Momentum and polarization dependence of single-magnon spectral weight for $\text{Cu}{L}_3$-edge resonant inelastic x-ray scattering from layered cuprates

Recently it was predicted theoretically and confirmed experimentally that in cuprates single-magnon dispersions can be mapped out with resonant inelastic x-ray scattering (RIXS) at the copper $L_3$ edge. To further establish RIXS as a viable technique we investigate the momentum and incident photon polarization dependence of the single-magnon spectral weight in a variety of layered undoped antiferromagnetic compounds. The agreement of experimental and theoretical results bolsters the assignment of RIXS spectral features to single magnons. This detailed analysis allows to disentangle single-magnon scattering from other spectral contributions. Moreover, it is a necessary premise for future research aimed at investigating processes that modulate spectral weights beyond the predictions of linear spin-wave theory.

Figure 1

(Color online) Panel (a): layout of the experiment and definition of angles $\alpha$, $\delta$, and $\theta$. The $q_{\parallel }$ is varied by rotating the sample around the vertical axis; as $q_{\parallel }=q\text{sin}\delta$, $q_{\parallel }>0$ indicates near normal incidence geometry $\left(\theta >\alpha /2\right)$. With the sample as in the figure one explores the green line in the BZ; the violet diagonal is explored after $45°$ rotation of the sample around its $c$ axis. Panel (b): a RIXS spectrum of LCO. Charge transfer excitations are labeled with CT and the main peak is due to $dd$ excitations; the MIR region (red box) is expanded in panel (c), where the magnon peak is labeled with B; peak A is the elastic intensity, feature C the multi-magnon spectral distribution, peak D the partly unresolved phonon contribution, as explained in Ref. 7. Panel (d): example of dispersion of the magnetic excitations in LCO for $\alpha =90°$, with intensities normalized to the $dd$ area put to 100; note that the intensities are not symmetric with respect to $q_{\parallel }=0$. Panel (e) and (f): for $\alpha =130°$, measured single magnon intensity normalized to the $dd$ intensity as explained for panel (d). Full circles and hollow squares are for $\pi$ an $\sigma$ polarization respectively. Raw data are shown in panel (e), self-absorption corrected data in panel (f).

Figure 2

(Color online) Panels (a)–(c): comparison of the normalized intensities in LCO with the theory in the conditions shown by the icons at the right. Panel (d) and (e): theoretical normalized intensity (red dotted and black solid, left scale) obtained by dividing the non-normalized intensity multiplied by 100 (thick dashed green, right scale) by the total $dd$ intensity (thin dash-dot green, right scale) for $\sigma$ and $\pi$ polarizations, respectively. We notice that, at $q_{\parallel }<0$, this normalization has a strong effect for $\pi$ but very little for $\sigma$.

Figure 3

(Color online) Comparison between experimental (symbols) and theoretical (lines) values of the linear dichroic ratio $R$ (see text for the definition). The open points refer to LCO, the blue dots to SCCO, and the purple stars to NdBCO.