ABSTRACT
A method is reported to determine the phase and amplitude of sinusoidally modulated event rates, binned into four bins per oscillation, based on data generated at the resonant neutron spin-echo spectrometer RESEDA at FRM-II. The presented algorithm relies on a reconstruction of the unknown parameters. It omits a calculation-intensive fitting procedure and avoids contrast reduction due to averaging effects. It allows the current data acquisition bottleneck at RESEDA to be relaxed by a factor of four and thus increases the potential time resolution of the detector by the same factor. The approach is explained in detail and compared with the established fitting procedures of time series having four and 16 time bins per oscillation. In addition the empirical estimates of the errors of the three methods are presented and compared with each other. The reconstruction is shown to be unbiased, asymptotic and efficient for estimating the phase. Reconstructing the contrast increases the error bars by roughly 10% as compared with fitting 16 time-binned oscillations. Finally, the paper gives heuristic, analytical equations to estimate the error for phase and contrast as a function of their initial values and counting statistics.
ABSTRACT
Recent theoretical and experimental findings suggest the long-known but not well understood low temperature resistance plateau of SmB6 may originate from protected surface states arising from a topologically non-trivial bulk band structure having strong Kondo hybridization. Yet others have ascribed this feature to impurities, vacancies, and surface reconstructions. Given the typical methods used to prepare SmB6 single crystals, flux and floating-zone procedures, such ascriptions should not be taken lightly. We demonstrate how compositional variations and/or observable amounts of impurities in SmB6 crystals grown using both procedures affect the physical properties. From X-ray diffraction, neutron diffraction, and X-ray computed tomography experiments we observe that natural isotope containing (SmB6) and doubly isotope enriched ((154)Sm(11)B6) crystals prepared using aluminum flux contain co-crystallized, epitaxial aluminum. Further, a large, nearly stoichiometric crystal of SmB6 was successfully grown using the float-zone technique; upon continuing the zone melting, samarium vacancies were introduced. These samarium vacancies drastically alter the resistance and plateauing magnitude of the low temperature resistance compared to stoichiometric SmB6. These results highlight that impurities and compositional variations, even at low concentrations, must be considered when collecting/analyzing physical property data of SmB6. Finally, a more accurate samarium-154 coherent neutron scattering length, 8.9(1) fm, is reported.
