Orbital excitation in ${\text{Sr}}_2{\text{CuO}}_2{\text{Cl}}_2$: Resonant inelastic x-ray scattering at the $\text{Cu}K$ pre-edge

We report resonant inelastic x-ray scattering (RIXS) study of $d\text{−}d$ orbital excitations in ${\text{Sr}}_2{\text{CuO}}_2{\text{Cl}}_2$ utilizing the intermediate state associated with a quadrupole transition. Fourfold azimuthal angle dependence of the pre-edge peak near the $\text{Cu}K$ absorption edge confirms that the in-plane pre-edge peak arises from the $1s\to 3d_{x^2-y^2}$ electric quadrupole transition. When the incident photon energy is tuned to this transition, we observed a RIXS excitation at 2 eV energy loss. This excitation is associated with the $d\text{−}d$ excitation of $d_{x^2-y^2}\to d_{yz,zx}$ based on the angular dependence of the quadrupole transition-matrix element of the scattered photon.

Figure 1

(Color online) (a) $\text{Cu}K$-edge XAS spectrum of ${\text{Sr}}_2{\text{CuO}}_2{\text{Cl}}_2$. The spectrum shown here is obtained with $\varphi =45°$ as shown in the inset. (b) $\varphi$ dependence of the pre-edge region XAS. (c) The pre-edge peak intensity $I\left(\varphi \right)$ as a function of $\varphi$. $I\left(\varphi \right)$ is normalized to have a maximum value of 1. The solid line is $0.05+0.95{\text{sin}}^2\left(2\varphi \right)$.

Figure 2

(Color online) (a) RIXS spectra near $\mathbf{Q}\sim \left(006.6\right)$ obtained with the incident photon energy of ${\omega }_i=8979\text{eV}$ and $\varphi =45°$. This is compared with spectra obtained with two independent off-resonance conditions: ${\omega }_i=8978\text{eV}$, $\varphi =45°$ and ${\omega }_i=8979\text{eV}$, $\varphi =0°$. (b) Difference curve between on and off resonances. The 2 eV feature is fitted by a Gaussian peak with linear background. (c) RIXS spectra at the $\underset{̱}{1s}\text{−}4p$ resonance $\left({\omega }_i=8995\text{eV}\right)$ at $\mathbf{q}\sim \left(0,0\right)$, $\left(\pi ,0\right)$, and $\left(0.9\pi ,0.9\pi \right)$.

Figure 3

(Color online) (a) Off-resonance data subtracted RIXS spectra $\left(\varphi =45°\right)$ near $\mathbf{q}\sim \left(0,0\right)$. From top to bottom, scattered angle relative to the sample surface normal $\left(\alpha \right)$ decreases indicating more sample normal scattering. (b) Schematic of the measurement geometry and angles. (c) The RIXS intensity normalized by ${\left|M_{abs}^{x^2-y^2}\right|}^2$ is plotted as a function of angle $\alpha$. The angular dependence of the calculated ${\left|M_{em}^{yz,zx}\right|}^2$ and ${\left|M_{em}^{3z^2-r^2}\right|}^2$ is also shown in an arbitrary scale.