X-ray techniques have been used for more than a century to study the atomic and electronic structure in practically any type of material. The advent of correlated electron systems, in particular complex oxides, brought about new scientific challenges and opportunities for the advancement of conventional X-ray methods. In this context, the need for new approaches capable of selectively sensing new forms of orders involving all degrees of freedom—charge, orbital, spin, and lattice—paved the way for the emergence and success of resonant X-ray scattering, which has become an increasingly popular and powerful tool for the study of electronic ordering phenomena in solids. We review the recent resonant X-ray scattering breakthroughs in the copper oxide high-temperature superconductors, in particular regarding the phenomenon of charge order, a broken-symmetry state occurring when valence electrons self-organize into periodic structures. After a brief historical perspective on charge order, we outline the mileston...

Resonant X-Ray Scattering Studies of Charge Order in Cuprates

A theoretical description of magneto-optical effects in metallic transition metal systems on the basis of an itinerant description for the underlying electronic structure is presented and applications to the magneto-optical Kerr effect and the circular dichroism in x-ray absorption are discussed Simple arguments based on symmetry considerations as well as electronic excitation schemes are given to show that magneto-optical effects are caused by the interplay of magnetic ordering and spin - orbit coupling The various band structure techniques developed to deal with this situation are reviewed with an emphasize on fully relativistic methods based on the Dirac equation The theoretical framework to calculate magneto-optical spectra on the basis of the underlying band structure is outlined in some detail In addition, a number of sum rules derived by various authors are presented that allow one to estimate spin and orbital magnetic moments of an absorbing atom from the magnetic x-ray dichroism spectra For the magneto-optical Kerr effect, as well as the magnetic x-ray dichroism, application of the theoretical formalism is presented for a great variety of systems, ie pure elements, compounds, alloys and multilayer systems For both kinds of spectroscopies it is demonstrated that model calculations which allow one to manipulate the exchange splitting and the spin - orbit coupling strength give valuable information for a better understanding of the rather complex spectra Concerning the sum rules, this technique together with the direct calculation of the dichroism spectra allow for a stringent test of the various assumptions on which these rules are based

https://iopscience.iop.org/article/10.1088/0034-4885/59/12/003/pdf

Magneto-optical effects in transition metal systems

Using x-ray absorption spectroscopy recent progress is achieved all over in solid state physics. This review focuses on these advances, with particular emphasis on applications to surface physics and to magnetism of ultrathin 3d and 5d films that are made possible by the use of undulators in third generation synchrotron radiation sources: the unambiguous appearance of an atomic extended x-ray absorption fine structure for atomic adsorbates and of σ* resonances in near-edge x-ray absorption fine structure spectra of oriented molecules is demonstrated. The induced magnetism at the interfaces of 3d and 5d layers is studied by x-ray magnetic circular dichroism. Fundamental aspects of the spectroscopy are clarified for rare earth crystals. The determination of the ground state properties and the detailed understanding of the underlying mechanisms was obtained by comparison of the experimental data to state-of-the-art ab initio calculations.

https://qmlab.ubc.ca/ARPES/PEOPLE/Andrea/Teaching/PHYS555_2007/XASreview.pdf

Recent advances in x-ray absorption spectroscopy

X-ray techniques have been used for more than a century to study the atomic and electronic structure in virtually any type of material. The advent of correlated electron systems, in particular complex oxides, brought about new scientific challenges and opportunities for the advancement of conventional x-ray methods. In this context, the need for new approaches capable of selectively sensing new forms of orders involving all degrees of freedom -- charge, orbital, spin, and lattice -- paved the way for the emergence and success of resonant x-ray scattering, which has become an increasingly popular and powerful tool for the study of electronic ordering phenomena in solids. Here we review the recent resonant x-ray scattering breakthroughs in the copper oxide high-temperature superconductors, in particular regarding the phenomenon of charge order -- a broken-symmetry state occurring when valence electrons self-organize into periodic structures. After a brief historical perspective on charge order, we outline the milestones in the development of resonant x-ray scattering, as well as the basic theoretical formalism underlying its unique capabilities. The rest of the review will focus on the recent contributions of resonant scattering to the tremendous advancements in our description and understanding of charge order. To conclude, we propose a series of present and upcoming challenges, and discuss the future outlook for this technique.

Resonant x-ray scattering studies of charge order in cuprates

A review is given of elastic spin-polarised low-energy electron diffraction (SPLEED) from crystalline surfaces. For the two relevant spin-dependent interaction mechanisms, spin-orbit coupling, and exchange, dynamical theories are presented with emphasis on symmetry principles, potential models and multiple scattering formalisms. Brief accounts of computational aspects and experimental apparatus (polarised-electron source, spin detectors) are followed by a survey and discussion of experimental and theoretical results for non-magnetic and magnetic surfaces. Finally, the impact of SPLEED on electron emission methods is pointed out, and the prospects of SPLEED as a powerful tool for surface analysis are assessed.

https://iopscience.iop.org/article/10.1088/0022-3719/14/15/006/pdf

Spin-polarised low-energy electron diffraction

A resonance-type X-ray magnetic scattering at the K -absorption edge was first observed in 220 Bragg reflection of ferromagnetic Ni single crystal. Further a theoretical discussion on the resonance magnetic scattering curve observed was carried out; A difference of the oscillator-strength density for each direction of the spins was also derived from this curve. The oscillator-strength density for minority spin excesses that for the majority spin between the Fermi level and 25 eV above the level. The difference of oscillator-strength density amounts to about 1×10 -4 /Ry at the maximum.

X-ray resonance magnetic scattering

Temperature dependence of the exchange diffraction spot intensity from the cleaved face (001) of nickel oxide is measured for the cases of very small and comparatively large penetration depth of electron beam concerning the surface barrier resonance in LEED. The exchange reflexion intensity is corrected for the Debye-Waller factors in order to reveal the temperature dependence of the sublattice magnetization. The effective critical exponent of the sublattice magnetization is determined to be 0.89±0.01 as the proper value for the top-most surface layer. The thickness of the surface layers, which is characterized by the same value of the critical exponent as the top-most surface layer, becomes thicker than the mean absorption distance when the temperature is raised up to 0.9 in T / T N .

LEED Investigation on Temperature Dependence of Sublattice Magnetization of NiO (001) Surface Layers

The nature of exchange reflexions in low-energy electron diffraction from antiferromagnetic nickel oxide was studied in particular reference to its dependence on the diffraction condition of electrons, which was, in the present study, changed primarily by rotating the crystal at a fixed electron energy. It was pointed out that the exchange reflexions are subject to the three-dimensional diffraction conditions appropriate to the reciprocal lattice points which correspond to the magnetic structure, and also that the intensities of these weak reflexions may be favourably enhanced by the dynamical diffraction effect under the condition which involves the simultaneous presence of a strong regular reflexion.

Exchange Reflexions in Low Energy Electron Diffraction from Antiferromagnetic Nickel Oxide Crystal

The fundamental equations of the dynamical theory of electron diffraction by an antiferromagnetic crystal are formulated by taking account of the spin dependent part of the exchange interaction between the incoming electron and the magnetic electrons in the crystal. As an application, the effect of intensity enhancement of a weak exchange reflexion with half-order indices in LEED caused by the simultaneous presence of a strong Bragg reflexion with ordinary indices is dealt with; the result generally agrees with previous LEED observation by the present authors on NiO (J. Phys. Soc. Japan 31 (1971) 1408). The values of Fourier components of the scattering factors due to the spin dependent part of the exchange interaction numerically calculated for various electron energies for NiO are found to be in a range of 1/10∼1/20 of ordinary Fourier potentials.

Kazumichi Namikawa

Papers

X-ray resonance magnetic scattering

LEED Investigation on Temperature Dependence of Sublattice Magnetization of NiO (001) Surface Layers

Exchange Reflexions in Low Energy Electron Diffraction from Antiferromagnetic Nickel Oxide Crystal

Intensity Behaviour of Exchange Reflexions in LEED from an Antiferromagnetic Crystal

Experimental Study of Ferroelectric Materials by Coherent X‐ray Scattering