Effect of delithiation on the dimer transition of the honeycomb-lattice ruthenate ${\mathrm{Li}}_{2-x}{\mathrm{RuO}}_3$

The honeycomb-lattice ruthenate ${\mathrm{Li}}_2{\mathrm{RuO}}_3$ is made heavily Li deficient by chemical oxidation by iodine. The delithiation induces a different phase ${\mathrm{Li}}_{2-x}{\mathrm{RuO}}_3$, the “D phase,” with superlattice. For the first time we disclose the magnetic and structural properties of the D phase in the dimer-solid state. The low-temperature magnetic susceptibility and the bond lengths indicate a bonding configuration consisting of both ${\mathrm{Ru}}^{4+}\text{−}{\mathrm{Ru}}^{4+}$ and ${\mathrm{Ru}}^{5+}\text{−}{\mathrm{Ru}}^{5+}$ dimers.

Figure 1

Composition variations of the high-energy powder XRD spectra at room temperature of ${\mathrm{Li}}_{2-x}{\mathrm{RuO}}_3$ samples with $x=0$, 0.34, and 0.73, taken with x rays of 30.993 keV $(\lambda =0.4000$ Å) at beam line ID22 of the ESRF. Data in the ranges (a) $0^{\circ }<2\theta <{20}^{\circ }$, (b) $3^{\circ }<2\theta <4.5^{\circ }$, and (c) $4.5^{\circ }<2\theta <6.5^{\circ }$. The peak indices of the stoichiometric ${\mathrm{Li}}_2{\mathrm{RuO}}_3$ are shown in (c) based on the room-temperature crystal structure reported by Miura et al. [9]. The $\left(10\overline{1}\right)$ peak is characteristic of the dimer-solid state [9, 12].

Figure 2

Rietveld refinement of the $\mathrm{Cu}K\alpha$ XRD $(\lambda =1.54184$ Å, $E=8.041$ keV) of samples of (a) ${\mathrm{Li}}_2{\mathrm{RuO}}_3$ with $x=0$ and (b) ${\mathrm{Li}}_{2-x}{\mathrm{RuO}}_3$ with $x=0.73$. In both cases SG $P{2}_1/m$ was used. Parameters of the fitting are listed in Table 1. The structure factor used in both cases is that of ${\mathrm{Ru}}^{4+}$ because the structure factors of ${\mathrm{Ru}}^{5+}$ are not available in our software. The measurement time for $x=0.73$ was approximately twice as long as that for $x=0$.

Figure 3

Bond lengths $L_1,L_2$, and $L_3$ of the S phase and D phase. The sum of the bond lengths $L_{\mathrm{T}}$ is given by $L_1+L_2+L_3$. Blue and brown spheres represent Ru and Li ions, respectively; red and green bars, short and long bonds. Figures were prepared with the program VESTA [25].

Figure 4

Temperature variations of the high-energy XRD spectra for the $x\approx 0.73$ sample with $E=87.5$ keV $(\lambda =0.141$ Å) measured at beam line ID11 of the ESRF. Colors of the spectral curves correspond to the temperature region in the magnetization curve of the $x\approx 0.73$ sample in Fig. 5. Inset: Spectra in the range $0.7^{\circ }<2\theta <1.5^{\circ }$. Spectra for 302 to 664 K were obtained during the heating process, while the spectrum at 333 K was measured after cooling. Vertical lines at the bottom indicate the expected peak positions for ${\mathrm{Li}}_2{\mathrm{RuO}}_3$ and ${\mathrm{RuO}}_2$.

Figure 5

Magnetic susceptibility vs temperature of the $x=0$ sample (S phase) and the $x\approx 0.73$ sample (mostly D phase) from 1.8 to 700 K at $H=10$ kOe. Corrections of diamagnetic contributions of ion cores have been made [27]. From 1.8 to 300 K, the magnetization was measured during warm up after ZFC. From 300 to 700 K the magnetization was measured in temperature upsweep, except for the purple curve, which is for the molar susceptibility of ${\mathrm{Li}}_2{\mathrm{RuO}}_3$ contained in the $x\approx 0.73$ sample upon cooling from 700 to 300 K (see text). Results of the Curie-Weiss fitting $[\chi =C/(T-\mathrm{\Theta })+{\chi }_0]$ are also shown, by dashed curves. Colors of the curve for $x\approx 0.73$ correspond to those in Fig. 4.

Figure 6

Magnetic susceptibility vs temperature of (a) ${\mathrm{Li}}_2{\mathrm{RuO}}_3$ and (b) ${\mathrm{Li}}_{2-x}{\mathrm{RuO}}_3$ $\left(x\approx 0.73\right)$ from 1.8 to 45 K at different magnetic fields measured in ZFC (filled symbols) and FC (open symbols) processes.

Figure 7

Molecular orbital diagrams of possible configurations of the dimers of ${\mathrm{Li}}_2{\mathrm{RuO}}_3$ (S phase) and ${\mathrm{Li}}_{2-x}{\mathrm{RuO}}_3$ (D phase). Molecular orbitals in the dimer-solid state consisting of (a) ${\mathrm{Ru}}^{4+}\text{−}{\mathrm{Ru}}^{4+}$, (b) ${\mathrm{Ru}}^{5+}\text{−}{\mathrm{Ru}}^{5+}$, and (c) ${\mathrm{Ru}}^{4+}\text{−}{\mathrm{Ru}}^{5+}$ dimers, respectively. The configuration in (c) is less likely to occur based on the observed magnetic susceptibility. (d) Molecular orbitals in the dimer-liquid state formed by ${\mathrm{Ru}}^{4+}\text{−}{\mathrm{Ru}}^{4+}$ ions proposed in Ref. [12]. $B$ is the bond order defined by Eq. (3).

Figure 8

High-energy XRD spectra of pristine ${\mathrm{Li}}_2{\mathrm{RuO}}_3$ sample at three temperatures: below $T_{\mathrm{d}}\sim 550$ K, close to $T_{\mathrm{d}}$, and above $T_d$ . It shows the coexistence of the dimer-solid and dimer-liquid states, which is typical of a first-order transition. Blue arrows indicate peaks characteristic of the dimer-solid state; red arrows, peaks of the dimer-liquid state. Measurements with $E=87.5$ keV $(\lambda =0.141$ Å) were performed at beam line ID11 of ESRF.