Frequency, amplitude of magnetic field and temperature characterization of YBCO using higher harmonics ac susceptibility measurements near Tc

PHYSICA ELSEVIER

Physica C 341-348 (2000) 1101-1102 .

www.elsevier.nl/locate/physc

Frequency, amplitude of magnetic field and temperature characterization o f YBCO using higher harmonics ac susceptibility measurements near Te Daniele Di Gioncchino (a), Paolo Tripodi (a. b), Francesco Celani (a), Donglu Sift (c) a) INFN-LNF, Via E.Fermi 40, 00044 Frascati, Italy b) SRI International, 333 Ravenswood Ave, 94025 Menlo Park, CA (USA) c) Dept.of Material Science and Eng.,University of Cincinnati,493 Rhodes Hall (Cincinnati) Ohio USA Analysis on the higher harmonic ac susceptibility of the YBCO samples at fixed temperature near T c versus frequency (107-1200 Ha) and magnitude (2-8 G) of the applied magnetic field have been done. The pinning potential Up and critical current density Jc have been achieved by comparison of experimental measurement with the numerical analysis of the non-linear magnetic diffusion equation inside the samples. 1. I N T R O D U C T I O N

The higher harmonic measurements of the s: susceptibility [1,2] joined with numerical solutions of the non linear magnetic diffusion equation [3,4,5], is a good tool for the superconducting characterization of critical current density Jc and pinning potential Up

magnetic field dependence: Up(B,T) = Uo" (I - t4) • 5

[6]. These non-destructive magnetic measures of the HTSC with the analysis of the non linear losses in the framework of the critical state model, give rise to a direct correlation and quantification between superconducting magnetic quantities and electrical transport mechanisms. 2. MEASUREMENTS

AND A N A L Y S I S

The ae magnetic susceptibilities were measured using a double coaxial pick-up coil susceptometer. The multi harmonic signals have been measured by a lock-in amplifier. Two platinum thermometers wee used; as one controller and the other as sensor for

temperature measurements. The temperature homogeneity of the Y B C O samples is assured by sapphire sample holder. The hystcreticmagnetic loops were calculatedby non lineardiffusionmagnetic equation.The Fourier transform coefficientscalculatedfrom the hystcrefic magnetic cycles represent higher harmonic susceptibilities. The flux creep description is used as the diffusion coefficientin the equation: Up(B,T)

P~,~ :P~r • e- ~r

/ i

'L

J

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J c ( B ' T ) = J ° ' ( 1 - t a(tf2) t 1 "I + B°

3. RESULTS AND D I S C U S S I O N

The higher harmonic ac magnetic susceptibilities were measured versus temperature at fxed f ~ (107Hz) and amplitude (4(3) of applied magnetic field. The figure 1 shows the imaginary part of the first and third harmonic of ae susceptibility. The onset temperature is 91K andthe peak temperature is 90K. In order to study thoroughly the hysteretic superconducting properties and losses it is necessmT to measure the higher harmonic susceptibility at fixed temperatme versus amplitude and versus frequencyof the applied ac magnetic field. 2.0

/'P\,,

1.5

d

l.O

'9 0.5

---"i"

s~x,.-

.....

% ~,~ -0.5 -I.0 *,** |t 1,, 1, ||1 ,, 1, ,, ,,i 88 88.5 89 89.5 90

The temperature dependenceof Up and Jc is described using the collective pinning [7] with a Kim like

/'/

1| |1 ,l| ,,it, |, 90.5 91 91.5

Temperature (K) F i g . l : Z"I ~ l z " 3 v s T (H~--4G, F-~107Hz)

0921-4534/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PlI S0921-4534(00)00803-0

°° 92

D. Di Gioacchino et al./Physica C 341-348 (2000) 1101-1102

1102

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vs [Hacl (T=90.1K, F=107Hz). It is shown the numerical curve.

Near T c at fixed temperature T=90.1K the imaginary component of the third harmonic versus amplitude of applied magnetic field at constant frequency (107Hz) is shown in figure 2. The oscillation of third harmonic is evident. These oscillations give a description of the ratio between the applied and the penetrated magnetic field. Using the critical state model, the penetrated magnetic field yields a measure of the critical current density Jc. At fixed temperature T=90.1K the imaginary component of the third harmonic versus frequency of applied magnetic field at constant amplitude (4(3) is shown in figure 3. The evident oscillations can not be explained with the critical state model only. It is necessary to consider losses mechanism that include a time dependent process. As previously said, hysteretic and ac losses are considered in a simple creep model. The results of the numerical analysis, based on the presented model, are shown (dashed line) in figures 2 and3. 4 .

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REFERENCES

-- - ~lumerical analysis J

[1] P. Tripodi et al, Physica C 282-287 (1997) 2329 [2] P. Tripodi et al, IEEE Trans. on Appl. Sup. 9

(1999) 2o5o

M

~,

xx 200

400

600

800

1(300

1200

F r e q u e n c y (tlz) Z"3 vs magnetic frequency (T=90.1K, H==7G). It is shown the numerical curve.

Fig.3:

measure,

c) Using numerical calculation to describe the experimental magnetic behavior of the samples, we obtain real values of the electrical transport properties of the samples.

d?

0

0

In figure 3, the increasing of the Z"3 in the range 500-1000Hz is not well described by numerical analysis. This is probably due to the presence of different kind of pinning processes with different characteristic time. This different pinning process is not evident in the Z"3 versus field (figure 2) because the frequency of applied magnetic field was set at 107 Hz. The fitting of experimental data is good for both fieldandfrequeneybehavior of the third harmonic of ac susceptibility. The same parameters and boundary conditions have been used for the calculation. Main parameters used for the solution of the non linear diffusion equation are Up(90.1K)=2.3meV, Jc(90.1K)---0.34Acm2, B0= 1000G, pn=150~tf~m. The small value of calculated Up is reasonably in agreement with experimental evidence, because these measurements are done near Tc where Up is obviously zero for T=Tc. Using this analysis of experimental data a realistic behavior for Up is obtained, whereas using other analysis of magnetization decay measurements, a wrong divergent value for Up is predicted[8]. Clear measurements of the higher harmonic ac susceptibility versus frequency and magnitude of applied magnetic field and a simultaneous very good fitting of third harmonic of ac susceptibility underlines: a) this approach describes well the superconducting properties of HTSC in the considered range of temperature and applied magnetic field; b) the tnu'ameters value used in the numerical calculation are significant and define the actual superconducting properties in a quantitative

[3] D. Di Gioacchino et al, Physica C 282-287 (1997) 2157 [4] D. Di Gioacchino et al, Phys. Rev. B 59 (1999) 11539 [5] D. Di Gioacchino et al, IEEE Trans. on Appl. Sup. 9 (1999) 2223 [6] T.Ishida,R.B.Goldfarb,Phys.Rev.B 41(1990)8937 [7] R. Griessen et al,Phys.Rev.Lett. 72 (1994) 1910 [8] R. Griessen et al,Cryogenics 30 (1990) 563