Effect of Ti-doping on the dimer transition in Lithium Ruthenate

We carried out a comprehensive crystal structure characterization of Ti-doped lithium ruthenate (Li$_2$Ti$x$Ru${1-x}$O$_3$), to investigate the effect of Ti-doping on the structural phase transition. Experimental tools sensitive to the average structure (X-ray diffraction), as well as those sensitive to local structure (Extended X-ray Absorption Fine Structure, EXAFS; pair distribution function, PDF) are used. We observed non-monotonic dependence of the structural transition temperature on the Ti-doping level. At low doping, the transition temperature slightly increases with doping, while at high doping, the temperature decreases significantly with doping. We note two important observations from our studies. First, Ti K-edge EXAFS data shows persistent Ti-Ru dimerization even with substantial Ti doping. Second, we were able to use the PDF data to estimate the dimer correlation length above the transition temperature, which would correspond to the size of the proposed local `dimer clusters’ formed by Ru-Ru and Ti-Ru neighbours. The dimer correlation length is found to be around 10~Å, which remains robust regardless of doping. Our study therefore suggests that Ti$^{4+}$ with its $d^0$ electronic configuration is a special type of dopant when replacing Ru.

💡 Research Summary

This study investigates how substituting Ti⁴⁺ (d⁰) for Ru⁴⁺ in the honeycomb lattice compound Li₂RuO₃ influences its well‑known dimerization transition. A series of polycrystalline Li₂TiₓRu₁₋ₓO₃ samples (0 ≤ x ≤ 0.5) were synthesized by solid‑state reaction, and their structures were probed using complementary techniques that sense the average lattice (X‑ray diffraction, XRD) and the local atomic environment (Ti and Ru K‑edge EXAFS, pair‑distribution‑function analysis, PDF).

XRD measurements as a function of temperature reveal a clear jump in unit‑cell volume at the transition for all compositions. By fitting the temperature dependence of the volume with a sigmoid function superimposed on a linear thermal‑expansion term, the transition temperature (T_c) and the width of the transition were extracted. At low Ti concentrations (x ≤ 0.15) T_c rises modestly from ~550 K (undoped) to ~600 K, indicating that a small amount of Ti actually stabilizes the dimer‑ordered phase. Above x ≈ 0.20, T_c decreases linearly (≈ 775 K – 1050 K·x), a non‑monotonic behavior that contradicts a simple percolation picture and suggests a more subtle competition between dimer formation and disorder.

Ti K‑edge EXAFS performed at room temperature shows a first peak near 1.5 Å corresponding to Ti–O bonds, confirming that Ti occupies the Ru octahedral site. Importantly, three additional peaks align with the three characteristic Ru–Ru distances (a₃, a₁, a₂) identified in the low‑temperature monoclinic structure. The presence of the a₃ peak (the short “dimer” distance) in every doped sample demonstrates that Ti–Ru dimers persist even at high Ti content. This is unexpected because dimerization in the parent compound is usually attributed to Ru–Ru molecular‑orbital formation; the data imply that Ti⁴⁺ can participate in a comparable σ‑bond with neighboring Ru, despite its d⁰ configuration. Ru K‑edge EXAFS corroborates that Ru–Ru dimers remain partially intact across the series.

PDF analysis, which captures correlations beyond the nearest neighbor, reveals a dimer correlation length of roughly 10 Å above the transition for all compositions. This length does not change with Ti concentration, indicating that short‑range dimer clusters (both Ru‑Ru and Ti‑Ru) survive in the high‑temperature “dimer‑liquid” phase. The robustness of this correlation length suggests that Ti introduces disorder without destroying the underlying network topology of dimers.

Taken together, the results paint a nuanced picture of Ti doping: (1) Ti⁴⁺ has an ionic radius (74.5 pm) almost identical to Ru⁴⁺ (76 pm), so lattice strain is minimal; (2) despite being electronically inert, Ti⁴⁺ forms short Ti‑Ru bonds that mimic Ru‑Ru dimers, effectively sharing the dimer network; (3) at low concentrations this sharing reinforces the ordered dimer phase, raising T_c, while at higher concentrations the cumulative disorder suppresses long‑range dimer order, lowering T_c. This behavior contrasts sharply with previous dopants such as Mn, Ir, or Li, which either introduce magnetic moments or large size mismatches and thus act as “strong” perturbations.

The non‑monotonic T_c trend underscores that the transition from a valence‑bond solid (ordered dimers) to a valence‑bond liquid (disordered dimers) is governed not merely by the dilution of Ru sites but by the balance between dimer bond strength and the spatial extent of dimer clusters. The persistence of a ~10 Å correlation length across the series suggests that the “liquid” phase retains a characteristic cluster size, a hallmark of a cooperative, yet locally disordered, electronic state.

These findings open several avenues for future work. Because Ti⁴⁺ does not carry a magnetic moment, it provides a clean platform to study how structural disorder alone influences the exotic physics predicted for 4d⁴ systems, such as excitonic magnetism arising from a J_eff = 0 ground state. Applying external pressure or strain, or combining Ti doping with other perturbations (e.g., carrier doping), could tip the balance toward novel quantum phases, including possible spin‑liquid or unconventional superconducting states. Moreover, the demonstrated ability of a d⁰ ion to participate in dimer bonding may inspire similar studies in other honeycomb or kagome lattices where valence‑bond physics is central.

In summary, the paper delivers a comprehensive structural investigation of Ti‑doped Li₂RuO₃, revealing that Ti⁴⁺ acts as a “special” dopant that both preserves short‑range dimer correlations and modulates the long‑range ordering temperature in a non‑monotonic fashion, thereby enriching our understanding of valence‑bond solids and liquids in strongly spin‑orbit‑coupled 4d transition‑metal oxides.