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Register a new userA critical re-examination of resonant soft x-ray Bragg forbidden reflections in magnetite
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Magnetite, Fe$_3$O$_4$, displays a highly complex low temperature crystal structure that may be charge and orbitally ordered. Many of the recent experimental claims of such ordering rely on resonant soft x-ray diffraction at the oxygen K and iron L edges. We have re-examined this system and undertaken soft x-ray diffraction experiments on a high-quality single crystal. Contrary to previous claims in the literature, we show that the intensity observed at the Bragg forbidden (001/2)$_c$ reflection can be explained purely in terms of the low-temperature structural displacements around the resonant atoms. This does not necessarily mean that magnetite is not charge or orbitally ordered, but rather that the present sensitivity of resonant soft x-ray experiments does not allow conclusive demonstration of such ordering.
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Identifying what broken symmetries are present in the cuprates has become a major area of research. Many authors have reported evidence for so-called $Q sim 0$ order that involves broken inversion, mirror, chiral, or time-reversal symmetry that is uniform in space. Not all these observations are well understood and new experimental probes are needed. Here we use resonant soft x-ray scattering (RSXS) to search for $Q sim 0$ order in Bi$_{2.1}$Sr$_{1.9}$CaCu$_2$O$_{8+x}$ (Bi-2212) by measuring the region of a forbidden Bragg peak, $(0,0,3)$, which is normally extinguished by symmetry but may become allowed on resonance if valence band order is present. Using circularly polarized light, we found that this reflection becomes allowed on the Cu $L_3$ resonance for temperatures $T_c < T < T^ast$, though remains absent in linear polarization and at other temperatures. This observation suggests the existence of spatially uniform valence band order near the pseudogap temperature. In addition, we observed periodic oscillations in the specular reflectivity from the sample surface that resemble thin film interference fringes, though no known film is present. These fringes are highly resonant, appear in all polarizations, and exhibit a period that depends on the location where the beam strikes the sample surface. We speculate that these fringes arise from interaction between some intrinsic valence band instability and extrinsic structural surface morphologies of the material. Our study supports the existence of some kind of $Q sim 0$ broken symmetry state in Bi-2212 at intermediate temperatures, and calls for further study using a microfocused beam that could disentangle microscopic effects from macroscopic heterogeneities.
Here we show that the low temperature phase of magnetite is associated with an effective, although fractional, ordering of the charge. Evidence and a quantitative evaluation of the atomic charges are achieved by using resonant x-ray diffraction (RXD) experiments whose results are further analyzed with the help of ab initio calculations of the scattering factors involved. By confirming the results obtained from X-ray crystallography we have shown that RXD is able to probe quantitatively the electronic structure in very complex oxides, whose importance covers a wide domain of applications.
We studied the (001/2) diffraction peak in the low-temperature phase of magnetite (Fe3O4) using resonant soft x-ray diffraction (RSXD) at the Fe-L2,3 and O-K resonance. We studied both molecular-beam-epitaxy (MBE) grown thin films and in-situ cleaved single crystals. From the comparison we have been able to determine quantitatively the contribution of intrinsic absorption effects, thereby arriving at a consistent result for the (001/2) diffraction peak spectrum. Our data also allow for the identification of extrinsic effects, e.g. for a detailed modeling of the spectra in case a dead surface layer is present that is only absorbing photons but does not contribute to the scattering signal.
We studied the resonant diffraction signal from stepped surfaces of SrTiO3 at the Ti 2p -> 3d (L2,3) resonance in comparison with x-ray absorption (XAS) and specular reflectivity data. The steps on the surface form an artificial superstructure suited as a model system for resonant soft x-ray diffraction. A small step density on the surface is sufficient to produce a well defined diffraction peak, showing the high sensitivity of the method. At larger incidence angles, the resonant diffraction spectrum from the steps on the surface resembles the spectrum for specular reflectivity. Both deviate from the XAS data in the relative peak intensities and positions of the peak maxima. We determined the optical parameters of the sample across the resonance and found that the differences between the XAS and scattering spectra reflect the different quantities probed in the different signals. When recorded at low incidence or detection angles, XAS and specular reflectivity spectra are distorted by the changes of the angle of total reflection with energy. Also the step peak spectra, though less affected, show an energy shift of the peak maxima in grazing incidence geometry.
Resonant Bragg diffraction of soft, circularly polarized x-rays has been used to observe directly the temperature dependence of chiral-order melting in a motif of Mn ions in terbium manganate. The underlying mechanism uses the b-axis component of a cycloid, which vanishes outside the polar phase. Melting is witnessed by the first and second harmonics of a cycloid, and we explain why the observed temperature dependence is different in the two harmonics. Our direct observation of melting is supported by a solid foundation of evidence, derived from extensive studies of the azimuthal-angle dependence of intensities with both linear and circular polarization.
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