Effects of Mn-substitution on the valence bond solid in ${\mathrm{Li}}_2\mathrm{Ru}{\mathrm{O}}_3$

${\mathrm{Li}}_2\mathrm{Ru}{\mathrm{O}}_3$ with a honeycomb structure undergoes a drastic transition from a regular honeycomb lattice with the $C2/m$ space group to a valence-bond solid state of the $P{2}_1/m$ space group with an extremely strong dimerization at 550 K. We synthesized ${\mathrm{Li}}_2{\mathrm{Ru}}_{1-x}{\mathrm{Mn}}_x{\mathrm{O}}_3$ with a full solid solution and investigated doping effects on the valence-bond solid state as a function of Mn content. The valence-bond solid state is found to be stable up to $x=0.2$, based on our extensive experiments: structural studies, resistivity, and magnetic susceptibility. On the other hand, the extended x-ray absorption fine-structure analyses show that the dimer local structure remains robust even above $x=0.2$ with a minimal effect on the dimer bond length. This indicates that the locally disordered dimer structure survives well into the Mn-rich phase even though the thermodynamically stable average structure has the $C2/m$ space group. Our results prove that the dimer formation in ${\mathrm{Li}}_2\mathrm{Ru}{\mathrm{O}}_3$ is predominantly a local phenomenon driven by the formation of orbitally assisted metal-metal bonds and that these dimers are relatively robust against doping-induced disorder.

Figure 1

(a) The crystal structures of ${\mathrm{Li}}_2\mathrm{Mn}{\mathrm{O}}_3$ (top) and ${\mathrm{Li}}_2\mathrm{Ru}{\mathrm{O}}_3$ (bottom). Both have a layered honeycomb structure separated by ${\mathrm{Li}}^{+}$ ions, but only ${\mathrm{Li}}_2\mathrm{Ru}{\mathrm{O}}_3$ has strong dimerization. The dimer (red) bonds are 2.57 Å, whereas the nondimer (black) bonds are about 3.05 Å. In contrast, ${\mathrm{Li}}_2\mathrm{Mn}{\mathrm{O}}_3$ has regular intertransition-metal ion bonds in the range of 2.82–2.84 Å. (b) XRD data for the ${\mathrm{Li}}_2{\mathrm{Ru}}_{1-x}{\mathrm{Mn}}_x{\mathrm{O}}_3$ systems with the $P{2}_1/m$ space group for $x\le 0.2$ and the $C2/m$ space group for $x>0.2$.

Figure 2

(a) Unit-cell volumes of the ${\mathrm{Li}}_2{\mathrm{Ru}}_{1-x}{\mathrm{Mn}}_x{\mathrm{O}}_3$ systems refined by the Le bail method. The blue-green line is a fitting result for the systems' volume data with $x>0.2$, and the burgundy line is that of the systems with $0\le x\le 0.2$. (b) The lattice parameters $a$ (blue triangles), $b$ (red diamonds), and the interlayer distance ($csin\beta$, green snowflake) of ${\mathrm{Li}}_2{\mathrm{Ru}}_{1-x}{\mathrm{Mn}}_x{\mathrm{O}}_3$ systems. Both $b$ and $csin\beta$ decrease monotonically with increasing Mn doping, whereas $a$ maximum is about at Mn 40%. The orange line in (b) is a guide to the eyes. (c) The distortion parameter $u=\frac{b}{a\sqrt{3}}-1$ is plotted as a function of Mn doping.

Figure 3

(a) Normalized magnetic susceptibility data taken at $H=1\mathrm{T}$ for ${\mathrm{Li}}_2{\mathrm{Ru}}_{1-x}{\mathrm{Mn}}_x{\mathrm{O}}_3$ systems. (b) Normalized resistivity data with $I=10\mu \mathrm{A}$ for ${\mathrm{Li}}_2{\mathrm{Ru}}_{1-x}{\mathrm{Mn}}_x{\mathrm{O}}_3$ systems. The black arrows indicate the phase-transition temperature of each resistivity curve. (c) Resistivity phase-transition temperature ($T_{\mathrm{Res}}$, left) and the ${\mathrm{Li}}_2{\mathrm{Ru}}_{1-x}{\mathrm{Mn}}_x{\mathrm{O}}_3$ systems' resistivity at 600 K (right). The red dashed line and the equation are a line fitting result of the transition temperatures.

Figure 4

(a) The $k^3$-weighted Fourier transform magnitudes of the Ru $K$-edge EXAFS spectra of the ${\mathrm{Li}}_2{\mathrm{Ru}}_{1-x}{\mathrm{Mn}}_x{\mathrm{O}}_3$ ($x=0$, 0.05, 0.1, 0.2, and 0.4) systems. (b) The doping dependency of the intertransition metal distances of Ru and Mn in the honeycomb layer. The blue circles (red diamond) indicate Ru dimer's lengths (interdimer), and the green squares indicate the distance between Ru and Mn. (c) Temperature dependence of the EXAFS spectra of ${\mathrm{Li}}_2{\mathrm{Ru}}_{0.9}{\mathrm{Mn}}_{0.1}{\mathrm{O}}_3$. The temperature dependencies of (d) the distances between Ru and Mn in the honeycomb layer and (e) their thermal factors. The black dashed lines in all graphs are the structural phase-transition temperatures of the system.

Figure 5

(a) DSC heat flow curves for a series of ${\mathrm{Li}}_2{\mathrm{Ru}}_{1-x}{\mathrm{Mn}}_x{\mathrm{O}}_3$ systems. The inset graph shows the phase-transition temperature $\left(T_{\mathrm{DSC}}\right)$ of the systems. The linear fitting result is shown as a dashed red line. The heating rate is 10 K/min. (b) Variation of enthalpy change $\mathrm{\Delta }H$ per Ru ion with $x$ for ${\mathrm{Li}}_2{\mathrm{Ru}}_{1-x}\mathrm{Mn}{\mathrm{O}}_3$. The inset graph shows the calculated entropy change $\mathrm{\Delta }S$ ($\int dQ/T$) per Ru ion during the phase transition.

Figure 6

(a) $k^3$-weighted $\chi \left(k\right)$ and (b) fitting data and curves of EXAFS signals for ${\mathrm{Li}}_2{\mathrm{Ru}}_{1-x}{\mathrm{Mn}}_x{\mathrm{O}}_3$ ($x=0$, 0.05, 0.1, 0.2, and 0.4).