis of the crystal.

A time dependence of local field B measured at 20K and H=400Oe.

Fig.3 shows a result at H = 400 Oe and the inset does an arrangement of the sample on the Hall probe array. The probe is in the center of the sample. Under several H's, the above measurements were performed.

The method for determining U(j, B)* Using B(x, t), the flux current density D(x, t) is numerically calculated.

-0.006 -0.008

H = 600 Oe

M [T]

-0.01 -0.012

Probe 4

-0.014

Time

-0.016 -0.018 -0.00015 -0.0001 -0.00005

Fig.4

0

0.00005 0.0001

0.00015

Distance [m]

The profile of local magnetization M measured at T=20K, H=600Oe and from 40 seconds to 14000 seconds. The solid lines

D(x,t) is calculated in the middle between probe 1 and 2 and associated with U(x, t) in the following equation .

show calculated magnetizations at 40µm distance from the sample surface.

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* Y. Abulafia et al, Phys. Rev. Lett. 75, 2404 (1995).

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2

0

J [10 A/m ]

5

10

H = 200 Oe

For estimating of the local current, we utilize a model proposed E. H. Brandt et al.*[Fig.5].

1sec -5

10000sec

- 10 - 0.0004

- 0.0002

0

0.0002

0.0004

Distance [m] Fig.5 The profile of calculated current density

Using the avobe model, we calculate the surface field and fit it to experimental results[Fig.6].

0.02 H = 200 Oe, 1000sec

B [T]

0.015

Fig.5 is the profile of calculated current density J at

0.01 0.005

T=20K and H=200Oe for 1, 10, 100, 1000 and 10000 sec.

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Fig.6 is the profile of flux-density B measured at T=20K, -0.0002 -0.0001

0

0.0001

0.0002

Distance [m]

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Fig.6 The profile of flux-density

H=200Oe and at 1000 seconds. The solid curve shows calculated B at 40mm distance from the sample surface. The dotted curve shows calculated internal B. *

E. H. Brandt et al, Phys. Rev. B, 48, 12893 (1993).

U [arb. unit]

U( j, B) plotted in a 3-D space 28 26 24

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J[

8

10 10 A/m 2 ]

10

B[ gau ss]

4

22 0 20 200 18 400 600 800 1000

Fig.7 3D plot of activation energy U calculated in the middle between probe 1 and 2.

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Using the Hall probe array, we get U, B and j simultaneously therefore U can be plotted in a 3-dimensional space[Fig.7].

Conclusion Using hall probe array technique, the model-independent U( B, j) can be obtained. Plotted U(B, J) in a 3-dimensional space using B, J and U axes, all data fall on a same curved surface.