Beyond layer stacking: molecular Ru₂O₉ dimer correlations in pressure-synthesized Ba₃NbRu₂O₉

Abstract

Ruthenium-based oxides featuring face-sharing octahedra provide a powerful chemical platform for tuning correlated electronic states through direct metal–metal interactions and valence control. Here we report the high-pressure, high-temperature synthesis and comprehensive characterization of Ba₃NbRu₂O₉, a previously unreported 6H-type hexagonal perovskite. Single-crystal and powder X-ray diffraction measurements confirm a fully ordered structure composed of face-sharing Ru₂O₉ dimers separated by corner-sharing NbO₆ octahedra, crystallizing in the P6₃/mmc space group. Charge balance analysis reveals an unusually low mixed Ru³⁺/Ru⁴⁺ oxidation state (nominal Ru^3.5+), representing a reduced Ru valence realized within the Ba₃MRu₂O₉ family. Magnetic susceptibility measurements show Curie–Weiss behavior at high temperatures with an effective magnetic moment of 2.39μ_B per formula unit and a negative Curie–Weiss temperature, indicating predominant antiferromagnetic interactions. Below ∼15 K, a bifurcation between zero-field-cooled and field-cooled susceptibilities emerges, while the absence of a frequency-dependent shift in AC susceptibility and the lack of a λ-type anomaly in specific heat down to 1.8 K indicate a frozen spin state with short-range correlations rather than long-range magnetic order or a canonical spin-glass transition. Electrical transport measurements reveal a broad resistivity maximum near 35 K followed by a low-temperature upturn and pronounced positive magnetoresistance. Remarkably, the temperature dependence of resistance closely resembles that of the nine-layer BaRuO₃ polytype, despite the structural similarity of Ba₃NbRu₂O₉ to the four-layer phase. These results demonstrate that the electronic and magnetic properties of Ba₃NbRu₂O₉ are governed primarily by the molecular electronic state of the Ru₂O₉ dimers rather than by crystallographic stacking alone, underscoring the central role of dimer-based correlations in low-valence ruthenates.

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Introduction

Ruthenium-based oxides have attracted sustained interest because the extended 4d orbitals of Ru and their strong hybridization with oxygen give rise to rich electronic behavior that often defies simple ionic descriptions. In barium ruthenates, substantial Ru–O covalency frequently invalidates strict integer oxidation-state assignments, leading instead to fractional valence states and itinerant or correlated electronic behavior.¹ When combined with face-sharing RuO₆ octahedra, this electronic flexibility enables direct Ru–Ru interactions and the formation of structural motifs such as dimers, trimers, and extended chains, whose electronic and magnetic properties are highly sensitive to cluster connectivity and Ru–Ru bonding. Layered BaRuO₃ polytypes provide a prototypical example of this structure–property interplay. The four-layer (4H) form, composed of RuO₆ dimers, behaves as a correlated metal, whereas the nine-layer (9R) polytype, containing linear chains of face-sharing trimers, exhibits a low-temperature resistivity upturn.² These contrasting behaviors within the same chemical composition demonstrate that subtle changes in Ru–Ru connectivity and cluster topology can dramatically reshape the low-energy electronic landscape of ruthenium oxides. Within this broader context, the hexagonal perovskite family Ba₃MRu₂O₉ offers a particularly versatile platform for systematically tuning Ru valence and dimer-based electronic states. These compounds crystallize in a 6H-type structure consisting of face-sharing Ru₂O₉ dimers separated by corner-sharing MO₆ octahedra, with the formal Ru oxidation state determined by the valence of the M-site cation. When M is tetravalent (e.g., Pr, Tb, Ce),³ Ru commonly adopts integer oxidation states such as Ru(IV), while divalent M-site substitutions (e.g., Co, Ni) stabilize Ru(V).^4–6 In systems containing odd-valent cations, including rare-earth and alkali metals, charge balance naturally leads to mixed-valent Ru states and enhanced tunability of magnetic and electronic behavior. For example, rare-earth members Ba₃RE(III)Ru₂O₉ typically host mixed Ru(IV/V) dimers,^7,8 whereas hydroxide-melt synthesis of Li- or Na-containing analogues stabilizes higher Ru(V/VI) oxidation states.⁹

Importantly, systematic trends reveal that decreasing the average Ru oxidation state shortens the Ru–Ru distance and strengthens intradimer interactions, promoting molecular-orbital-derived electronic states and unconventional magnetic responses. In contrast, higher-valent compounds with longer Ru–Ru separations approach the limit of weakly interacting spin-only moments.^10,11 These observations establish Ba₃MRu₂O₉ as a chemically tunable framework in which modest changes in valence and bonding can substantially alter emergent properties.

While hydroxide melts provide highly oxidizing conditions that stabilize elevated Ru oxidation states, comparatively little attention has been devoted to accessing the opposite regime of unusually reduced Ru valence within this structural family. High-pressure synthesis offers a complementary strategy by stabilizing dense frameworks capable of accommodating larger, more weakly oxidized cations and promoting shorter metal–metal contacts. Here we report the high-pressure, high-temperature synthesis and characterization of Ba₃NbRu₂O₉, a previously unreported 6H-type hexagonal perovskite containing mixed Ru³⁺/Ru⁴⁺ (nominal Ru^3.5+), representing the lowest Ru oxidation state realized to date within the Ba₃MRu₂O₉ family. This compound provides a new opportunity to examine how reduced valence and enhanced Ru–Ru interactions govern dimer-based electronic and magnetic behavior in 4d transition-metal oxides.

Experimental section

Synthesis of Ba₃NbRu₂O₉

Precursor preparation. The ambient-pressure precursor Ba₄NbRu₃O₁₂ was prepared by conventional solid-state reaction using BaCO₃, RuO₂, Nb₂O₅, and Ru powders (Alfa Aesar, 99.99%).¹² Initially, Ba₅Ru₂O₁₂ was synthesized by heating a stoichiometric mixture of BaCO₃ and RuO₂ in air at 1000 °C for 12 h. The resulting Ba₅Ru₂O₁₂ was then thoroughly mixed with RuO₂, Nb₂O₅, and Ru metal powder in the appropriate stoichiometric ratio. The mixture was heated in air in alumina crucibles at 1000 °C for 12 h, reground, pelletized, and subsequently annealed at 1100 °C for 12 h and 1300 °C for an additional 12 h to obtain phase-pure Ba₄NbRu₃O₁₂.

High-pressure high-temperature transformation. Polycrystalline Ba₃NbRu₂O₉ was obtained by transforming the Ba₄NbRu₃O₁₂ precursor under high-pressure and high-temperature conditions. The precursor powder was sealed in a Pt capsule, inserted into an alumina sleeve, and compressed using a Walker-type multi-anvil press.¹³ The pressure assembly consisted of a Ceramacast 646 octahedral pressure medium, a Re heater, and Toshiba Tungaloy tungsten-carbide anvils.¹⁴ The sample was compressed to 7 GPa at room temperature over 24 h, heated to 1350 °C, and held at that temperature for 3 h. The sample was then quenched to room temperature before slow decompression to ambient pressure. The resulting Ba₃NbRu₂O₉ product was stable in air.

Crystal structure determination. Single-crystal X-ray diffraction (SCXRD) was performed to determine the crystal structure. Small single-crystalline grains suitable for SCXRD were identified within the bulk high-pressure product, mechanically extracted under an optical microscope and selected based on their diffraction quality. The selected crystal (0.051 × 0.018 × 0.017 mm³) was mounted on a nylon loop with Paratone oil and measured at ambient conditions using a Rigaku XtaLAB Synergy Dualflex diffractometer equipped with a Hypix detector and a microfocus Mo Kα radiation source (λ = 0.71073 Å, 50 kV, 1 mA). Data were collected using ω scans, with optimal strategies generated by CrysAlisPro (Rigaku OD, version 1.171.42.101a, 2023). Data reduction included Lorentz and polarization corrections. Absorption corrections were applied using numerical Gaussian integration over a multifaceted crystal model,¹⁵ followed by empirical spherical harmonics scaling (SCALE3 ABSPACK).¹⁶ The structure was solved and refined using the SHELXTL software package.^17,18 Note that single crystals obtained from high-pressure synthesis are typically very small and may exhibit internal strain, lattice defects, or mosaicity introduced during synthesis, quenching, or decompression. These factors can affect the consistency of equivalent reflections and contribute to an elevated R_int and residual electron-density features. Despite these limitations, the refinement converged to a chemically reasonable structural model.

Powder X-ray diffraction and phase analysis. Phase purity of the bulk sample was verified by powder X-ray diffraction (PXRD). Crystals were ground into a fine powder and mounted on a zero-background single-crystal silicon holder. PXRD data were collected at room temperature using a Rigaku MiniFlex II diffractometer (Bragg–Brentano geometry, Cu Kα radiation, λ = 1.5406 Å) over a 2θ range of 5°–100° with a step size of 0.01° and a dwell time of 3 s per step. Rietveld refinement was performed using the GSAS-II software suite.¹⁹

Physical property measurements. Temperature- and field-dependent magnetic measurements were carried out using a Quantum Design Magnetic Property Measurement System (MPMS) over the temperature range 1.8–300 K in applied fields up to 9 T. AC susceptibility measurements were performed at frequencies between 10 and 1000 Hz. Electrical resistivity was measured using a standard four-probe configuration on pelletized samples with platinum contacts in a Quantum Design Physical Property Measurement System (PPMS) from 1.8 to 300 K. Specific heat measurements were conducted using a PPMS DynaCool equipped with a heat-capacity option over the temperature range 1.8–150 K.

Results and discussion

The high-pressure phase of Ba₃NbRu₂O₉ crystallizes in the hexagonal P6₃/mmc space group, as determined by single-crystal X-ray diffraction (SCXRD) (crystallographic details are provided in Tables S1 and S2). The bulk phase purity and structural consistency were verified by powder X-ray diffraction (PXRD) using the SCXRD-derived model. Rietveld refinement of the PXRD data (Fig. 1) yields a final weighted R-factor (wR) of 10.14% based on 7391 observations, which is considered satisfactory given the limited sample quantity and the internal strain commonly associated with metastable phases synthesized under high pressure. The refined PXRD profile is in good agreement with the SCXRD structural model, confirming the phase purity and crystallographic assignment. A two-phase Rietveld refinement suggests the presence of a minor BaRuO₃ impurity (∼7.7 wt%), while Ba₃NbRu₂O₉ remains the dominant phase. The presence of a minor BaRuO₃ impurity does not affect the overall magnetic and transport behavior. Structurally, Ba₃NbRu₂O₉ consists of face-sharing RuO₆ octahedral pairs forming Ru₂O₉ dimers arranged in a honeycomb network within the ab-plane. These dimers alternate along the c-axis with corner-sharing NbO₆ octahedra, generating the characteristic 6H-type hexagonal perovskite framework.²⁰ A related structural motif has been reported for the iridium analogue.²¹ However, whereas partial Nb/Ir site mixing (∼9 : 1 occupancy ratio) is observed in that system, no detectable cation disorder is found in Ba₃NbRu₂O₉.

Fig. 1 Powder X-ray diffraction (PXRD) pattern and crystal structure of high-pressure Ba₃NbRu₂O₉. The experimental data (red circles) are fitted by Rietveld refinement (black solid line), and the blue curve represents the difference between the observed and calculated profiles. Bragg reflection positions for Ba₃NbRu₂O₉ and BaRuO₃ are indicated by green and red tick marks, respectively. The structural model highlights the arrangement of face-sharing RuO₆ octahedra forming Ru₂O₉ dimers within the 6H-type hexagonal perovskite framework.

Bond-valence-sum (BVS) calculations²² based on the refined structural parameters yield oxidation states of +4.81 for Nb and +3.74 for Ru, in good agreement with the nominal charge balance and supporting a mixed Ru³⁺/Ru⁴⁺ configuration. It is important to note that BVS values reflect spatially (and potentially temporally) averaged oxidation states over the crystallographic Ru site and therefore may not fully capture the local electronic configurations within individual Ru₂O₉ dimers. This averaged structural picture is consistent with the magnetic behavior discussed below, where the susceptibility can be understood as a statistical average over multiple dimer spin configurations associated with distinct local electronic states. Among reported 6H-type perovskites of the general formula Ba₃MRu₂O₉, ruthenium typically adopts significantly higher oxidation states. For example, Ba₃M¹⁺Ru^5.5+₂O₉ (M = Li, Na)⁹ stabilizes Ru^5.5+, Ba₃M²⁺Ru⁵⁺₂O₉ (M = Ca, Co, Ni, Zn)^4,5,23,24 hosts Ru⁵⁺, Ba₃M³⁺Ru^4.5+₂O₉ (M = Y, In, La, Nd, Sm, Eu, Lu)^7,8 contains Ru^4.5+, Ba₃M⁴⁺Ru⁴⁺₂O₉ (M = Ce, Pr, Tb)³ stabilizes Ru⁴⁺. To our knowledge, no member of this structural family has previously exhibited a Ru oxidation state approaching +3.5. To further contextualize this unusually reduced valence, we compared the average Ru–O bond distances within the Ru₂O₉ dimers to those reported for other Ba₃MRu₂O₉ compounds (Fig. 2). As expected, the average Ru–O bond length systematically increases with decreasing Ru oxidation state, consistent with reduced coulombic attraction between the less positively charged Ru cations and surrounding oxide anions. In contrast, the intradimer Ru–Ru separation exhibits the opposite trend, decreasing as the Ru oxidation state is lowered (Fig. S1), reflecting enhanced direct metal–metal interaction in the more reduced regime.

Fig. 2 Dependence of the average Ru–O bond distance within the Ru₂O₉ dimers on the formal Ru oxidation state in Ba₃MRu₂O₉ compounds. Comparative data are included for M = Li, Na (Ru^5.5+);⁹ M = Ca, Co, Ni, Zn (Ru⁵⁺);^4,5,23,24 M = Y, In, La, Nd, Sm, Eu, Lu (Ru^4.5+);^7,8 and M = Ce, Pr, Tb (Ru⁴⁺).³ Literature sources are provided in the main text.

To probe the magnetic behavior of the high-pressure phase, temperature-dependent magnetic susceptibility measurements were performed under both zero-field-cooled warming (ZFCW) and field-cooled (FC) protocols (Fig. 3). Between 15 and 300 K, the ZFCW and FC curves overlap under applied magnetic fields ranging from 100 Oe to 50 kOe, indicating the absence of magnetic irreversibility in this temperature range. In contrast, a clear bifurcation between the ZFCW and FC susceptibilities emerges below approximately 15 K under an applied field of 10 kOe (left inset, Fig. 3), signaling the onset of a frozen spin state. The right inset shows the temperature derivative of χT, where χ was calculated as M/H under the applied magnetic field.²⁵ A pronounced anomaly in this derivative at low temperatures further supports the development of spin freezing.

Fig. 3 Temperature-dependent magnetic susceptibility of high-pressure Ba₃NbRu₂O₉ measured under zero-field-cooled warming (ZFCW) and field-cooled (FC) protocols at various applied magnetic fields. The left inset highlights the low-temperature region, showing the bifurcation between ZFCW and FC curves. The right inset displays the temperature derivative d(χT)/dT.

The observed magnetic response is consistent with frustrated magnetism accompanied by short-range correlations. Although a bifurcation between ZFC and FC susceptibilities is evident in the DC measurements, the absence of a clear frequency-dependent shift in the AC susceptibility peak (Fig. S2) argues against a canonical spin-glass transition.²⁶ Notably, a spin-glass ground state has been reported in Ba₃TiRu₂O₉ and attributed to significant Ti/Ru site disorder.²⁷ In contrast, Ba₃NbRu₂O₉ exhibits a chemically ordered structure without detectable mixing yet displays similar low-temperature spin freezing. This comparison suggests that the freezing behavior in the present compound is intrinsic to the Ru₂O₉ dimer network rather than arising from chemical disorder. The high-temperature magnetic susceptibility (100–300 K) measured under an applied field of 100 Oe is well described by the modified Curie–Weiss expression,

as shown in Fig. 4, where χ₀ represents the temperature-independent contribution, C is the Curie constant, and θ_cw is the paramagnetic Curie temperature. Least-squares fitting yields χ₀ = 1.04 × 10⁻³ emu mol⁻¹ Oe⁻¹ and θ_cw = −63.2 K, the negative value indicating dominant antiferromagnetic interdimer interactions. The extracted effective magnetic moment, µ_eff = 2.39µ_B f.u.⁻¹, lies between the Hund's-rule limits expected for S = 1/2 (1.73µ_B f.u.⁻¹) and S = 3/2 (3.87µ_B f.u.⁻¹). Given the possible presence of a minor impurity phase, the absolute value of µ_eff may contain some uncertainty because the magnetization was normalized using the total sample mass. Nevertheless, the intermediate value is consistent with a dimer-based magnetic state influenced by mixed valence and electronic correlations.

Fig. 4 Curie–Weiss fitting of the temperature-dependent magnetic susceptibility measured under zero-field-cooled warming (ZFCW) conditions in an applied field of 100 Oe over the temperature range 100–300 K. The inset shows the linear dependence of 1/(χ − χ₀) versus temperature used to extract the Curie constant and paramagnetic Curie temperature.

Because Nb⁵⁺ is nonmagnetic, the magnetic response of Ba₃NbRu₂O₉ originates predominantly from the Ru₂O₉ dimers. Owing to the short Ru–Ru separation, the relevant magnetic degrees of freedom are more appropriately described at the dimer level rather than in terms of isolated Ru ions. Within a molecular-orbital framework for a mixed-valent Ru–Ru dimer, multiple total spin configurations (e.g., S = 1/2 or S = 3/2; Fig. S3) may be stabilized depending on the competition among intradimer hopping, Hund's exchange, on-site Coulomb repulsion, and spin–orbit coupling.^28,29 The temperature dependence of the χT product provides insight into this dimer-based magnetism. Notably, χT does not exhibit clear saturation up to 300 K and already exceeds the Curie-limit value expected for an isolated S = 1/2 moment (0.375 emu K mol⁻¹ Oe⁻¹; Fig. S4), thereby excluding a simple S = 1/2 high-temperature limit. This behavior indicates that the extracted μ_eff reflects an apparent moment within an intermediate-temperature regime, where electronic correlations remain significant, rather than a fully uncorrelated paramagnetic limit. Consequently, a higher-spin dimer configuration (e.g., S = 3/2) cannot be excluded within the accessible temperature window. Importantly, Ba₃NbRu₂O₉ contains an unusually low mixed Ru³⁺/Ru⁴⁺ valence distributed over a single crystallographically unique Ru site. This implies electronic (valence) disorder at the microscopic level within the Ru–Ru dimers, leading to a distribution of local electronic configurations and spin states. The measured magnetic susceptibility therefore represents a thermal and configurational average over multiple dimer spin configurations on the experimental timescale, consistent with the structurally averaged mixed-valence state inferred from the BVS analysis.

Field-dependent magnetization measurements further support this picture (Fig. 5). At temperatures below 3 K, the magnetization exhibits a small hysteresis loop without saturation up to 5 T, consistent with short-range magnetic correlations and frozen spin components. In contrast, at temperatures above 50 K, the magnetization varies linearly with applied field, indicative of a paramagnetic state consistent with the Curie–Weiss analysis.

Fig. 5 Field-dependent magnetization of high-pressure Ba₃NbRu₂O₉ measured up to 5 T at selected temperatures. The low-temperature curves exhibit a small hysteresis without magnetic saturation, while higher-temperature data show linear field dependence characteristic of paramagnetic behavior.

The temperature-dependent specific heat of high-pressure Ba₃NbRu₂O₉ was measured under applied magnetic fields of 0 and 9 T over the range 1.8–150 K (Fig. 6a). A subtle deviation near 15 K is observed, consistent with the development of short-range magnetic correlations. However, no λ-type anomaly is detected down to 1.8 K, indicating the absence of long-range magnetic ordering within the measured temperature window. At elevated temperatures, the specific heat is dominated by lattice (phonon) contributions. To quantify the phonon background, the high-temperature data (30–150 K) were fitted using harmonic lattice models. Neither a single Debye model (eqn (2)) nor a single Einstein model (eqn (3)) alone provides an adequate description of the experimental data, necessitating a more comprehensive treatment of the lattice contribution.

where n is the number of atoms per formula unit, R is the gas constant, θ_D is the Debye temperature and θ_E is the Einstein temperature.

Fig. 6 (a) Temperature dependence of C_p/T for high-pressure Ba₃NbRu₂O₉ measured under applied magnetic fields of 0 T (black) and 9 T (red). (b) Fit of the specific heat data using a combined two-Debye–Einstein model (orange solid line). The green, red, and purple dotted curves represent the 1^st Debye, 2^nd Debye, and Einstein contributions, respectively.

The specific heat data in the temperature range 30–150 K are well described by a combined two-Debye–Einstein model (eqn (4)), as shown in Fig. 6b. The fitting yields characteristic temperatures of θ_D1 = 399(81) K, θ_D2 = 208(14) K, θ_E = 579(43) K, with corresponding oscillator strengths s_D1 = 5.0(5), s_D2 = 3.2(9), and s_E = 5.3(1.2). The total lattice heat capacity is expressed as

The resulting phonon model converges to a high-temperature heat capacity of 42(3)R, which is in good agreement with the Dulong–Petit limit of 3nR for n = 15 atoms per formula unit. This consistency confirms that the model provides a reasonable description of the phonon-dominated regime. Due to the absence of a nonmagnetic structural analogue, however, the magnetic contribution to the specific heat cannot be quantitatively isolated.

As shown in Fig. S5, the low-temperature specific heat in the range 1.8–10 K follows a linear dependence of C_p/T versus T², which is well described by

C_p/T = γ + βT² (5)

where γ = 0.0626(3) J mol⁻¹ K⁻² and β = 3.83(6) × 10⁻⁴ J mol⁻¹ K⁻⁴ represent the electronic and lattice contributions, respectively. The finite γ term indicates the presence of additional low-energy excitations beyond conventional acoustic phonons, consistent with correlated electronic or magnetic degrees of freedom. From the β coefficient, the Debye temperature can be estimated usingyielding θ_D = 424 K. This value is comparable to the characteristic Debye temperatures extracted from the high-temperature phonon model, demonstrating internal consistency between the low- and high-temperature lattice analyses.

The electrical transport data were normalized to their respective values at 300 K, where the absolute resistance ranges from approximately 0.25 to 0.28 Ω. The temperature dependence of the normalized resistance under applied magnetic fields up to 9 T is shown in Fig. 7 over the range 1.8–300 K. A broad resistivity maximum appears near 35 K, followed by an upturn upon further cooling, indicating a crossover from a relatively metallic regime to a weakly localized transport state. The magnitude of this maximum increases systematically with applied magnetic field, indicating positive magnetoresistance. Notably, this crossover closely resembles that reported for the nine-layer (9L) BaRuO₃ polytype, rather than the four-layer (4L) phase, despite the structural analogy of Ba₃NbRu₂O₉ to the 4L stacking motif. This comparison suggests that transport in Ba₃NbRu₂O₉ is governed primarily by the molecular electronic structure of the Ru₂O₉ dimers, particularly mixed valence and correlated spin or charge fluctuations, rather than by the crystallographic stacking sequence alone. Further electronic structure calculations would help clarify the microscopic origin of this transport behavior.

Fig. 7 Temperature dependence of the normalized electrical resistance of Ba₃NbRu₂O₉ under applied magnetic fields up to 9 T. The resistance is scaled to its respective value at 300 K for each field.

The resemblance to the transport behavior of 9L-BaRuO₃ further indicates that the dominant energy scale for charge transport is set by intra-dimer electronic interactions. In the present system, the short Ru–Ru distance and mixed-valence configuration favor the formation of molecular orbitals within the Ru₂O₉ dimers, including partially occupied antibonding states. This electronic structure can lead to enhanced carrier scattering from low-energy spin and charge fluctuations localized on the dimers. Within this framework, the broad resistivity maximum is interpreted as a crossover from a high-temperature incoherent transport regime to a low-temperature state dominated by local electronic correlations and fluctuation-driven scattering, rather than a simple gap opening or polaronic freezing. This interpretation is consistent with the absence of a sharp anomaly in the specific heat and the presence of short-range magnetic correlations inferred from susceptibility measurements.

Conclusion

In summary, we have synthesized and characterized Ba₃NbRu₂O₉, a new member of the Ba₃MRu₂O₉ family stabilized under high-pressure and high-temperature conditions. Structural analysis confirms a fully ordered 6H-type hexagonal perovskite framework composed of face-sharing Ru₂O₉ dimers separated by NbO₆ octahedra, with bond-valence analysis indicating an unusually low mixed Ru³⁺/Ru⁴⁺ configuration corresponding to a nominal oxidation state of +3.5, the most reduced Ru valence reported to date within this structural family. Magnetic measurements reveal Curie–Weiss behavior with dominant antiferromagnetic interactions and the emergence of a frozen spin state with short-range correlations below ∼15 K, in the absence of long-range magnetic order or a canonical spin-glass transition. The extracted effective moment reflects an intermediate-temperature average over multiple dimer spin configurations, consistent with a molecular-orbital description of mixed-valent Ru–Ru dimers governed by competing hopping and correlation effects, while specific heat data further support this picture by showing no sharp thermodynamic anomaly but evidence of additional low-energy excitations. Electrical transport measurements place Ba₃NbRu₂O₉ in a weakly localized regime characterized by a broad resistivity maximum, low-temperature upturn, and positive magnetoresistance. The similarity of its transport behavior to that of nine-layer BaRuO₃, despite structural analogy to the four-layer polytype, demonstrates that crystallographic stacking alone does not dictate the electronic response; rather, the molecular electronic structure of the Ru₂O₉ dimers plays the central role in governing correlated behavior. These results establish Ba₃NbRu₂O₉ as a new chemically accessible platform for investigating low-valence dimer-based correlations in 4d transition-metal oxides.

Conflicts of interest

The authors declare no conflict of interests.

Data availability

The datasets supporting this article have been uploaded as part of the supplementary information (SI). Supplementary information: the crystal structure and refinement of Ba₃NbRu₂O₉; atomic coordinates and equivalent isotropic atomic displacement parameters; variation of the average Ru–Ru bond distance with Ru oxidation state; temperature-dependent AC magnetic susceptibilities at various frequencies; energy-level and spin occupation diagram for a hybridized Ru^3.5+–Ru^3.5+ dimer; the temperature dependence of χT; low-temperature heat capacity plotted as C_p/T vs. T². (DOS). See DOI: https://doi.org/10.1039/d6dt00401f.

Data is available from the authors upon reasonable request.

CCDC 2549437 for Ba₃NbRu₂O₉ contains the supplementary crystallographic data for this paper.³⁰

Acknowledgements

The work at Michigan State University is supported by NSF-DMR-2422361. The work at the University of Michigan was supported by NSF-DMR-2422362.

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