Material Studies with Microwaves
Traditional Microwave Studies of Electrodynamics in Materials
Traditional microwave studies use the perturbation that a sample introduces to a microwave resonator to study the electrodynamics in materials. By measuring the transmitted signal (two-port) or the reflected signal (one-port) from a microwave resonator, one can fully address the electromagnetic (EM) characteristics of the resonator, including its resonant frequencies, f0’s, losses (through quality factor measurements), couplings (through phase-sensitive or S-parameter measurements), etc. When a resonator is coupled to a sample, above characteristics of the resonator will be slightly changed. This is because the resonator is no longer the same but includes the coupled sample. Typically a sample is placed inside a resonant cavity or on top of a strip-line resonator and coupled to the resonator by immersing in uniform fields of the resonator. The extraction of EM properties of materials is made possible by the well established cavity perturbation theory.[1-2] By comparing the perturbed (with samples) characteristics with the unperturbed (no sample) ones, it allows one to address electromagnetic properties, e.g. surface impedance, complex conductivity, and so on.
Scanning Near-field Microwave Microscopy (SNMM)
However, the spatial resolution of the traditional microwave methods is limited by the wavelengths of microwaves, typically on the length scales of cm or larger, hence only good for studies of bulk material properties. To overcome this limitation in far-field measurements and enable studies of local microwave properties of materials, experimental methods with near-field microwaves have been developed and the applications have been expanded over the years.
The earliest work of near-field microwave measurements was done by Frait [3-4] and Soohoo [5] who used resonators with small apertures to couple to samples and scan for local properties of interests. The near-field coupling does not suffer from the resolution limit set by the free-space wavelengths, and can achieve sub-mm resolution which is determined by the coupling geometries. Similar microwave analysis is carried out as in the traditional measurements, but in this scenario, the perturbation is induced by a very small portion of a sample which couples to the microwave system through the near-field. Various forms of near-field microwave microscopy were developed for frequencies ranging from optical to microwaves using optical fibers, waveguides, microstrip resonators, coaxial cables, and so on.[6-28] I have first-hand experience with several novel forms of Scanning Near-field Microwave Microscopes (SNMM) through the work in Anlage’s group in UMD,[29-37] and pursue opportunities for developing a similar instrumentation in Mercer.
Microwave Properties of Superconductors
Non-linear Microwave Properties of Superconductors
Nonlinear properties of superconductors have drawn both industrial and academic interests in the past decades since the discovery of high-temperature superconductors (HTSC). Considering microwave devices made of HTSC, higher order harmonics and/or inter-modulation distortions (IMD) arise due to the nonlinear properties of the superconductors, and consequently limit the applications of HTSC to low microwave power applications. Great industrial efforts had been made to reduce the nonlinear behaviors significantly through improving the quality of the HTSC films and eliminating/minimizing the structural defects. However, nonlinearities in superconductors can not be completely eliminated because superconductivity is intrinsically nonlinear, as described by the nonlinear Meissner effect. The following discusses this phenomenon in greater details.
The nonlinear Meissner effect is a phenomenon expected in all superconductors. When a superconducting current flows in a superconductor, the current also breaks Cooper pairs and enhances quasi-particle excitations. The consequence of this effect is the reduction of the super-fluid density and the magnetic screening effectiveness, which leads to a supercurrent-dependent super-fluid density or magnetic penetration depth, predicted by both the BCS[38-40] and Ginzburg-Landau theories.[41] Fig. 1 shows the nonlinear responses from a superconductor measured as a function of temperature near Tc. Dramatic enhancement is observed near Tc due to the very weak superconductivity which is most accessible to the pair-breaking effect of supercurrents.
Fig. 1 Third harmonic responses from a YBCO thin film near Tc.
It should also be noted that the nonlinear Meissner effect is merely responsible for the nonlinear responses from superconductors due to the intrinsic superconductivity, and is normally very weak and only becomes dominant and observable near Tc (for all superconductors) or at low temperature limits (for d-wave superconductors). When other sources of nonlinearity are present, such as structural defects (boundaries, edges, cracks, etc.) and impurities, they dominate the nonlinear responses for the majority of the temperature range. Fig. 2(a) & (b) demonstrate the local nonlinear responses measured at second and third harmonics on YBCO bi-crystal boundaries (Tc = 89 K) at T = 60 K. At this temperature, the nonlinear Meissner effect is not observable and the nonlinear responses are solely dominated by the structural defects, the bi-crystal boundary in this case. While the majority of the film shows no signs of nonlinear responses, tremendously enhancements are observed near the boundary. The width of the feature (~ 0.5 mm) shown in the images is determined by the spatial resolution of the scanning probe available then.[36-37] 
Fig. 2
Second and third harmonic images on a YBCO bi-crystal grain boundary. The enhanced responses in the middle of the images mark the approximate location of the grain boundary.
Magnetic Imaging
Local Magnetic Resonance Phenomena
The rapidly increasing read/write speed and density of the magnetic storage media has led to an increasing interest in local microwave magnetic properties of materials, the homogeneity of Curie temperatures, local magnetizations, and phase separation into magnetic/non-magnetic domains. While scanning microscopes have been designed to image radio frequency magnetic fields,[42-44] electron paramagnetic resonances (EPR),[45] and ferromagnetic resonances (FMR),[3,46-48] very few of these techniques measure magnetic properties on sub-mm length scales.[49-50] Our studies of local magnetic properties using the SNMM developed in UMD was one of the pioneering works to measure local magnetic permeability and FMR fields with the spatial resolution of ~ 0.5 mm.[31] As shown in Fig. 3(a) & (b), the SNMM is able to distinguish between the metallic glasses with the same electric resistivity (r = 150 mWcm) and very similar geometries, but substantially different magnetic properties (paramagnetic vs. ferromagnetic). This result demonstrates the unique ability of the SNMM in measuring local variations of permeability. 
Fig. 3
Line-scans of Df and Q accross ferromagnetic and paramagnetic metallic glasses tapes with the (a) the magnetic and (b) the electric sensing probe. Constrast in magnetic properties is observed in the magnetic sensing probe, but not in the electric one.I also used the same SNMM to study the local FMR in a colossal magnetoresistive (CMR) material, La0.8Sr0.2MnO3 (LSMO) with Curie temperature TC = 305.5 K. The magnetic dipoles in the material undergo precessions in an external dc magnetic field. If an ac magnetic field is applied at just the frequency of the precession frequency in a given dc field, the energy of the ac magnetic field will be absorbed, exhibiting a phenomenon generally called "magnetic resonance". However, due to the inevitable variation of local magnetization in any given sample, the external magnetic field experienced by each magnetic dipole is different. In another word, if an ac magnetic field is applied at a fixed frequency, the corresponding dc magnetic field for "magnetic resonance" to occur will vary over a sample. By applying microwaves at a fixed frequency to an LSMO crystal at T = 301.5 K, the local FMR field is imaged as shown in Fig. 4(a) & (b). Details of these studies are found in Ref.[31]. 
Fig. 4
Variations of Df and Q in a CMR crystal indicating the variation of FMR fields in the crystal.
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