Determination of the angular dependence of Hc2 in high Tc single crystals by a microwave technique

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Determination of the angular dependence of Hc2 in high Tc single crystals by a microwave technique

SHALTIEL, David, et al.

Abstract

It is shown that using an ESR spectrometer with magnetic field modulation and sweeping the temperature across Tc (at a constant and a very low magnetic field), is equivalent to temperature modulation. The signal intensity obtained when crossing Tc is proportional to 1/(

delta Hc2/ delta T) at T=Tc. Using the WHH relation Hc2(T=0)=0.7 Tc( delta Hc2/ delta T)T=Tc enabled the measurement of the relative angular variation of Hc2 in single crystals of YBaCuO with Tc approximately 85 K. The data fit the Ginzberg-Landau theory. This very sensitive technique can be used to characterize properties of high Tc superconducting materials. Results on thin films is also be presented.

SHALTIEL, David, et al. Determination of the angular dependence of Hc2 in high Tc single crystals by a microwave technique. Superconductor Science and Technology, 1991, vol. 4, no. 1S, p. 85-87

DOI : 10.1088/0953-2048/4/1S/014

Available at:

http://archive-ouverte.unige.ch/unige:3050

Disclaimer: layout of this document may differ from the published version.

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Supercond. Sci. Technol. 4 (1531) 585-37. Printed in the UK

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sensitivity than the first method, to the best of addition to the difficulties in devising such a our knowledge it has not yet been reported. In modulation, the drawback is, that only low

Determination of the Angular Dependence of €IQ in High Tc Single Crystals by a Microwave Technique.

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equivalent to temperature modulation when sweeping the temperature across T, at constant and low magnetic field. Using this property, we have measured the relative angular variation

of &2 in single crystals. The method also enables us to characterize properties of high Tc

superconductors in polycrystaline materials, single crystals and thin films.

7 ThPn-tiP.1 Pnnrirl'=mtin"r

1 . I . . \ I " I " L I U . U I U " . L Y I U I I Y I I " I . Y

Fig.

IC

schematically shows the H,2(T) curve as a function of temperature. When the modulating magnetic field AH = AH,sinwt, crosses the H,2 curve, it shifts the superconducting material into the normal state or the superconducting state whenever it adds magnetic field modulation is equivalent to temperature modulation and the amplitude ATo is given by ATo = AH,J(aH,fiT). For constant and close to zero magnetic fields

[a%./aT]

at T = T, is H,.2(pj)/(0.7Tc)(2). Hence

to, or is subtracted froni the conspant Kc2(Tj fieid respecfveiy. As Seen in fig. IC

ATo = AH0(0.7 Tc/Hc2)(~=o) at H = 0 ₍₁₎ Thus, in single crystals with anisotropic properties, ATo will depend on the orientation of the crystal with respect to the magnetic field. Therefore, as disussed above, sweeping the temperature will show a signal proportional to the derivative of the microwave surface resistivity. Its maximum intensity, I, will be proportional to ATo and therefore inversely proportional to ?&~/~T(T=T,) or to &(T=o~&.

In uniaxial superconductors it has been confirmed that the mass tensor formulation of Ginzburg-Landau theory holdd3). The upper critical fields is given by l&2(8) = m3cos20

+

mlsin*8 where ml = m,, = myy and m3 = m,,, H&) and %z(p) are the critical fields normal or parallel to the CuO layers respectively and 8 is the angle between normal to the CuO layers and the magnetic field. Hence:

and for 8 = go", ATo(n)/ATo(p) = I(n)/I(p) = H,.,.(p)/Hcz(n). Thus, measuring the ratio of the microwave absorption intensities normal and parallel to the CuO planes in a single crystal should give the ratio of the critical fields in these two directions. Furthermore the angular dependence of the critical field should follow eq. 2.

Here, effects of demagnetization, due to shielding currents induced by the magneti'c modulation, have been neglected. They will depend on the shape of the crystal and its anisotropy properties and hence on the orientation with respect to the magnetic field. The calculation of the demagnetization effects is complex, however it can be argued that in high

&2 superconductors such as the high T, compounds, the contribution of the demagnetising

field is negligible.

3 . Experimental

Single crystals and oriented thin films of YBa2CU30(6+,) x=0.9 have been used in this experiment. They were prepared by the flux method and evaporation techniques respectively then treated to maximize the oxygen content. A Varian spectrometer with low frequency (150Hz) modulation coils attached to the magnetic poles has been used. The sample was introduced on the side wall of a cavity. The angular dependence was obtained by rotating the magnet and therefore the microwave field around the sample did not vary during the measurements. The variation of the temperature was always obtained by slowly cooling the cavity from above to below T,. Fig. 2 shows typical microwave absorption spectra of two single crystals in the form of platelets and an oriented thin film where the c axis was

S86

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perpendicular to their plane (The spectra ⁴⁰⁰

-

were taken for ^€I= 90. Only minute for different angles.). One single crystal shows a narrow line with maximum at T = 88.5K and whose width is about 1K. The

~&! 300

changes in the line shape were observed

c 7

m

e

²⁰⁰

>

z v) c

other crystal shows a structure composed

of several peaks indicatng that this crystal 9

-

¹⁰⁰

contains regions with slightly different transition temperatures. The microwave absorption spectrum of the thin fiim shows a broad transition of 20K though its resistivity curve has indicated a sharp transition of a few degrees. Part of this

width may be attributed to Fig. 2 Microwave absorbtion vs. temperatureof inhomogeneities in the edges of the film.

0 55 60 65 70 75 80 8 5 90 95

Temperature IK)

two single c r y s t a l s and a thin film

Fig. 3 shows the angular dependence of t h e maximum intensity for the single crystal with one peak whose spectrum was shown

in fig. 2. The full line is the presentation of eq. 2 and therefore the results are in good agreement with the Ginzburg Landau theory.

The ratio of .HC2(p)&2(n)=3 is in agreement with measurements obtained from the slope of aH,,/dT using direct susceptibility

-

1.0

c L n

c

3

.-

, 0.8 D m

0.6

C 0 U3 .-

p

^0.4

2

m

& 0.2

r:

._

I I 1

0.0 ^€!-Angle⁰

-

between C-axis and magnetic field ³⁰ ^{6 0} ⁹⁰

Fig. 3 Angular dependence of the microwave absorption intensity. The full line presents eq. 2.

4. Conclusion

Using the microwave absorption technique we were able to measure the relative angular behavior of H,-2(0) in high quality single crystals of Y B a 2 C u 3 0 ~ + ~ x= 0.9. We found an agreement with the Ginzburg-Landau theory and results obtained by other methods on the numerical values Hc2@)&2(n) for single crystals were in agreement. Oriented thin films show very broad transition temperatures, in variance with results obtained by susceptibility and resistivity measurements. The method also enables us to determine transition temperatures and to characterize the quality of superconducting materials. It has the advantage of being contactless and very sensitive (around 10-8 gram of YBaCuO).

References 1.

2.

3.

4.

Acknowledgement - This work was partly supported by BSF Grant No. 87-00275

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