Browsing by Author "Hamrick, Michael David"

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    Magnetic and chemical effects in x-ray resonant exchange scattering in rare earths and transition metal compounds
    (1994) Hamrick, Michael David; Trammell, George T.
    The increased availability of synchrotron x-ray sources has facilitated the development of new diffraction techniques based on x-ray resonant exchange scattering (XRES). Resonant electric dipole (E1) and quadrupole (E2) scattering involving virtual transitions between occupied core and empty valence levels is sensitive to the splitting and filling of the valence shells, thus providing information about the spin and orbital distributions of the valence electrons. This sensitivity to electronic properties makes x-ray resonant exchange scattering (XRES) a useful probe of rare earth magnetism as well as effects due to crystal fields (or molecular orbitals) in transition metal compounds. In spiral antiferromagnets, such as holmium, the magnetic sensitivity results in a series of off-Bragg magnetic diffraction peaks. Resonant scattering calculations provide good predictions of the experimental observations, including diffraction conditions, intensities, lineshapes, and polarization dependence. Coefficients giving the magnitude of the scattering are computed for the rare earths. These are then related to effective scattering operators which can be expressed in terms of the angular momentum J in rare earths, making it possible to extend the results of calculations at zero temperature and zero crystal field to finite temperatures and crystal fields. Resonant scattering from transition metal ions in crystal fields includes contributions sensitive to the chemical environment of the ion. The amplitude for E1 resonances exhibits 1- and 2-fold azimuthal patterns in C$\sb1$ and C$\sb2$ symmetries respectively, but cannot distinguish C$\sb3$ and higher order symmetries. E2 amplitudes exhibit these patterns as well as 3- and 4-fold patterns in C$\sb3$ and C$\sb4$ symmetries. The anisotropy in the scattering from a single ion can result in diffraction at Bragg-forbidden reflections which are associated with glide plane or screw axis symmetries in the space group of the crystal. The theory provides a good description of experimental observations in hematite, including the intensity, lineshape, azimuthal pattern, Bragg-forbidden reflection, and scattered polarization.
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    Theory of elastic x-ray resonant exchange scattering in lanthanides and actinides
    (1990) Hamrick, Michael David; Trammell, George T.
    Resonant X-ray scattering has been observed in lanthanides and actinides. The observed scattering is sensitive to magnetization, but it arises primarily from electric, rather than magnetic, multipole transitions. The magnetic sensitivity is due to "exchange" effects and to spin-orbit correlations in one or both of the levels involved in the resonance. "Exchange" effects include the exclusion principle, which permits transitions only to vacant orbitals in partially filled shells, and exchange splitting in band states. The elastic scattering amplitude contains terms dependent on the direction of the magnetic moment up to quadratic order for E1 transitions and up to quartic order for E2 transitions. In coherent scattering of X-rays from spiral antiferromagnets, the magnetic sensitivity results in the formation of resonant magnetic satellites associated with the Bragg peaks. This effect provides a new type of probe for the investigation of magnetic structures.