High-resolution resonant inelastic extreme ultraviolet scattering from orbital and spin excitations in a Heisenberg antiferromagnet

We report a high-resolution resonant inelastic extreme ultraviolet (EUV) scattering study of the quantum Heisenberg antiferromagnet ${\mathrm{KCoF}}_3$. By tuning the EUV photon energy to the cobalt $M_{23}$ edge, a complete set of low-energy $3d$ spin-orbital excitations is revealed. These low-lying electronic excitations are modeled using an extended multiplet-based mean-field calculation to identify the roles of lattice and magnetic degrees of freedom in modifying the resonant inelastic x-ray scattering (RIXS) spectral line shape. We have demonstrated that the temperature dependence of RIXS features upon the antiferromagnetic ordering transition enables us to probe the energetics of short-range spin correlations in this material.

Figure 1

The ${\mathrm{KCoF}}_3$ lattice structure and a pictorial representation of the mean-field magnetic Hamiltonian. A single Co atom (red arrow) is coupled to six neighbors, each of which has a mean-field spin moment (yellow arrow) for the second sublattice.

Figure 2

(a) Co $M_{23}$-edge XAS spectrum recorded in total electron yield (TEY) mode at 80 K. (b) Stacked plot of Co $M_{23}$-edge RIXS spectra measured at 80 K. The RIXS spectra are plotted as a function of energy loss. The excitation photon energies are listed next to the curves and also denoted by red and blue squares in (a). A strong elastic peak at zero energy loss is not fully displayed. (c) Comparison of two RIXS spectra measured above (150 K) and below (80 K) the Néel temperature. Each spectrum at the respective temperature is produced by summing individual spectra taken at the excitation photon energies marked by the blue squares in (a). The blue dashed line is the optical absorption spectrum of ${\mathrm{KCoF}}_3$ reproduced from Ferguson et al. [28]. The main visible absorption bands are labeled in the figure.

Figure 3

(a), (b) $dd$ excitations (features A, B, C, and D) as a function of sample temperature. The RIXS spectra at selected temperatures (black curves) are plotted after subtracting the background (see text). The red dashed line is the theoretical RIXS spectrum. The high- and low-energy loss sides of feature A are marked by blue and red shading, respectively, in (a) (see text). The blue lines in (b) are the fitting functions overlaid on top of the RIXS spectra (see text for details of the fitting functions). (c) Temperature dependence of experimental (blue squares) and theoretical (red squares) peak positions. Experimental peak positions are determined from the fitting of experimental RIXS spectra. Two theoretical curves are shown in each subpanel: The curve with solid red squares considers the mean-field thermalization of near-neighbor magnetic moments, whereas the curve with open red squares fixes the near-neighbor magnetic moments to their $T=10$ K value. Both curves include the effects of lattice expansion and thermalization of electronic states. Numbers in meV in the figure show the overall energy dispersion (ED) of each feature with respect to temperature. (d) Temperature dependence of experimental (blue triangles) and theoretical (red triangles; only for feature A) FWHM of the leading edge of four RIXS features.

Figure 4

The theoretical RIXS map at 10 K around the Co $M_{23}$ edge, with 20 meV spectral broadening applied to account for the experimental energy resolution. Two theoretical RIXS spectra at 63.5 eV (red curve) and 62.5 eV (black curve) excitation photon energies are shown in the top panel. The experimental XAS spectrum is shown in the right panel. The charge density variations $\mathrm{\Delta }{e}_g$ for each principal excitation are listed in the figure.