Spatially Resolved Nonlinearity Measurements of YBa2_2Cu3_3O7−d_{7-d} Bi-crystal Grain Boundaries

We have developed a near-field microwave microscope to locally excite a superconducting film and measure second and third harmonic responses at microwave frequencies. We study the local nonlinear response of a YBa$_2$Cu$_3$O$_{7-d}$ thin film grown on a bi-crystal SrTiO$_3$ substrate. The location of the bi-crystal grain boundary is clearly identified by the microscope through higher harmonic response, and the spatial resolution is on the order of the magnetic loop probe size, about 500$\mu m$. The harmonic power and spatial resolution are successfully modeled with a one-dimensional extended Josephson junction simulation. From the model, the 2nd order harmonic response is dominated by Josephson vortex generation and flow. A geometry-free nonlinear scaling current density $J_{NL}\simeq 10^4\sim 10^5 A/cm^2$ is also exstracted from the data, indicating that the grain boundary weak link is the dominant nonlinear source in this case.Comment: 4pages, 4figure

Likelihood-based statistical estimation from quantized data

Most standard statistical methods treat numerical data as if they were real (infinitenumber- of-decimal-places) observations. The issue of quantization or digital resolution is recognized by engineers and metrologists, but is largely ignored by statisticians and can render standard statistical methods inappropriate and misleading. This article discusses some of the difficulties of interpretation and corresponding difficulties of inference arising in even very simple measurement contexts, once the presence of quantization is admitted. It then argues (using the simple case of confidence interval estimation based on a quantized random sample from a normal distribution as a vehicle) for the use of statistical methods based on rounded data likelihood functions as an effective way of dealing with the issue. --

Doping dependent time-reversal symmetric nonlinearity of YBa_2Cu_3O_7-d thin films

We have measured the temperature dependent third harmonic response from a series of under-doped YBa_2Cu_3O_7-d thin films to address the mechanism of nonlinearity in these samples. We find that the intrinsic Ginzburg-Landau nonlinearity near Tc is doping dependent, with the sample becoming more nonlinear as it is under-doped. The results are consistent with the doping dependence of the condensation energy of YBa_2Cu_3O_7-d.Comment: 2 pages, 3 figures, submitted to Physica C for M2S-Rio conference pres

Study of Local Nonlinear Properties Using a Near-Field Microwave Microscope

We have developed a near-field microwave microscope to locally apply microwave frequency currents and fields to superconductors, and dielectric substrates, and measure the locally generated 2nd and 3rd harmonic responses. We measure the local nonlinear response of a Tl_2Ba_2CaCu_2O_y film grown on an MgO substrate, and observe a large response due to the enhanced current density near the edge. We also study the local nonlinear response of a YBa_2Cu_3O_7-d thin film grown on a bi-crystal SrTiO_3 (STO) substrate, and spatially identify the grain boundary through higher harmonic measurements. The spatial resolution is determined by the magnetic loop probe size. A scaling current density JNL is extracted to quantify the magnitude of the nonlinearity of the superconductor. Preliminary results on the nonlinear properties of some commonly used substrates, e.g. MgO and STO, have also been obtainedComment: 4 pages, 7 figures, presented in Applied Superconductivity Conference 2002, submitted to IEEE Trans. Appl. Supercon

Measurements of Doping-Dependent Microwave Nonlinearities in High-Temperature Superconductors

I first present the design and use of a near-field permeability imaging microwave microscope to measure local permeability and ferromagnetic resonant fields. This microscope is then modified as a near-field nonlinear microwave microscope to quantitatively measure the local nonlinearities in high-Tc superconductor thin films of YBa2Cu3O7-d (YBCO). The system consists of a coaxial loop probe magnetically coupling to the sample, a microwave source, some low- and high-pass filters for selecting signals at desired frequencies, two microwave amplifiers for amplification of desired signals, and a spectrum analyzer for detection of the signals. When microwave signals are locally applied to the superconducting thin film through the loop probe, nonlinear electromagnetic response appearing as higher harmonic generation is created due to the presence of nonlinear mechanisms in the sample. It is expected that the time-reversal symmetric (TRS) nonlinearities contribute only to even order harmonics, while the time-reversal symmetry breaking (TRSB) nonlinearities contribute to all harmonics. The response is sensed by the loop probe, and measured by the spectrum analyzer. No resonant technique is used in this system so that we can measure the second and third harmonic generation simultaneously. The spatial resolution of the microscope is limited by the size of the loop probe, which is about 500 mm diameter. The probe size can be reduced to ~ 15 mm diameter, to improve the spatial resolution. To quantitatively address the nonlinearities, I introduce scaling current densities JNL(T) and JNL'(T), which measure the suppression of the super-fluid density as , where J is the applied current density. I extract JNL(T) and JNL'(T) from my measurements of harmonic generation on YBCO bi-crystal grain boundaries, and a set of variously under-doped YBCO thin films. The former is a well-known nonlinear source which is expected to produce both second and third harmonics. Work on this sample demonstrates the ability of the microscope to measure local nonlinearities. The latter is proposed to present doping dependent TRS and TRSB nonlinearities, and I use my nonlinear microwave microscope to measure the doping dependence of these nonlinearities