Hybridized orbital states in spin-orbit coupled $3d-5d$ double perovskites studied by x-ray absorption spectroscopy

We investigated the orbital hybridization mechanism in $3d-5d$ double perovskites (DPs) of ${\mathrm{La}}_2{\mathrm{CoIrO}}_6$ and ${\mathrm{La}}_2{\mathrm{CoPtO}}_6$ using x-ray absorption spectroscopy. It is clearly evidenced by O $K$-edge and Co $K$-edge x-ray absorption spectra that the Co $3d$ orbitals hybridize not only with the half-filled Ir/Pt $j_{\mathrm{eff}}$ states but also with the fully empty (unpolarized) Ir/Pt $e_g$ states in both DPs. The Co $3d$ $e_g$-Ir $5d$ $e_g$ hybridization cannot contribute to the ferrimagnetic long-range order in ${\mathrm{La}}_2{\mathrm{CoIrO}}_6$ established by spin-selective Co $3d$ $t_{2g}$-Ir $5d$ $j_{\mathrm{eff}}$ hybridization through the intermediate oxygen $p$ state but could serve as an origin of paramagnetism. The strengths of such orbital hybridizations were found to be almost invariant to temperature, even far above the Curie temperature, implying persistent paramagnetism against the antiferromagnetic ordering in the spin-orbit entangled $3d-5d$ DPs.

Figure 1

(a) The $B{\mathrm{O}}_6$ octahedron ($B$ = TM cation) with the energy split for $d$-orbital states according to the octahedral crystal field ($10Dq$) with an additional large spin-orbit coupling ${\lambda }_{SOC}$ in the case of ${\mathrm{Ir}}^{4+}$ ($5d^5$). (b) Simplified picture of alternating ordering of ${\mathrm{Co}}^{2+}$ (purple) and ${\mathrm{Ir}}^{4+}$ (blue) with intervening ${\mathrm{O}}^{2-}$ (red) in an $A_{2}B{B}^{\prime }{\mathrm{O}}_6$ DP, e.g., ${\mathrm{La}}_2{\mathrm{CoIrO}}_6$. The solid black box shows a single pair of $B{\mathrm{O}}_6-B^{\prime }{\mathrm{O}}_6$ for clarity. (c) Antiferromagnetic coupling of spins between $B$ (${\mathrm{Co}}^{2+}$) and $B^{\prime }$ (${\mathrm{Ir}}^{4+}$) in the case of ${\mathrm{La}}_2{\mathrm{CoIrO}}_6$. Spin-selective intersite hybridization between the adjacent cations through the oxygen orbital states stabilizes the antiferromagnetic alignments of spins (colored arrows).

Figure 2

The O $K$-edge XAS spectra of (a) ${\mathrm{La}}_2{\mathrm{CoIrO}}_6$, ${\mathrm{La}}_2{\mathrm{NiIrO}}_6$, and ${\mathrm{La}}_2{\mathrm{ZnIrO}}_6$ and (b) ${\mathrm{La}}_2{\mathrm{CoIrO}}_6$ and ${\mathrm{La}}_2{\mathrm{CoPtO}}_6$. Peaks $\alpha$, $\beta$, and ${\beta }^{\prime }$ are attributed to the $d$-orbital states of the transition-metal (TM) ions, including Ir/Pt $5d$ and Co (or Ni) $3d$, while $\gamma$ and $\delta$ are attributed mainly to the La $4f$ and $5d$ orbital states, respectively. Peaks $\epsilon$ and $\eta$ can be attributed to the $sp$ orbital states from all the cations.

Figure 3

(a) The Co $K$-edge XAS (Co $1s\to p$) spectra of ${\mathrm{La}}_2{\mathrm{CoIrO}}_6$ and ${\mathrm{La}}_2{\mathrm{CoPtO}}_6$ with the simulated spectra from feff8. (b) The enlarged view of the preedge regions with the Ir/Pt $d$ local densities of states (LDOSs) obtained from feff8. The shaded regions highlight the correspondence to the peaks ($\beta$ and ${\beta }^{\prime }$) in the experimental data. Peaks $\alpha$, $\beta$, and ${\beta }^{\prime }$ correspond to those in Fig. 2. The presence of peaks $\beta$ and ${\beta }^{\prime }$ evidently shows the effects of orbital hybridization between the Ir/Pt $5d$ and Co $4p$ orbitals.

Figure 4

$T$-dependent Co $K$-edge XANESs of ${\mathrm{La}}_2{\mathrm{CoIrO}}_6$ and ${\mathrm{La}}_2{\mathrm{CoPtO}}_6$. The features denoted by $\alpha$ to $\eta$ coincide with those in Figs. 2 and 3. The preedge features ($\alpha$, $\beta$, and ${\beta }^{\prime }$) are nearly independent of $T$ even up to room temperature, suggesting that the Co $4p$-Ir/Pt $5d$ orbital hybridization should play a substantial role in determining the magnetic orders in the $3d-5d$ DP systems at $T$ even far above the Curie temperature.

Figure 5

$T$-dependent XANESs of (a) ${\mathrm{La}}_2{\mathrm{CoIrO}}_6$ and (b) ${\mathrm{La}}_2{\mathrm{CoPtO}}_6$ at Ir/Pt $L_3$ edges. The electronic structures of Ir/Pt $5d$ orbitals barely evolved with thermal disorders (with increasing $T$).

Figure 6

Schematic diagrams of hybridized orbital states of (a) (Ir/Pt $5d$ $j_{\mathrm{eff}}=1/2$)-(Co $3d$ $t_{2g}$) and (b) (Ir/Pt $5d$ $e_g$)-(Co $3d$ $e_g$ that is mixed with Co $4p$). The unoccupied $5d$ $e_g$ as well as the involvement of nonmagnetic Co $4p$ in the Co-O-Ir hybridization would not contribute to a spin ordering resulting in a paramagnetism, as is highlighted by the staggering spins in the energy level diagram in (b). The relevant spectroscopic techniques to observe the orbital hybridizations with peak assignments are also depicted.