We present a new technique to measure the complex surface impedance of the mixed state of superconducting thin films over the broad frequency range 45 MHz-20 GHz. The surface impedance is extracted from measurements of the complex reflection coefficient made on the film using a vector network analyzer. The technique takes advantage of a special geometry in which the self-fields from currents flowing in the film are everywhere parallel to the film surface, making it an ideal configuration in which to study vortex dynamics in superconductors. The broadband nature of the measurement system allows us to explore a region of magnetic field-temperature-frequency parameter space of superconductors previously inaccessible with other measurement techniques. The power of the technique is illustrated by measurements on thin films of the high temperature superconductor YBa,Cu,07 _ 8

Measurements of the field-dependent radio-frequency penetration depth \(H,T) are used to delineate the lower-critical-field H c \-T phase boundary, and to study flux dynamics, in YBa2Cu30 v crystals. For both H lie and HJLC, H C \ obeys a BCS temperature dependence, with a temperature-independent anisotropy of 3.4 ±0.3. In the mixed state, the data obey X 2 {H)=[<(>dpQa(T)]B{H), and yield both the functional dependence B(H) and the pinning force constant a(T). The latter is anisotropic, obeys an approximately (1 -t 2 ) 2 temperature dependence, and vanishes slightly below the bulk transition temperature.

We report a systematic investigation of dynamical fluctuation effects in the frequency-dependent microwave conductivity (45 MHz-45 GHz) of YBa 2 Cu 3 O 72d thin films for T * T c . Our measurements directly yield a dynamical critical exponent z in the range 2.3 -3.0, and the fluctuation lifetime t fl , which diverges more quickly than Gaussian theory predicts as the temperature approaches T c from above, independent of sample quality. In addition, both the temperature and the frequency dependence of the fluctuation conductivity s fl exhibit scaling behavior for temperatures 1 -2 K above T c , and can be collapsed onto the same universal curve. [S0031-9007(96)01664-X] PACS numbers: 74.25.Nf, 74.40.tk Dynamic fluctuation effects have become an intriguing subject of research in statistical and condensed matter physics, as they depend on the equations of motion of the system, and are not simply determined by the equilibrium distribution of particles at a given instant of time. Over the years, there have been both theoretical and experimental investigations of the static and dynamic fluctuations of many different types of systems. In the high T c superconductors (HTSC), measurements of fluctuation effects reveal unusual behavior, such as 3D XY critical behavior observed in the microwave penetration depth l͑T ͒ over a range of temperature 5-10 K wide below T c [1]. Heat capacity measurements are also consistent with 3D XY critical fluctuations for T T c 6 10 K [2]. In contrast to these results, temperature-dependent dc conductivity measurements have been interpreted in terms of simple 2D or 3D Gaussian fluctuation theory for T . T c [3,4]; also, low frequency penetration depth measurements have been interpreted as consistent with Gaussian fluctuations [5]. Furthermore, analysis of the nonlinear currentvoltage characteristics near T c in the HTSC yield a wide range of values for the relevant critical exponents [6,7].In this Letter we report a systematic experimental study of the microwave fluctuation conductivity s fl obtained from thin films and a single crystal of YBa 2 Cu 3 O 72d (YBCO). The study provides direct information about the fluctuation lifetime t fl , which is one of the important parameters for the identification of the universality class of the phase transition, and which describes the relevant dynamics of the fluctuations in the HTSC. We employ a swept-frequency technique (45 MHz -45 GHz) to measure both the frequency and temperature dependence of the conductivity of YBCO thin films in the vicinity of T c with nominally zero external magnetic field. The extra experimental degree of freedom afforded by access to the measured conductivity over three decades in frequency provides essential additional information about the dynamics of the system not available to temperature dependent measurements alone. Previous experiments have exploited frequency dependent techniques to verify the Gaussian dynamics of fluctuations in thin films of conventional superconductors [8,9]. More recently, frequencydependent co...