Magneto-optical image of the dendritic flux penetration in the coplanar resonator (detail) at and , in the absence of the microwave signal (a). Brighter gray levels correspond to higher magnetic flux density regions, while the black zones inside the sample correspond to regions in the Meissner state. Panel (b) shows the image obtained as the difference between two frames of the same region (a detail of the central strip) taken at consecutive field values (61 and 46 Oe). Panel (c) shows the differential image of the same region for the field-increase step from 61 to 76 Oe. Circles in (b) and (c) indicate that a dendrite grown during the first field-increasing step is frozen during the second step [uniform gray level in the differential image (c)].
Resonance frequency as a function of dc magnetic field at and at , normalized to the value at zero field, [ and 7.9722 GHz at and 8.5 K, respectively]. The effective field, , has been obtained from the applied field by considering the field-focusing effect due to the close proximity of the ground planes and the central strip. The shadowed region represents possible values of the first penetration field, , at . The insets show examples of direct measurements, corresponding to the points marked by arrows in the main frame. In inset (b), discontinuities in the transmitted signal are encircled.
Surface resistance as a function of the effective dc magnetic field at and at . Data at have been obtained by selecting, from the same measurements shown in Fig. 2, the resonance curves where the quality factor can be derived at least by the method. The shadowed region denotes possible first penetration field, , at .
Jumps (arrows) detected at in the microwave response of the resonator (solid symbols), following flux avalanches generated by dc field enhancements from 18.25 to 18.70 Oe (a) and from 51.15 to 51.60 Oe (b). Jumps always lead to improvement of the resonator performance since they mark the shift toward different resonance curves (qualitatively represented by dotted lines) with increasing resonant frequency and maximum transmission coefficient, for a forward frequency sweep.
Features shown by the microwave response of the resonator. Frame (a) shows that jumps are irreproducible even for the same resonator in the same starting conditions (in this specific case, each curve was measured with a delay of 2 s after the same 0–13.35 Oe field step). Frame (b) shows that their number and size depend on the magnetic field step (curve 1: from 12.90 to 13.35 Oe; curve 2: from 0 to 13.35 Oe; curve 3: from 0 to 0.45 Oe). Frame (c) shows that jumps appear only above a threshold field, 10.4 Oe in this case, comparable to the first penetration field . All measurements shown in all the frames started after a zero-field cooling procedure down to .
Resonance curves measured at in the absence of applied magnetic field, after a field-cooling (FC) procedure in the presence of , and after a zero-field-cooling (ZFC) procedure, followed by the application of the same field. In the inset, the calculated distribution of the microwave current density across the central conductor width is reported.
Normalized time-distribution of dendritic events collected during several frequency scans. The three curves concern data selected in three different intervals of microwave energy transferred to the resonator. The dashed line represents the case of a homogeneous time distribution of events.
Resonance frequency-shift histograms for the pristine resonator (a), for the same resonator after Au-ion irradiation with a fluence of (b), and after a subsequent irradiation up to a total fluence of (c). Data were collected at and in external magnetic field increasing from 0 to 93.45 Oe, with 0.45 Oe steps. The insets (logarithmic scales) show the probability to detect events of size , fitted to a power law.
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