Electronic structure and evolution of the orbital state in metallic ${\mathrm{Ca}}_{2-x}{\mathrm{Sr}}_x\mathrm{Ru}{\mathrm{O}}_4$

We investigated the electronic structure of a layered ${\mathrm{Ca}}_{2-x}{\mathrm{Sr}}_x\mathrm{Ru}{\mathrm{O}}_4$ in a metallic regime $(0.15⩽x⩽2.0)$ using a polarization dependent O $1s$ x-ray absorption spectroscopy. The spectrum shows strong variations with the polarization especially in Ru $4d$ region, which enables us to identify the electronic states. The spectral line shape gradually changes with increase of Sr concentration, and agrees well with an unrestricted Hartree-Fock analysis, which suggests evolution of the orbital states and provides clues for how the lattice distortion affects the orbital occupations.

Figure 1

(a) O ${\mathrm{Ca}}_{1.1}{\mathrm{Sr}}_{0.9}\mathrm{Ru}{\mathrm{O}}_4$ at two polarization geometries $\mathrm{Sr}\mathrm{Ru}{\mathrm{O}}_3$. The wide range spectra are shown in the inset. (b) Ru $4d\text{−}\mathrm{O}2p$ bonded orbital geometries in the $\mathrm{Ru}{\mathrm{O}}_6$ octahedron. ${\mathrm{O}}_A$ and ${\mathrm{O}}_P$ denote the apical and in-plane oxygens, respectively.

Figure 2

Schematic energy diagrams of Ru $4d$ states. $\mid \nu ⟩(\nu =xy,yz,zx,x^2-y^2,z^2)$ denotes a mainly $\nu$-orbital state partially mixed with other orbitals.

Figure 3

Polarization dependent O $1s$ XAS spectra in Ru $4d$ region of metallic ${\mathrm{Ca}}_{2-x}{\mathrm{Sr}}_x\mathrm{Ru}{\mathrm{O}}_4$ ($x=0.09$, 0.15, 0.2, 0.4, 0.5, 0.7, 0.9, 1.5, 2.0).

Figure 4

Calculated O $1s$ XAS spectra of the Ru $t_{2g}$ states for $\vartheta =0°$ and 60° in comparison with the corresponding experimental spectra for different $x$ values.

Figure 5

The rotation angle $\phi$ and tilting angle $\theta$ quoted from Ref. 5, and the hole numbers obtained from the HF analysis; $N_h\left(\nu \right)$ denotes the number of holes per Ru of the $\nu (=xy,yz∕zx,x^2-y^2,z^2)$ orbital symmetry state at both Ru and O sites.