Satellite holmium M-edge spectra from the magnetic phase via resonant x-ray scattering

TL;DR

This paper develops a resonant x-ray scattering analysis for Ho's magnetic phases, demonstrating the localized electron picture's validity and linking spectral shape changes to magnetic structure transitions.

Contribution

It introduces a convenient RXS amplitude expression for higher rank tensor contributions and analyzes Ho spectra near M edges, connecting spectral features to magnetic phases.

Findings

Spectra at the M5 edge match experimental data, validating the localized picture.

Temperature-dependent spectral shape changes indicate magnetic structure transitions.

Predicted intensity at the fourth satellite spot in the conical phase.

Abstract

Developing an expression of resonant x-ray scattering (RXS) amplitude which is convenient for investigating the contributions from the higher rank tensor on the basis of a localized electron picture, we analyze the RXS spectra from the magnetic phases of Ho near the $M_{4,5}$ absorption edges. At the $M_5$ edge in the uniform helical phase, the calculated spectra of the absorption coefficient, the RXS intensities at the first and second satellite spots capture the properties the experimental data possess, such as the spectral shapes and the peak positions. This demonstrates the plausibility of the adoption of the localized picture in this material and the effectiveness of the spectral shape analysis. The latter point is markedly valuable since the azimuthal angle dependence, which is one of the most useful informations RXS can provides, is lacking in the experimental conditions. Then, by focusing on the temperature dependence of the spectral shape at the second satellite spot, we expect that the spectrum is the contribution of the pure rank two profile in the uniform helical and the conical phases while that is dominated by the rank one profile in the intermediate temperature phase, so-called spin slip phase. The change of the spectral shape as a function of temperature indicates a direct evidence of the change of magnetic structures undergoing. Furthermore, we predict that the intensity, which is the same order observed at the second satellite spot, is expected at the fourth satellite spot from the conical phase in the electric dipolar transition.