Instrumentation & Measurement Magazine 24-9 - 14

Table 1 - Samples list
Ref.
S1 [16]
S2 [17]
S3 [18]
S4 [19]
S5 [20]
Material
YBa2Cu3
YBa2Cu3
Nb3
Sn
FeSe0.5
MgB2
Te0.5
O7-x
O7-x
+5 % BaZrO3
Sample type
80 nm thick film
100 nm thick film
bulk
240 nm thick film
bulk
model, however, foresees a frequency dependence where the
role of χ can be relevant, as shown in Fig. 1b and Fig. 1c. As
it can be seen, at a given frequency f, χ and fc
fraction of the asymptotic dissipation ρff
and thus the overall
response of the superconductor.
Wideband measurements (over more than a decade in frequency
around fc
) with the so-called Corbino disk [14], [15]
validated the model on several SCs, assessed its range of applicability
and showed that below a few GHz a more complex
description applies [14]. Nevertheless, the reliable determination
of χ, fc
and ρff
high-frequency measurements on SCs in dc magnetic fields.
Materials and Methods
The surface impedance Z = R + iX of several SC samples is
measured in dc magnetic fields to obtain ρvm
and the vortex
motion parameters described in the previous section. In this
paper, we show the results obtained on the materials and samples
detailed in Table 1, for the purpose of comparing their
performances. The functional relation Z(ρvm
Substrate
LaAlO3
SrTiO3
CaF2
Tc (K)
~91
~91
- ~18
~18
- ~39
1
determine the
u
Δf0
Perspective high-frequency
applications in particle physics
beam screen coating, haloscopes
haloscopes, RF cavities
still unexplored
RF cavities
R
QG
 
fG

0,ref
ΔX
2
bckgQ ,
bckgf 0
(2)
,
(3)
where G is the geometrical factor of the sample loaded into
the DR at the electromagnetic resonance mode of interest, and
Δy = y − yref
is the main metrological challenge in
spect to the reference value yref. Finally, bckgQ and bckg are the
background contributions on Qu and f0
, respectively, given by
the resonator itself.
Relevant metrological aspects, with the contextual identification
of the main sources of uncertainties, can be derived
from (2) and (3):
◗ The quantities of interest (R and X) can be obtained after
the Qu
and f0
) depends on the
geometry of the sample and will be detailed in the experimental
section in the different case studies presented.
Even if wideband measurements spanning more than a decade
in frequency would be the most direct way to determine
the vortex motion parameters, such methods have intrinsically
low sensitivity, being usually relegated to the measurements
on medium to high loss materials. In fact, wideband methods
are used only in the very high dissipation regime [21], [22].
When high sensitivity is needed, resonant measurement methods
are preferred [23]. In fact, resonant methods can even be
used to study the residual surface resistance of SCs, which can
be of the order of 10−9
and Xm
measurement, only if bckgQ
and bckg are
f 0
removed through a calibration of the DR. The DR calibration
would require a conducting standard, of known
Rm
by inverting (2) and (3), bckgQ
from Qu and f0
tive standards exist with Rm and Xm
, to be loaded in place of the sample, so that,
and bckg could be derivedf 0
measurements. However, no conducknown
with high
enough accuracy, in the whole magnetic field, cryogenic
temperature, and microwave frequency ranges desired.
A differential end-wall replacement perturbation method
[23] is preferred instead: the variations on Qu
and f0
with
respect to a reference state of the sample are used to obtain
the variations ΔZ considering, in the small perturbation
limit, that all the other instrumental contributions are not
changed. In particular:
Ω at few GHz [1], while the resolution of
traditional wideband reflection methods are usually limited at
some tens of mΩ [14], [21].
A powerful resonant method to measure the surface impedance
in superconducting samples relies on the use of
dielectric loaded resonators (DRs) [13], [24]-[27]. A DR is a
metallic cavity loaded with a low loss dielectric crystal in order
to increase the measurement sensitivity. In Fig. 2, a sketch
of a typical measurement system, a picture of a DR used at
Roma Tre University, and some measured resonance curves
are shown. The sample under investigation is loaded as an
end-wall of the DR, and its Z is obtained from the resonator
unloaded quality factor Qu
and resonance frequency f0
the following equations [23], [25]:
14
through
QQ G


u ref
,
0,ref

 
0,ref
2
11 RRref
u
f f XX
fG
ref
.
,
(4)
(5)
The subscript 'ref' denotes the reference value, and
with this approach, the problem of the DR calibration
is overcome. Since bckgQ
and bckg depend on the temf
perature T, this technique is particularly accurate for
measurements at fixed T and varying magnetic field,
provided that the DR is specifically realized with nonmagnetic
materials. Thus, at fixed T, (4) and (5) directly
yield the variations on R and X using the zero field state
IEEE Instrumentation & Measurement Magazine
December 2021
indicates the variation of the quantity y with ref

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