Dispersion of Magnetic Excitations in the Cuprate ${\mathrm{La}}_2{\mathrm{CuO}}_4$ and ${\mathrm{CaCuO}}_2$ Compounds Measured Using Resonant X-Ray Scattering

By resonant inelastic x-ray scattering in the soft x-ray regime we probe the dynamical multiple-spin correlations in the antiferromagnetic cuprates ${\mathrm{La}}_2{\mathrm{CuO}}_4$ and ${\mathrm{CaCuO}}_2$. High resolution measurements at the copper $L_3$ edge allow the clear observation of dispersing bimagnon excitations. Theory based on the ultrashort core-hole lifetime expansion fits the data on these coherent spin excitations without free parameters.

Figure 1

The $L_{2,3}$ edge RIXS process and the experimental geometry. (a) Schematic representation of the resonant scattering leading to a bimagnon; the actual spin alignment direction does not matter in the proposed scattering mechanism as long as an antiferromagnetic interaction is present. (b) The experimental scattering geometry, where the scattering angle is fixed at 110° (70° back scattering) and the sample can be rotated around its $a$ axis. (c) determination of ${\mathbf{q}}_{\parallel }(\theta )$, projection onto the $ab$ plane of the $\Delta \mathbf{k}$ momentum lost by the scattering photons. Panel (d) Points in the reciprocal space corresponding to the spectra measured for $\theta =10°\to 90°$.

Figure 2

Experimental results of ${\mathrm{CaCuO}}_2$ (a) Cu $L_3$ x-ray absorption spectrum (XAS), the vertical lines indicate the excitation energy. (b) CCO RIXS spectra for various incidence angles $\theta$ with $\sigma$ polarization: the $dd$ excitations ($E=1.5–3\mathrm{eV}$) evolve in shape but do not disperse, whereas the low energy feature below 1 eV disperse versus $q_{\parallel }$, as highlighted in (d), where the value of $q_{\parallel }$ is indicated. In (c) the $\pi$ (circles) and $\sigma$ (lines) cases are compared after normalization to the $dd$ peak, which is almost equivalent to scaling to the absorption cross section.

Figure 3

Experimental results of ${\mathrm{La}}_2{\mathrm{CuO}}_2$. In (a) the low energy feature with $\theta =35°$ ($q_{\parallel }=1.03$) measured at room $T$ and 30 K are compared. In (b),(c), and (d) same as in Fig. 2.

Figure 4

Data treatment and summary of dispersion results. In (a) the LCO spectrum at $\theta =35°$, $\sigma$ polarization: from raw data (full circles) the experimental elastic peak (red line) is subtracted, giving the inelastic spectrum (open circles) to be compared with theoretical spectral shape (light blue line). In (b) and (c) the low energy feature peak position is plotted vs $q_{\parallel }$ (experiment: red squares for $\sigma$, blue squares with error bars for $\pi$). In (c) also the one magnon dispersion (purple line) from Ref. 3 is shown. Brown lines correspond to theoretical dispersion calculated with $J=120\mathrm{meV}$ [3], and accounting for the experimental resolution.