Defect control in the Heisenberg-Kitaev candidate material NaRuO₂

Polycrystalline members of the Na_3+xRu_3-xO₆ solid solution were synthesized using the same mechanochemical methods detailed in our recent work [4]. Na₂O₂ beads (Sigma, 97%), RuO₂ powder (Alfa, 99.95%), and Na metal (Alfa 99.8%) were combined in a pre-seasoned tungsten carbide ball mill vial and sealed under Ar. Due to the volitility of Na and and potential oxygen off-stoichiometry in RuO_2-x, adjustments are required to the nominal Na:Ru:O ratios. Specifically, both the compositions for Na₂RuO₃ and NaRuO₂ were empirically tuned to yield phase-pure compositions at Na_1.07(RuO₂)_1.13(Na₂O₂)_0.70 (Na_2.0Ru_0.9O_3.0) and Na_1.07(RuO₂)_1.37(Na₂O₂)_0.37 (Na_1.0Ru_0.8O_2.0) respectively. Using a combination of excess Na metal, Na₂O₂ and RuO₂, we iteratively narrowed down the single-phase region of the NaRuO₂–Na₂RuO₃ alloy, adjusting the compositional vectors until secondary phases were eliminated. All alloys were generated through a subsequent linear interpolation of the tuned compositions of Na₂RuO₃ and NaRuO₂. Empirical tuning and interpolation is essential, as the compensating ratio of Na:Ru:O that yields phase pure NaRuO₂ is not the same as the compensation required for Na₂RuO₃.

The resulting mixture was milled for 60 min in a Spex 8000D Mixer/Mill using four 7.9 mm tungsten carbide balls. The reaction generates a substantial amount of heat, and care must be taken with large sample volumes. The resulting precursor is confirmed amorphous by powder x-ray diffraction. The milled powder was then lightly ground in an agate mortar under Ar to disperse any agglomerates, sieved through a 100 micron sieve, and loaded into 2 mL alumina cylindrical crucibles (CoorsTek). In addition, a small portion of the milled powder was cold-pressed into 5 mm diameter pellets and buried within the powder bed. The crucibles were subsequently sealed under 1 atm of Ar in fused silica ampoules and placed within a 900^∘C preheated furnace. Samples were annealed for 30 min and then immediately air-quenched before extracting powders under Ar. The final powders and sintered pellets are largely phase pure with trace amounts of Ru metal ($<$2 %). Powders are black and moisture sensitive, with sensitivity increasing dramatically with additional Na content.

Phase purity was initially examined with powder x-ray diffraction (XRD) measurements at room temperature on a Panalytical Empyrean diffractometer (Cu K${}_{\alpha_{1,2}}$) in Bragg-Brentano ($\theta$-$\theta$) geometry. Na_3+xRu_3-xO₆ powders were placed on a Si zero-diffraction plate under argon and capped with a 12 mm$\times$12 mm piece Kapton film to shield against atmospheric moisture. Pawley and Rietveld refinements were performed using TOPAS Academic v6 [10]. Structural models and visualization utilized the VESTA software package [11].

Temperature dependent dc-magnetization data under zero-field-cooled (ZFC) and field-cooled (FC) conditions were collected on a 7 T Quantum Design Magnetic Property Measurement System (MPMS3) SQUID magnetometer. Samples were sealed in polypropylene holders under argon to minimize absorption of atmospheric moisture. Data was collected continuously in sweep mode with a ramp rate of 2 K/min in the presence of an external DC field of 1000 Oe. Isothermal dc-magnetization measurements at 2 K were collected continuously in sweep mode with a ramp rate of 100 Oe/sec.

Resistivity measurements were performed on sintered pellets of Na_3+xRu_3-xO₆ that were sectioned into rectangular bars with approximate dimensions of 1$\times$2$\times$0.5 mm. Electrical contacts were made in a standard four-point geometry with contacts being made with a combination of gold wire and silver paint. Thermal contact and electrical isolation was ensured using layers of GE varnish and cigarette paper. The temperature dependence of the electrical resistivity was measured with the Electrical Transport Option (ETO) in a 9 T Quantum Design Dynacool Physical Property Measurement System (PPMS) using a drive current of 10 $\mu$A and drive frequency of 100 Hz. Data was collected continuously in sweep mode with a ramp rate of 2 K/min.

Motivated by the combination of strong spin-orbit coupling, the expanded nature of the Ru $d$-orbitals, and remnant Coulomb interaction effects, ruthenates have continued to garner substantial attention. Owing to the many stable oxidation states of Ru, the Na–Ru–O phase diagram is remarkably complex. Within a relatively narrow set of chemical potentials there are at least 7 reported Na–Ru–O ternary compounds: NaRuO₂ [12], NaRu₂O₄ [13], Na₂RuO₃ [9], Na₃RuO₄ [14], Na₂RuO₄ [9], Na₂₇Ru₁₄O₄₈ [15], and Na_3-xRu₄O₉ [16].

NaRuO₂ is of particular interest due to the triangular sublattice of Ru³⁺ and the potential applications as a QSL candidate material [4]. Remarkably, a survey of adjacent phases to NaRuO₂ reveals the “disordered” ($R\bar{3}m$) polymorph of Na₂RuO₃ is structurally identical to NaRuO₂, except for the random dilution of the Ru³⁺ triangular sublattice with nonmagnetic Na${}_{\text{Ru}}$ defects. It is important to note that while Na₂RuO₃ can also crystallize in a ordered $C2/c$ monoclinic structure, it is not clear which phase is the thermodynamic ground state.

Such a relationship and the resulting potential for off-stoichiometry in NaRuO₂ is supported by a comparison the available crystallographic data. The original synthesis procedure reported for NaRuO₂ involves a three step decomposition process where: 1) \ceNa2RuO4 was synthesized from a stoichiometric mixture of \ceNa2O2 and \ceRuO2, 2) stoichiometric amounts of \ceNa2RuO4 and Ru metal were mixed, dried, and sealed inside gold tubing, and finally 3) the mixture was heated at 1173 K for 12 h and then 1273 K for 120 h [13]. This processing route produces material with lattice parameters [$a,c$] : [3.02 Å, 16.49 Å]. We have developed a new, rapid, mechanochemical route for the synthesis of NaRuO₂ [4], which is the method utilized in the present study. This processing route renders NaRuO₂ with lattice parameters [3.06 Å, 16.18 Å].

The difference observed in the $c$-axis lattice parameters reported in this work [4] and prior work by Shikano et al. [12] is substantial and noteworthy. One potential origin of this discrepancy is the impact of Na off-stoichiometry, which would naturally impact the interlayer spacing. Looking to the analogous titanate structure (Na_1-xTiO₂), detailed structural studies have identified a contraction along c and an expansion in a as Na-vacancies were eliminated and the composition approached nominal NaTiO₂ [8]. We suggest that the smaller c-axis lattice parameter of NaRuO₂ synthesized via the mechanochemical route presented herein are closer to the ideal 1:1:2 stoichiometry. This is further supported by our previous neutron powder diffraction refinement [4], which indicates that the tuned NaRuO₂ composition is stoichiometric within the resolution of our measurement. The discrepancy between the prior report and our results suggests that off-stoichiometry and defect control are important factors in NaRuO₂.

Drawing inspiration from the thermoelectric community and the concept of “phase boundary mapping” [17, 18, 19, 20], we sought to map the phase space surrounding NaRuO₂. Wide swaths of the space immediately surrounding NaRuO₂ are dominated by 2-phase equilibria, which is unexpected if NaRuO₂ is a prototypical line compound. This is instead consistent with the formation of a large single-phase region or an extended alloy. Furthermore, NaRuO₂ shows an unusual proclivity to incorporate excess Na into the structure. Considering the structural similarity of disordered Na₂RuO₃, we suspected that a solid solution between NaRuO₂ and Na₂RuO₃ could exist. In support of this conjecture, synthesizing Na₂RuO₃ using the same synthetic conditions as NaRuO₂ results in the formation of disordered $R\bar{3}m$ Na₂RuO₃. This disordered Na₂RuO₃ polymorph persists after extended annealing and appears to be the stable structure under our processing conditions.

To verify the solid-solution hypothesis, a series of samples ranging from NaRuO₂–Na₂RuO₃ were synthesized. For the sake of convenience, we will refer to the series using the renormalized stoichiometry Na_3+xRu_3-xO₆ where the end members of $x$=0 and $x$=1 correspond to nominal NaRuO₂ and Na₂RuO₃, respectively. As illustrated in Fig. 2, x-ray diffraction data confirm that the series of alloys constructed along the NaRuO₂–Na₂RuO₃ pseudobinary phase diagram are predominantly single phase, with a only a small secondary fraction of Ru metal. In the spirt of phase-boundary mapping [20, 18, 19, 17], this impurity was intentionally introduced to pin the samples to the Ru-rich edge of the single-phase region. Significant changes in peak positions and the corresponding lattice parameters (Fig. 3) are clearly observed in the x-ray scattering measurements.

A summary of the changes in the crystallographic parameters accompanying the transition from NaRuO₂ to Na₂RuO₃ is presented in Fig. 3. The cell volume increases both monotonically and linearly from NaRuO₂ ($x$=0) to Na₂RuO₃ ($x$=1), consistent with Vegard’s Law. This serves as confirmation of a solid solution, and further highlights the propensity for the formation of Na${}_{\text{Ru}}$ antisite defects in NaRuO₂. Unexpectedly, the off-stoichometry of disordered Na₂RuO₃ is similarly complex and has the ability to absorb excess Na up to $x$=4/3. Past this point, samples become multiphase and exhibit a mixture of Na-rich Na_3+xRu_3-xO₆ and Na₃RuO₄. It is interesting to note that the symmetry of Na₃RuO₄ (space group $C2/m$) is a subgroup for $R\bar{3}m$ and is structurally similar to NaRuO₂ and Na₂RuO₃ ($e.g.$ 6-coordinate Na/Ru, approximate planes of metal cations).

The volumetric expansion of the lattice observed in Fig. 3 with additional Na-loading can be rationalized through simple ionic radii arguments. In a 6-coordinate environment, the Shannon radius of Ru³⁺ is 0.68 Å and Ru⁴⁺ is 0.62 Å. While excess Na is expected to convert Ru³⁺ to Ru⁴⁺, the effect of substituting the much larger Na⁺ (1.02 Å) on Ru³⁺ dominates. Thus, a general expansion of the lattice is expected as Na${}_{\text{Ru}}$ defects accumulate.

The Na_3+xRu_3-xO₆ solid solution poses a synthetic challenge, particularly when the stoichiometry of polycrystalline NaRuO₂ needs to be tightly controlled. As illustrated in Fig. 3(b), the Na_3+xRu_3-xO₆ solid solution creates several large 2-phase (blue) regions where Na_3+xRu_3-xO₆  is at equilibrium with NaRu₂O₄ under O-rich conditions, Ru metal under O-poor conditions, and Na₃RuO₄ under Na-rich conditions. Three unique three-phase (gray) equilibria were identified between Na_3+xRu_3-xO₆–NaRu₂O₄–Ru, Na_3+xRu_3-xO₆–Na₂RuO₄–Na₃RuO₄, and Na_3+xRu_3-xO₆–Na₃RuO₄–Ru. In our experience, the NaRuO₂–Na₂RuO₃ alloy does not readily support off-stoichiometry in the Ru-rich direction beyond NaRuO₂. Employing the principles of phase boundary mapping, we would aim to synthesize NaRuO₂ under conditions that place it in equilibrium with NaRu₂O₄ and Ru metal. A convenient metric would be to minimize the cell volume of NaRuO₂.

Attempts to make samples in the O-rich region above nominal Na₂RuO₃ indicate the presence of at least one unknown Na–Ru–O ternary, complicating the mapping process. Although we would naïvely suspect samples to contain Na₂₇Ru₁₄O₄₈ [15], this phase could not be reproduced using the processing techniques described here. Considering the potential complexity in this region of the diagram, we refrain from postulating on the phase equilibria in this region. This is complicated by the existence of the Na_3-xRu₄O₉ solid-solution, creating large swaths of 2-phase regions. Future work will be required to fully understand the O-rich side of the Na–Ru–O phase diagram.

Regardless of the additional complexities present in the O-rich regime, the isothermal phase diagram presented here establishes a reliable method for Ru-rich processing of NaRuO₂, minimizing the substitution of nonmagnetic Na${}_{\text{Ru}}$ defects on the Ru triangular lattice. Compositions located in the three-phase NaRuO₂–NaRu₂O₄–Ru Alkemade triangle will reliably produce NaRuO₂ at the compositional invariant point where the ternary Alkemade triangle adjoins the vertex of the Na_3+xRu_3-xO₆ single-phase region. Tuning the composition to produce NaRuO₂ at this vertex with minimal contributions from Ru-metal and NaRu₂O₄ enables stoichiometry control in a system with a complex phase diagram containing volatile elements.

Our prior investigation on both the magnetic and electronic properties of stoichiometric NaRuO₂ identified the system as a magnetic insulator with a quantum disordered ground state [4]. Considering that Na₂RuO₃ was considered a distinct compound to date, the discovery of the Na_3+xRu_3-xO₆ solid solution should provide an experimental route to exploring the physical properties and possibly unique crossovers ($e.g.$ metal-to-insulator) between the endpoint members. However, literature reports on the magnetic and electronic properties of Na₂RuO₃ are varied. Much of the variation stems from the ambiguity whether the ordered or disordered polymorph is present. Even within studies focused predominantly on disordered Na₂RuO₃ or mixtures of the ordered/disordered phase, there are conflicting reports. Some works suggest insulating behavior with long-range antiferromagnetic order [21, 22], while others report a paramagnetic, moderately correlated electron metal with no observable magnetic excitations [23].

This lack of consensus on Na₂RuO₃ is likely driven by the existence of the Na_3+xRu_3-xO₆ solid-solution. Since Na₂RuO₃ is not a line compound, the stoichiometry of a given synthesis is not well-defined. In the case of disordered Na₂RuO₃, the majority of samples were produced as a product of decomposition reactions, yielding lattice parameters a : [3.11–3.17 Å] and c : [15.94-16.04 Å] [9, 24, 23]. One of the “hallmark” features of disordered Na₂RuO₃ in prior work is the merger of the (101) and (006) peak positions. In good agreement with prior literature, we find that the peak merger occurs with a=3.11 Å and c=15.94 Å. However, our nominal stoichiometry at that point is only $x$=2/3 instead of $x$=1. This is conceptually consistent with our findings that the Na–Ru–O systems require additional Na and O to compensate for volitility issues. Furthermore, Na incorporation continues well past the point of peak merger – and well beyond nominal Na₂RuO₃ (Fig. 3).

The Na_3+xRu_3-xO₆ solid solution presents an opportunity to study the defect-sensitivity of NaRuO₂ and the consequence of diluting the Ru-sublattice. We first address the electrical resistivity to determine whether all members of the Na_3+xRu_3-xO₆ solid solution remain insulating, or whether the Na${}_{\text{Ru}}$ defects cause any increase in the free carrier concentration. As illustrated in Fig. 4, the resistivity at room temperature for many of the series falls within the lightly doped semiconducting regime (10-100 m$\Omega$-cm), and rises exponentially with decreasing temperature. Both observations suggest that members of the Na_3+xRu_3-xO₆ solid solution up to $x$=2/3 are insulators or small-gap semiconductors.

The isothermal resistivity at 300 K (Fig. 4(inset)) exhibits an exponential increase with Na content, contradicting the most facile defect formation ($e.g.$ $\text{Na}_{\text{Ru}}+2\text{h})$ and instead supports the localization of holes via a shift of Ru into a higher oxidation state. The influence of poorly screened, higher charged Ru⁴⁺ – coupled with increased alloy/disorder scattering likely contribute to the strong resistivity increases. Potentially more complex compensation reactions such as oxygen vacancies could be present, and more research (e.g. DFT defect studies) will be important for fully understanding the defect energetics in the alloys. We note here that members with higher Na content ($x\geq$1) become progressively deliquescent and will condense atmospheric water on the surfaces, precluding reliable measurement of their resistivity.

The dc susceptibility data for select Na_3+xRu_3-xO₆ compositions are plotted in Fig. 5(a). A manual vertical offset has been introduced to facilitate a visual qualitative comparison, and an unscaled set of magnetization curves is included in the supplementary information for comparison [25]. Notably, an onset of irreversibility in the ZFC/FC curves appears in compositions with noninteger $x$. This irreversibility is absent in the stoichiometric $x$=0 end member above 2 K. Then, as summarized in Fig. 5(b), ZFC/FC irreversibility onsets at finite $x$ and increases in temperature as further disorder is introduced. Near the midpoint between NaRuO₂ and Na₂RuO₃, the irreversibility temperature reaches a local maximum and then begins to decrease again as $x=1$ is approached. In the nominal $x$=1 composition with uniform Ru⁴⁺ sites, the system naively assumes a $J_{\text{eff}}=0$ nonmagnetic singlet state and irreversibility vanishes. With continued Na loading beyond $x=1$, moments are reintroduced and a sharp reemergence of irreversibility occurs. It should be noted that as $x=0,1/6,1$ samples exhibit no discernible splitting by 2 K (though the curvature of $x=1/6$ is suggestive of a splitting proximal to 2 K), this lower limit on the onset of an irreversibility temperature is denoted as open circles in Fig. 5(b).

As illustrated in Figs. 5(c,d), the main qualitative trends presented in Fig. 5(b) are also reflected in the compositional dependence of the dc magnetization. Compositions with higher irrversibility temperatures exhibit larger coercivity, particularly for those samples where $x>1$ (Fig. 5(d)). Irreversibility in FC/ZFC data reflect that local Ru moments freeze, and Fig. 5(e) illustrates this freezing further in the Na-rich side of the phase diagram with ac-susceptibility measurements over the splitting temperature for $x$=2/3 and $x$=4/3. The ac-susceptibility data reveal a clear frequency-dependence associated with local moment freezing in both samples.

High activation energy barriers are obtained for both $x$=2/3 and $x$=4/3 (130 K and 640 K, respectively) when analysis is performed solely using the Arrhenius model. Attempting to utilize alternative models (e.g., Vogel-Fulcher) yield similarly unusual characteristic times. Understanding the freezing dynamics in the Na_3+xRu_3-xO₆ alloys will require more detailed measurements and neutron scattering measurements on single crystals. However, qualitatively these results demonstrate that the chemical and valence disorder imparted by Na${}_{\text{Ru}}$ defects throughout the magnetic sublattice acts to initiate freezing, consistent with our prior work suggesting that NaRuO₂ possesses a quantum disordered ground state [4].

It is worth stressing here that even in the nominal $x=0$ composition, a low-temperature cusp appears in the ac-susceptibility below 2 K [4]. Near 1.7 K, signs of partial moment freezing were observed, indicating a weak spin freezing transition and crossover in the low frequency spin dynamics. This crossover/partial freezing is likely driven by a small percentage of remnant Na defects ($\approx 1$ $\%$). This is consistent with the amplification of the freezing onset upon the intentional introduction of additional Na defects along the solid solution line between NaRuO₂ and Na₂RuO₃.