Resonant inelastic x-ray scattering in electronically quasi-zero-dimensional ${\text{CuB}}_2{\text{O}}_4$

We present a resonant inelastic scattering (RIXS) study using of ${\text{CuB}}_2{\text{O}}_4$, which contains a lattice of ${\text{CuO}}_4$ plaquettes electronically isolated by ${\text{B}}^{+3}$ ions. The observed $\text{Cu}K$-edge spectra show a small number of well-separated features, and the simple electronic structure of ${\text{CuB}}_2{\text{O}}_4$ allows us to explore RIXS phenomenology. We find a low-energy feature that cannot be attributed to the same charge-transfer excitation discussed in other cuprates and is likely a $d\to d$ transition thought to be forbidden under common considerations of $K$-edge RIXS.

Figure 1

(Color online) (a) Schematic structure of ${\text{CuB}}_2{\text{O}}_4$ with undistorted Cu(1) plaquettes (red, lying flat) and distorted Cu(2) plaquettes (blue, standing out of page). B atoms are not shown. (b) Elementary ${\text{CuO}}_4$ unit and local coordinate system. (c) XPS spectrum. Lines are the result of a fit to Lorentzian lineshapes and a constant slope plus broad Lorentzian to represent the background. (d) XAS (solid curve) and integral of corrected RIXS intensity (symbols) versus incident photon energy.

Figure 2

(Color online) (a) Momentum independence of the raw RIXS spectra for $\hslash {\omega }_{\text{in}}=8992\text{eV}$. Various spectrum components are indicated. (b) Angle dependence of the MO RIXS signal for three orientations $\left(\varphi \right)$ of the crystal ($\hslash {\omega }_{\text{in}}=8989\text{eV}$ and $\Delta E=6.75\text{eV}$). The lines indicate fits to the function $A+B{\text{cos}}^2\left(2\theta -{\varphi }_0\right)$. (c) False color plot of RIXS spectrum with $2\theta =93°$, $\varphi =0$, around $\mathbf{Q}=\left(9,0,4\right)$. Data were corrected for self-absorption using a polarization-dependent mass absorption derived by merging the calculated value with the measured XAS spectra in the region of the edge. This step produces a spectrum which is closer to the RIXS cross section, but with systematic errors largest when the incident and/or final energy is near the edge at 8985 eV.

Figure 3

(Color online) (a) Calculated RIXS spectrum for the simple ${\text{CuO}}_4$ plaquette model. (b) Extended calculation of RIXS spectra, including all $\text{Cu}3d$ and $\text{O}2p$ orbitals, in the experimental configuration appropriate to one unit cell of ${\text{CuB}}_2{\text{O}}_4$(12 plaquettes).

Figure 4

(Color online) (a) Optical absorption from (Ref. 17) with assignments of the crystal field levels. [(b) and (c)] Cu(1) (red) and Cu(2) (blue) plaquette orientations in the two scattering geometries. (d) Resonance profile of the $d\to d$ excitation in the two geometries. [(e) and (f)] The $d\to d$ excitations energies (vertical lines) together with the low-energy feature seen in the RIXS data. (c) shown as vertical lines. Data in the ${ϵ}_i\parallel 100$ geometry were scaled to give the same $K{\beta }_{2,5}$ fluorescence intensity as in the ${\widehat{ϵ}}_{\text{in}}\parallel 001$ geometry.