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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