The Verwey transition in magnetite is of fundamental importance for the understanding of metal-insulator transitions but, in spite of being the subject of many studies over the last century, its nature is not fully understood. This is even more true in the case of the magnetite surface, where the low dimensionality plays an additional role in the determination of the Verwey transition temperature. We have atomically resolved the ͑ ͱ 2 ϫ ͱ 2͒R45°reconstructed surface by scanning tunneling microscopy and we have modeled our experimental results by density functional theory calculations. We attribute the observed pattern to the charge ordering of Fe 2+-Fe 2+ and Fe 3+-Fe 3+ dimers. We propose a mechanism for the formation of this charge ordered surface and provide an explanation for the increase of the Verwey transition temperature at the (001) surface of magnetite.
We propose a matrix method for the description of light reflection and transmission by an anisotropic multilayer system consisting of thin and thick layers. A method based on partial-wave matrix summations is applicable in the field of reflection and transmission photometry and ellipsometry. In the case of a thin anisotropic film, the interference effects were described by use of a coherent summation of Jones matrices. Incoherent intensity summations for a thick weakly anisotropic layer were characterized by use of the coherency vector formalism. Observable quantities or Mueller matrix components were obtained from the matrix describing transformation of the coherence vectors.
Abstract-In this paper, we propose methods for the measurement of electric intensities of a microwave field above the surface of microwave circuits. Using miniaturized coaxial antennas, we measure all spatial components of the induced field above device-under-test. A special position/signal difference method is used to better localize the measured field and increase the spatial resolution of the field mapping. During the scanning process, the antenna is driven at the defined distance above the sample surface according to previously acquired topographic data. For measurement of the tangential-field components parallel to the sample surface, the antenna is tilted by approximately 45 relative to the sample surface. By its rotation about the vertical axis, various components of the field are measured, and vertical and horizontal electric-field intensities are recalculated. The probes are calibrated in a well-defined field standard and allow good quantitative characterization of the measured field.Index Terms-Coaxial antennas, near-field measurements, scanning near-field microscopy.
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