Crystal-Field Level Inversion in Lightly Mn-Doped ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$

${\mathrm{Sr}}_3({\mathrm{Ru}}_{1-x}{\mathrm{Mn}}_x{)}_2{\mathrm{O}}_7$, in which $4d$-Ru is substituted by the more localized $3d$-Mn, is studied by x-ray dichroism and spin-resolved density functional theory. We find that Mn impurities do not exhibit the same $4+$ valence of Ru, but act as $3+$ acceptors; the extra $e_g$ electron occupies the in-plane $3d_{x^2-y^2}$ orbital instead of the expected out-of-plane $3d_{3z^2-r^2}$. We propose that the $3d-4d$ interplay, via the ligand oxygen orbitals, is responsible for this crystal-field level inversion and the material’s transition to an antiferromagnetic, possibly orbitally ordered, low-temperature state.

Figure 1

Isotropic Mn $L_{2,3}$-edge XAS data from ${\mathrm{Sr}}_3({\mathrm{Ru}}_{0.9}{\mathrm{Mn}}_{0.1}{)}_2{\mathrm{O}}_7$ and stoichiometric Mn oxides of known valences. Inset: detailed view of the $L_3$-edge chemical shift.

Figure 2

(a) Polarization-dependent Mn $L_{2,3}$-edge XAS spectra from ${\mathrm{Sr}}_3({\mathrm{Ru}}_{0.9}{\mathrm{Mn}}_{0.1}{)}_2{\mathrm{O}}_7$ at $T=295\mathrm{K}$. (b) Scheme of the XAS process: the $L_2$ ($L_3$) edge corresponds to the excitation of a Mn $2p_{1/2}$ ($2p_{3/2}$) electron to the Mn $3d$ valence shell. The $L_3\mathrm{\text{−}}{L}_2$ energy separation is due to the $2p$ core level spin-orbit coupling. (c) Corresponding experimental linear dichroism (LD), defined as $\mathrm{LD}=[I_{\mathrm{XAS}}(\mathbf{E}\perp c)-I_{\mathrm{XAS}}(\mathbf{E}\parallel c)]$. (d) Calculated LD spectra for two possible $e_g$-orbital occupations ($x\parallel a$, $y\parallel b$, $z\parallel c$).

Figure 3

Density-of-states (DOS) of stoichiometric (a) ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ (Ru327), (b) ${\mathrm{Sr}}_3{\mathrm{Mn}}_2{\mathrm{O}}_7$ (Mn327) with the crystal structure of Ru327, and (c) ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ (Ru214).

Figure 4

(a), (b) Spin-up density of states (DOS) from LSDA calculations for out-of-plane $d_{3z^2-r^2}$ and in-plane $d_{x^2-y^2}$ Mn $e_g$ orbitals in 11% Mn-doped Ru oxides. (c)–(f) $\mathrm{Ru}\mathrm{\text{−}}\mathrm{O}/\mathrm{Mn}$-impurity hybridization leading to the Mn orbital hierarchy inversion: energy of (c) out-of-plane and (f) in-plane Mn-impurity and O orbitals in the ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ host material before the Mn-O hybridization is turned on; (d), (e) once the $\mathrm{O}/\mathrm{Mn}$-impurity hybridization is considered, the Mn $e_g$-orbital hierarchy is inverted (${\Delta }_{CF}>0$) if ${\tau }_z^2/{\Delta }_z-{\tau }_x^2/{\Delta }_x>\delta$.