The performance of superconducting radio-frequency (SRF) cavities is sometimes limited by local defects. To investigate the RF properties of these local defects, a near-field magnetic microwave microscope is employed [1-3]. The superconducting materials are subjected to intense RF magnetic fields using a commercial magnetic write head with multi-GHz bandwidth wiring positioned over the material. Local second- (P2f) and third-harmonic response (P3f) and its temperature-dependence and input RF power-dependence are measured for numerous Nb/Cu films grown by several techniques with systematic variation of deposition conditions. Many of the Nb/Cu films show a strong third harmonic response that is likely coming from a low-Tc surface defect with a transition temperature below 7 K, suggesting that this defect is a generic feature of air-exposed Nb/Cu films. One possible origin of such a defect is grain boundaries hosting a low-Tc impurity such as oxidized Nb.
The measured harmonic response is modeled using time-dependent Ginzburg-Landau (TDGL) numerical simulations of the probe/sample interaction [4]. We simulate the nucleation of RF semi-loop vortices, and the response of trapped DC vortices, in Nb in the presence of surface defects when the material is subjected to an intense RF magnetic field in the GHz regime. In this work, we solve the TDGL equations, and Maxwell’s equations, for a spatially nonuniform RF magnetic field created by a point RF magnetic dipole above the Nb surface. Here surface defects are notionally modeled as grain boundaries filled with a low-Tc impurity, such as oxidized Nb. The dynamics of RF currents induced in the resulting proximity-coupled superconductor are studied, and it is observed that RF vortex semi-loops penetrate the surface through the grain boundaries [5]. Besides the RF vortex dynamics, the resulting third harmonic nonlinear response of the superconductor is calculated, and is shown to be closely related to RF vortex nucleation. The simulations show that RF vortex nucleation by surface defects can be studied by analyzing the third harmonic response of the superconductor [5]. Similarly, we study the response of trapped DC magnetic flux when subjected to the same fields created by the RF magnetic dipole. It is found that the response of DC vortices are primarily captured in the second harmonic signal, allowing us to distinguish the two different types of defects in SRF materials. We make connections between these numerical studies and the results of our scanned near-field microwave microscopy efforts on a variety of SRF materials.
[1] Tamin Tai, Behnood G. Ghamsari, Thomas R. Bieler, Teng Tan, X. X. Xi, and Steven M. Anlage, “Near-field microwave magnetic nanoscopy of superconducting radio frequency cavity materials,” Applied Physics Letters 104, 232603 (2014).
[2] Tamin Tai, Behnood G. Ghamsari, Tom Bieler, and Steven M. Anlage, “Nanoscale nonlinear radio frequency properties of bulk Nb: Origins of extrinsic nonlinear effects,” Physical Review B 92, 134513 (2015).
[3] Bakhrom Oripov, Thomas Bieler, Gianluigi Ciovati, Sergio Calatroni, Pashupati Dhakal, Tobias Junginger, Oleg B. Malyshev, Giovanni Terenziani, AnneMarie Valente-Feliciano, Reza Valizadeh, et al., “High frequency nonlinear response of superconducting cavity grade Nb surfaces,” Physical Review Applied 11, 064030 (2019).
[4] Bakhrom Oripov and Steven M. Anlage, “Time dependent Ginzburg-Landau treatment of rf magnetic vortices in superconductors: Vortex semiloops in a spatially nonuniform magnetic field,” Physical Review E 101, 033306 (2020).
[5] Chung-Yang Wang, Carlota Pereira, Stewart Leith, Guillaume Rosaz, Steven M. Anlage, “Microscopic Examination of SRF-quality Nb Films through Local Nonlinear Microwave Response, arXiv:2305.07746.
We thank Carlota Pereira, Stewart Leith, and Guillaume Rosaz of CERN, as well as Cougar Garcia of NGC, for samples. This work is funded by US Department of Energy / High Energy Physics through grant # DE-SC0017931 and the Maryland Quantum Materials Center.