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Register a new userX-ray polarization: General formalism and polarization analysis
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The polarization of x-rays plays an outstanding role in experimental techniques such as non-resonant magnetic x-ray scattering and resonant x-ray scattering of magnetic and multipolar order. Different instrumental methods applied to synchrotron light can transform its natural polarization into an arbitrary polarization state. Several synchrotron applications, in particular in the field of magnetic and resonant scattering rely on the improvement in the signal/noise ratio or the deeper insight into the ordered state and the scattering process made possible through these polarization techniques. Here, we present the mathematical framework for the description of fully and partially polarized x-rays, with some applications such as linear x-ray polarization analysis for the determination of the scattered beams polarization, and the Ge K-edge resonant scattering.
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The polarization of K-edge resonant scattering at the space group ``forbidden (0 0 6) reflection of Ge was measured as function of the azimuthal angle, psi. The experimental results are compared to model calculations based on symmetry analysis of the resonant scattering tensors.
In order to shed light on the electronic structure of Na_xCoO_2, and motivated by recent Co L-edge X-ray absorption spectra (XAS) experiments with polarized light, we calculate the electronic spectrum of a CoO_6 cluster including all interactions between 3d orbitals. We obtain the ground state for two electronic occupations in the cluster that correspond nominally to all O in the O^{-2} oxidation state, and Co^{+3} or Co^{+4}. Then, all excited states obtained by promotion of a Co 2p electron to a 3d electron, and the corresponding matrix elements are calculated. A fit of the observed experimental spectra is good and points out a large Co-O covalency and cubic crystal field effects, that result in low spin Co 3d configurations. Our results indicate that the effective hopping between different Co atoms plays a major role in determining the symmetry of the ground state in the lattice. Remaining quantitative discrepancies with the XAS experiments are expected to come from composition effects of itineracy in the ground and excited states.
We present a detailed analysis of the incident-photon-energy and polarization dependences of the resonant inelastic x-ray scattering (RIXS) spectra at the Cu $K$ edge in La$_{2}$CuO$_{4}$. Our analysis is based on the formula developed by Nomura and Igarashi, which describes the spectra by a product of an incident-photon-dependent factor and a density-density correlation function for 3d states. We calculate the former factor using the $4p$ density of states from an ab initio band structure calculation and the latter using a multiorbital tight-binding model within the Hartree-Fock approximation and the random phase approximation. We obtain spectra with rich structures in the energy-loss range 2-5 eV, which vary with varying momentum and incident-photon energy, in semi-quantitative agreement with recent experiments. We clarify the origin of such changes as a combined effect of the incident-photon-dependent factor and the density-density correlation function.
One of the difficulties with performing polarization analysis is that the mean polarization fraction of sub-divided data sets is larger than the polarization fraction for the integrated measurement. The resulting bias is one of the properties of the generating distribution discussed in this work. The limitations of Gaussian approximations in standard analysis based on Stokes parameters for estimating polarization parameters and their uncertainties are explored by comparing with a Bayesian analysis. Different signal-to-background scenarios are considered making the analysis relevant for a large variety of observations. The effect of uncertainty on the modulation factor is also shown, since it can have a large impact on the performance of gamma-ray burst polarimeters. Results are related to the minimum detectable polarization (MDP), a common figure of merit, making them easily applicable to any X-ray polarimeter.
High-harmonic generation (HHG), a typical nonlinear optical effect, has been actively studied in electron systems such as semiconductors and superconductors. As a natural extension, we theoretically study HHG from electric polarization, spin current and magnetization in magnetic insulators under terahertz (THz) or gigahertz (GHz) electromagnetic waves. We use simple one-dimensional spin chain models with or without multiferroic coupling between spins and the electric polarization, and study the dynamics of the spin chain coupled to an external ac electric or magnetic field. We map spin chains to two-band fermions and invoke an analogy of semiconductors and superconductors. With a quantum master equation and Lindblad approximation, we compute the time evolution of the electric polarization, spin current, and magnetization, showing that they exhibit clear harmonic peaks. We also show that the even-order HHG by magnetization dynamics can be controlled by static magnetic fields in a wide class of magnetic insulators. We propose experimental setups to observe these HHG, and estimate the required strength of the ac electric field $E_0$ for detection as $E_0sim100$kV/cm--1MV/cm, which corresponds to the magnetic field $B_0sim0.1$T--1T. The estimated strength would be relevant also for experimental realizations of other theoretically-proposed nonlinear optical effects in magnetic insulators such as Floquet engineering of magnets.
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