Magnetic circular dichroism in soft X-ray resonant inelastic scattering

We discuss the application of resonant inelastic X-ray scattering to the study of magnetic systems in the soft X-ray range. To this end we distinguish two broad areas. In the first the layout of the experiment is such that the absorption magnetic circular dichroism (MCD) is not zero. In the second the magnetisation is perpendicular to the incident helical beam so that the absorption MCD is zero. In the first area we summarise published results on Fe-Co alloys and we present new data on Mn impurities in Ni together with calculations. In the second area we summarise published results on Ni in Ni-ferrite with final 3s shell excitation and we present new results on Co-metal and Co in Co-ferrite measured with a new approach. This is based on the incident energy dependence of the integral of the Raman spectrum in inner shell excitation (integrated resonant Raman scattering). The potentialities and the limitations of the above methods are critically presented. Received: 23 May 2001 / Accepted: 4 July 2001 / Published online: 5 October 2001     

Electronic structure of single-wall carbon nanotubes studied by resonant inelastic X-ray scattering

F in the nanotubes, indicating that metallic nanotubes are present in the sample. Received: 2 April 1998     

Spin-resolved NEXAFS from resonant X-ray scattering (RXS): Application to MnO

Resonantly excited metal K core line spectra of NiO, MnO, CuO and other compounds have been investigated at the beamlines X21 (NSLS/BNL), BW1 and W1.1 (HASYLAB/DESY). A novel technique for quantitative resolution of NEXAFS spectra into spin-up and spin-down components has been developed. Since the method employs spin conservation and local spin references, it needs no circularly polarized radiation and no sample magnetization for taking both the RXS and NEXAFS spectra. Hence antiferromagnetic and paramagnetic materials can be investigated as well.By utilizing linear dichroism with angular-dependent measurements on single-crystal samples, additional resolution of NEXAFS spectra is possible with respect to the orbital symmetry. Application of the method to paramagnetic MnO, for the first time, provides new and unambiguous experimental results confirming modern (LSDA+U) calculations. Received: 29 May 2001 / Accepted: 4 July 2001 / Published online: 5 October 2001     

Magnetic structure determination using polarised resonant X-ray scattering

Full polarisation analysis of resonant X-ray magnetic scattering (RXMS) is shown to advance the determination of magnetic moment directions of complex magnetic structures within single crystals. Key features of this novel method are the variation of the incident beam polarisation through the use of an X-ray phase plate, and the measurement of the scattered beam polarisation in terms of Poincaré-Stokes parameters. Contrary to the established method, no azimuthal rotation is required. Thus, the major sources of systematic error are eliminated, and the method is compatible with exotic and complex sample environments. The technique is demonstrated with the example of TbMn₂O₅. The RXMS theory briefly outlined in this paper was fitted to the data, and the local and delocalized, band-specific moment directions associated with the magnetic order of the resonating species was refined with a high degree of accuracy.     

Refraction effect of scattered X-ray fluorescence at surface

The angular distribution of X-ray fluorescence shows anisotropic radiation. We proved that the origin of the anisotropic radiation is X-ray refraction by using a scattered X-ray fluorescence model. Utilizing the refraction effect of X-ray fluorescence, we can obtain much information: for example, surface density, chemical condition, surface roughness, and particle diameter of element, as a new tool of studying surfaces and interfaces. We introduce a new X-ray dispersive system utilizing X-ray refraction.     

Coherent X-ray scattering by phonons

Interference effects arising from coherently coupled X-ray beams inelastically scattered from phonons have been used to determine phonon eigenvectors in Si and GaAs crystals. An outline of the method, experimental requirements, and theoretical background is presented. The experimental results are analyzed with the help of different lattice dynamical model calculations. Best overall agreement is found with phonon eigendata based on the bond charge model.     

Polarization dependence of L- and M-edge resonant inelastic X-ray scattering in transition-metal compounds

The resonant inelastic x-ray scattering (RIXS) cross section at the L and M edges of transition-metal compounds is studied using an effective scattering operator. The intensities of the elastic peak and for spin-flip processes are derived. It is shown how the polarization dependence can be used to select transitions. Comparisons are made with experiment. A detailed analysis of the polarization and angular dependence of L- and M-edge RIXS for divalent copper compounds, such as the high-Tc superconductors, is given.     

The local electronic structure of tin phthalocyanine studied by resonant soft X-ray emission spectroscopies

The electronic structure of thin films of the organic semiconductor tin phthalocyanine (SnPc) has been investigated by resonant and non-resonant soft X-ray emission (RXES and XES) at the carbon and nitrogen K-edges with excitation energies determined from near edge X-ray absorption fine structure (NEXAFS) spectra. The resultant NEXAFS and RXES spectra measure the unoccupied and occupied C and N 2p projected density of states, respectively. In particular, RXES results in site-specific C 2p and N 2p local partial density of states (LPDOS) being measured. An angular dependence of C 2p and N 2p RXES spectra of SnPc was observed. The observed angular dependence, the measured LPDOS and their correspondence to the results of density functional theory calculations are discussed. Observed differences on the same site-specific features between resonant (non-ionising) and non-resonant (ionising) NXES spectra are attributed to symmetry selection and screening.     

Theoretical analysis of the spectra of X-ray resonant magnetic reflectivity

We have developed the general computer code for the calculations of reflectivity with polarization analysis from an arbitrary anisotropic multilayer, which allows us to test different approaches for the Bragg reflectivity spectrum treatment. We have proved the validity of the usage of the Bragg peak position for the determination of the energy dependence of the diagonal component of resonant susceptibility tensor, but revealed the essential discrepancy of this procedure for the off-diagonal term determination. The explanation lies in the polarization mixture by multiple reflections at large glancing angles. By the model calculations we have shown that in L-MOKE geometry the observed difference of the integrated Bragg peak reflectivity for the (+) and (−) field direction is predominantly caused by the magnetization of the central part of resonant layer at the first-order Bragg peak, but it is very sensitive to the interface magnetization at the second-order Bragg peak.     

Magnetic and resonant X-ray scattering investigations of strongly correlated electron systems

Resonant X-ray scattering is a method which combines high- resolution X-ray elastic diffraction and atomic core-hole spectroscopy for investigating electronic and magnetic long-range ordered structures in condensed matter. During recent years the development of theoretical models to describe resonant X-ray scattering amplitudes and the evolution of experimental techniques, which include the control and analysis of linear photon polarization and the introduction of extreme environment conditions such as low temperatures, high magnetic field and high pressures, have opened a new field of investigation in the domain of strongly correlated electron systems. To cite this article: L. Paolasini, F. de Bergevin, C. R. Physique 9 (2008).     

Theory of indirect resonant inelastic X-ray scattering

We express the cross section for indirect resonant inelastic X-ray scattering in terms of an intrinsic dynamic correlation function of the system that is studied with this technique. The cross section is a linear combination of the charge response function and the dynamic longitudinal spin density correlation function. This result is asymptotically exact for both strong and weak local core-hole potentials. We show that one can change the relative charge and spin contribution to the inelastic spectral weight by varying the incident photon energy.     

Application of resonant X-ray emissions for molecular/electronic structure analysis of boron nitrides

* –B1s^-1 transitions were observed in w-BN composed of four-fold boron atoms and in h-BN composed of three-fold boron atoms, when the photon energy of the incident undulator beams coincided with the B1s–B2pπ^* absorption energy. However, no resonance was observed in c-BN composed of four-fold boron atoms. The resonant X-ray emission reflects the electronic structure of unoccupied molecular orbitals which strongly depend on the conformnations of the boron atoms. These findings confirm that resonant X-ray emissions can be useful indices for molecular and electronic structure analysis of boron nitrides. Accepted: 6 March 1997     

Thermodynamic evolution of antiphase boundaries in GaP/Si epilayers evidenced by advanced X-ray scattering

We have investigated quantitatively anti-phase domains (APD) structural properties in 20 nm GaP/Si epilayers grown by molecular beam epitaxy, using fast, robust and non-destructive analysis methods. These analyses, including atomic force microscopy and X-ray diffraction, are applied to samples grown by various molecular beam epitaxy growth modes. Roughness, lateral crystallite size of the epilayer, ratio of antiphase domains and their relationship are discussed. It is shown that both these analysis methods are useful to clarify the physical mechanisms occurring during the heterogeneous growth. Low temperature migration enhanced epitaxy is found to guarantee smoother surface than conventional molecular beam epitaxy. Effect of annealing temperature on antiphase boundaries (APBs) thermodynamics is discussed. The modification of the thermodynamic equilibrium through a thermal activation of APBs motion is expected to play an important role in the dynamic evolution of surfaces during thermal annealing and growth.     

Thermal phase transition of RbMnFe(CN)6 observed by X-ray emission and absorption spectroscopy

The thermal phase transition of RbMnFe(CN)₆ has been observed by Mn and Fe 3p-1s X-ray emission spectroscopy (XES) and 1s X-ray absorption spectroscopy (XAS). The thermal variations of the spin states and the valences of Mn and Fe were determined to be Mn²⁺(S=5/2)-NC-Fe³⁺(S=1/2) for the high-temperature (HT) phase and Mn³⁺(S=2)-NC-Fe²⁺(S=0) for the low-temperature (LT) phase. These transitions are thus caused by charge transfer between Mn and Fe. The temperature dependences of Mn and Fe 3p-1s XES and 1s XAS were observed as the composition of the spectra of the HT and LT phases. The ratios of the HT component in each spectrum show good agreement with the thermal transition curves observed with magnetic susceptibility measurements.     

Local probing of the surface chemical bond using X-ray emission spectroscopy

2 and CO on Ni(100), benzene on Ni(100) and Cu(110), and glycine adsorbed on Cu(110). New types of molecular states are observed which are directly related to the surface chemical bond. The long-accepted Blyholder model which is based on a frontier orbital concept cannot explain our results for N₂ and CO chemisorption. We find it necessary to offer a new picture where changes in the whole molecular orbital framework have to be considered. We show that both π and σ type interactions are important in describing the bonding in benzene to metal surfaces. The future prospect is illustrated by the adsorption of the simplest amino acid, glycine, on Cu(110). The adsorbate has four different atomic centers where X-ray emission spectra are obtained, providing a unique view of the local electronic structure. Accepted: 6 March 1997     

Calculation of valence electron momentum densities using the projector augmented-wave method

We present valence electron Compton profiles calculated within the density-functional theory using the all-electron full-potential projector augmented-wave method (PAW). Our results for covalent (Si), metallic (Li, Al) and hydrogen-bonded ((H₂O)₂) systems agree well with experiments and computational results obtained with other band-structure and basis-set schemes. The PAW basis set describes the high-momentum Fourier components of the valence wave functions accurately when compared with other basis set schemes and previous all-electron calculations.     

Resonant inelastic scattering at the L edge of Ti in Barium Strontium Titanate by soft X-ray fluorescence spectroscopy

3 and L₂ resonances, especially strong at the L₃ resonance, while inelastic peaks were observed from well below the resonance and showed complex features at the excitation energies between the Ti L₃ and L₂ resonances. The measured spectra were explained based on radiative and non-radiative electronic processes near the Ti-L_2,3 edge in the titanate. Received: 6 March 1997     

Theory of resonant inelastic X-ray scattering spectrum for Ni impurities in cuprates

We perform the numerically exact diagonalization calculation for small Cu-O clusters with a Ni impurity site, representing the Ni-substituted cuprate, to examine the single-particle excitation spectra as well as the resonant inelastic X-ray scattering (RIXS) spectra. We clarify relations between low-energy electronic structures near the Ni site and excitations seen in the RIXS spectra.     

Deduction of the temperature-dependent structure of the four-layer intermediate smectic phase using resonant X-ray scattering

A binary mixture of an antiferroelectric liquid-crystal material containing a selenium atom and a highly chiral dopant is investigated using resonant X-ray scattering. This mixture exhibits a remarkably wide four-layer intermediate smectic phase, the structure of which is investigated over a temperature range of 16K. Analysis of the resonant X-ray scattering data allows accurate measurement of both the helicoidal pitch and the distortion angle as a function of temperature. The former decreases rapidly as the SmC ^* phase is approached, whilst the latter remains constant over the temperature range studied at 8^°±3^° . We also observe that the senses of the helicoidal pitch and the unit cell of the repeating four-layer structure are opposite in this mixture and that there is no pitch inversion over the temperature range studied.