Stephen W. Lovesey

Introduction to the Graphical Theory of Angular Momentum

Properties of 3- and 3-Symbols.- Basic Tools for the Graphical Method.- Orthogonality Relations for 3-Symbols.- Properties of the 6-Symbol.- Properties of the 9-Symbol.- General Principles for Diagrams.- Closed Diagrams.- Open Diagrams.- Application in Atomic Physics.

A theoretical framework for absorption (dichroism) and the resonance-enhanced scattering of x-rays by magnetic materials: I

The scattering length common to the attenuation coefficient and cross-sections for the resonance-enhanced scattering of x-rays suffers from a dependence on a spectrum of virtual, intermediate states which contain next to no useful information about the environment of the atoms. It is the dependence of the scattering length on intermediate states that sets the x-ray techniques apart from neutron scattering and other techniques which directly probe properties of magnetic materials, and limits the usefulness of physical intuition in the interpretation of empirical x-ray data. As a step toward a legible interpretation, in a language of standard atomic variables, an investigation is reported of a modified scattering length constructed to possess a structure similar to the scattering length for magnetic neutron scattering, namely, it has the mathematical structure of a spherical tensor operator, to which all Racahs methods for electrons in an open valence shell can be applied. In the process of reaching this goal, the influence of the intermediate states on the scattering length is reduced by summing over a limited set of quantum numbers for the intermediate states. Topics covered in the investigation include the attenuation coefficient for x-rays passing through a foil of magnetic material, dichroism, and the cross-sections for resonance-enhanced elastic (Bragg) and inelastic scattering of x-rays by magnetic materials. The treatment of polarization in the primary beam admits states of partial polarization, described by a Stokes vector. Both jj-coupling and Russell - Saunders coupling schemes for the valence states are explored.

Chirality, magnetic charge and other strange entities in resonant x-ray Bragg diffraction

Subtleties in the electronic structure of complex materials can be directly observed, in great detail, by means of the Bragg diffraction of x-rays whose energy matches an atomic resonance. Strange atomic multipoles can be encountered in the interpretation of measured Bragg intensities, e.g., chirality and magnetic charge. Additionally, the x-ray technique allows the direct observation of the enantiomorphic screw-axis in chiral crystals, such as tellurium, low quartz and berlinite.

Symmetry of reentrant tetragonal phase in Ba 1 − x Na x Fe 2 As 2 : Magnetic versus orbital ordering mechanism

Magnetostructural phase transitions in Ba1−xAxFe2As2 (A = K, Na) materials are discussed for both magnetically and orbitally driven mechanisms, using a symmetry analysis formulated within the Landau theory of phase transitions. Both mechanisms predict identical orthorhombic space-group symmetries for the nematic and magnetic phases observed over much of the phase diagram, but they predict different tetragonal space-group symmetries for the newly discovered reentrant tetragonal phase in Ba1−xNaxFe2As2 (x∼0.24–0.28). In a magnetic scenario, magnetic order with moments along the c axis, as found experimentally, does not allow any type of orbital order, but in an orbital scenario, we have determined two possible orbital patterns, specified by P4/mnc1′ and I4221′ space groups, which do not require atomic displacements relative to the parent I4/mmm1′ symmetry and, in consequence, are indistinguishable in conventional diffraction experiments. We demonstrate that the three possible space groups are, however, distinct in resonant x-ray Bragg diffraction patterns created by Templeton & Templeton scattering. This provides an experimental method of distinguishing between magnetic and orbital models.

Experimental evidence of anapolar moments in the antiferromagnetic insulating phase of V 2 O 3 obtained from x-ray resonant Bragg diffraction

We have investigated the antiferromagnetic insulating phase of the Mott-Hubbard insulator vanadium sesquioxide

Dichroism and resonant diffraction in x-ray scattering by complex materials

({\text{V}}_{2}{\text{O}}_{3})

High-order Dy multipole motifs observed in DyB2C2 with resonant soft x-ray Bragg diffraction

by resonant x-ray Bragg diffraction at the vanadium

X-ray diffraction by CeB6

K

Diffraction and absorption of x-rays by 3d transition ions: the process

edge. Combining the information obtained from azimuthal angle scans, linear incoming polarization scans and by fitting collected data to the scattering amplitude derived from the established chemical

Spin and orbital magnetisation densities determined by compton scattering of photons

I2/a