Nonlinear Microwave Spectrometer for Investigating HighTc Superconductors

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12 Congresso Nazionale sulla Superconduttività
ad Alta Temperatura di TransizioneUniversità di
Roma "La Sapienza" 21-23 Aprile 2004
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Surface Barrier Effects in the Microwave
Second-Order Response of Superconductors

• Aurelio Agliolo Gallitto, M. Li Vigni and G.
  Vaglica
• INFM and Dipartimento di Scienze Fisiche ed
  Astronomiche,
• Via Archirafi 36, I-90123 Palermo

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Abstract

• We report experimental results on the time
  evolution of the Second Harmonic (SH) signal
  observed in Nb and MgB2 samples having different
  surface roughness.
• We have observed that the SH signal of
  superconductors in the mixed state shows a
  transient response
• during the first 10 s the SH signal shows an
  exponential decay
• At longer times the SH signal decays following a
  logarithmic law.
• We have found that, in the time scale of minutes,
  the decay rate of the SH signal depends on the
  roughness of the sample surface. This suggests
  that such effects can be ascribed to the
  relaxation of the magnetic flux through the
  surface barrier.

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Experimental Apparatus
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Experimental procedure Samples
The sample is placed in a bimodal cavity,
resonating at ? and 2?, with ?/2? ? 3 GHz, in a
region in which H? and H2? are maximal and
parallel to each other and also parallel to H0.
Before any measurement, the sample was
zero-field cooled down to T4.2K H0 was
increased up to 10kOe and then decreased down to
the residual field. This preliminary procedure
ensures that SH signals arising from processes
occurring in weak links are suppressed by the
trapped flux.
Measurements in MgB2 have been performed in the
same sample in the two different orientations H0
parallel and perpendicular to the rough surface,
respectively. Measurements in Nb have been done
on two samples, extracted from the same batch,
having different surface roughness. All
measurements have been performed at T4.2K.
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MgB2 Sample rough surface
? ? 3 s
Figure 1
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Nb Samples rough surface
? ? 2 s
Figure 3
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Discussion on the results
To deduce the characteristic parameters of the
SH-signal decay, we have fitted the data by
SH A B exp(-t/?) for 0 lt t lt 10
s and SH A1 - D log(t/t0) for t gt 10
s, with t0 10 s. For the initial decay,
we have obtained ? ? 3 s for MgB2 and ? ? 2
s for Nb, independently of the surface roughness
and the way in which H0 has been reached.
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MgB2 Sample smooth surface
? ? 3 s
Figure 2
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Nb Samples smooth surface
? ? 2 s
Figure 4
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The values of the normalized logarithmic decay
rate D which best fit the data of MgB2 samples
are reported in the inset of Figures 1 and 2.

• D depends on the way in which H0 has been reached.

• D depends on the feature of the surface through
  which the field penetrates in particular, for
  the rough surface it is two times greater than
  that obtained for the smooth surface.

Also in the Nb samples we observed a dependence
of D on the surface roughness but the complete
analysis is difficult because of the weak SH
signal emitted and the low decay rate observed
even for the rough surface.
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Discussion and Conclusion
During the first seconds, after the dc field
sweep has been stopped, the SH signal decays
exponentially, while in the time scale of minutes
it shows a logarithmic decay. The process
responsible for the SH-signal decay can be
figured out as follows according to Clem, when
H0 is varying, the surface barrier is absent
provided that H0gtHen or H0ltHex for positive and
negative field variations, respectively (Hen and
Hex are the threshold fields for vortex entry and
exit).
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During the field sweep, some fluxons are
accumulating near the surface as soon as the
field sweep is stopped, a diffusive motion of
fluxons sets in the process ends when the flux
density reaches the appropriate value for the
critical state. This process gives rise to the
exponential decay of the SH signal. At the same
time, motion of fluxons through the surface
barrier takes place and it is responsible for the
logarithmic decay. The latter hypothesis is
corroborated by the fact that the
logarithmic-decay rate depends on the way in
which H0 is reached and on the roughness of the
sample surface, which controls the surface
barrier.
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References

• J.R. Clem, Proceedings of the 13rd Conference on
  Low Temperature Physics, K.D. Timmerhaus et al.
  ed.s, Vol. 3 (1974) 102.
• L. Burlachkov, Phys. Rev. B 47 (1993) 8056.
• A. Agliolo Gallitto et al., Physica C 402 (2004)
  309.