Bi and Sr substitution effects on the spin-gap system ${\mathrm{Pb}}_2{\mathrm{V}}_3{\mathrm{O}}_9$

We report the magnetic properties of Sr- and Bi-substituted samples of the one-dimensional alternating $S=1∕2$ spin chain compound ${\mathrm{Pb}}_2{\mathrm{V}}_3{\mathrm{O}}_9$. In the Sr-substituted system, we obtained two series of samples synthesized by different heat treatments; one series shows the reduction of the spin gap without antiferromagnetic long-range order (AF-LRO) and the other shows AF-LRO at low temperatures. We also observed impurity-induced AF-LRO in the Bi-substituted system. The fitting results of magnetic susceptibilities imply the possible coexistence of a spin gap and AF-LRO in both AF-LRO systems. These observations of AF-LRO with a small amount of substitution indicate that the magnetic instability involving a quantum critical point is inherent in the spin-gap system ${\mathrm{Pb}}_2{\mathrm{V}}_3{\mathrm{O}}_9$.

Figure 1

Crystal structure of ${\mathrm{Pb}}_2{\mathrm{V}}_3{\mathrm{O}}_9$. Two Pb sites are labeled as Pb(1) and Pb(2) indicated by light gray and dark gray spheres, respectively.

Figure 2

Evolution of the lattice constants of Sr-substituted samples. Solid circles and open squares represent the data of 600 and $650°\mathrm{C}$ heat-treatment samples, respectively. The solid lines are guides for the eyes. The inset shows the unit-cell volume plotted against $x$.

Figure 3

Temperature and $x$ dependences of $\chi$ of ${\left({\mathrm{Pb}}_{1-x}{\mathrm{Sr}}_x\right)}_2{\mathrm{V}}_3{\mathrm{O}}_9$: (a) with $600°\mathrm{C}$ and (b) $650°\mathrm{C}$ heat treatments. Two types of Sr-substituted series show quite different magnetic properties. The peak magnitude and temperature of $\chi$ systematically decrease with increasing Sr content $x$ in the Sr(A) series. In the Sr(B) series, with increasing $x$, the peak of $\chi$ at $T=20\mathrm{K}$ indicating a low-dimensional feature faded and enhancement of Curie-Weiss-like behavior was observed.

Figure 4

Evolution of lattice constants as a function of $x$ in ${\left({\mathrm{Pb}}_{1-x}{\mathrm{Bi}}_x\right)}_2{\mathrm{V}}_3{\mathrm{O}}_9$. The solid lines are guides for the eyes. The inset shows the unit-cell volume plotted against $x$.

Figure 5

Temperature and $x$ dependences of $\chi$ of ${\left({\mathrm{Pb}}_{1-x}{\mathrm{Bi}}_x\right)}_2{\mathrm{V}}_3{\mathrm{O}}_9$. As the Bi concentration $x$ increases, the value of $\chi$ increases due to the doped electrons by Bi substitution. The arrows indicate the temperature where $\chi$ shows kinks, denoted by $T_N$. The inset is the temperature dependence of the specific heat divided by the temperature for ${\left({\mathrm{Pb}}_{1-x}{\mathrm{Bi}}_x\right)}_2{\mathrm{V}}_3{\mathrm{O}}_9$ with $x=0.020$. The arrowed temperature denoted by $T_N$ agrees with $T_N$ determined by $\chi$.

Figure 6

The typical fitting curves of $\chi$ in (a) Sr(A), (b) Sr(B), and (c) Bi systems. Open marks show the raw data, and solid lines are fitting curves.

Figure 7

$T\text{−}x$ phase diagram of each substituted system: (a), (b), and (c) are for Sr(A)-, Sr(B)-, and Bi-substituted systems, respectively. Solid circles and open squares represent the Néel temperature $T_N$ and spin gap ${\Delta }_{\mathit{cal}}$ in kelvin, respectively. Solid lines for ${\Delta }_{\mathit{cal}}$ values are fitting results by the least-squares method. Dashed lines are a guide for the eyes. The inset of (a) shows the evolution of the fitting parameter of $J_1$ and $\alpha$ as a function of $x$ in ${\left({\mathrm{Pb}}_{1-x}{\mathrm{Sr}}_x\right)}_2{\mathrm{V}}_3{\mathrm{O}}_9$.

Figure 8

Pb cations and $6s^2$ lone-pair environment. Pb(1) and Pb(2) are coordinated to seven and nine oxygen ions, respectively. The shaded planes show (100) planes. The labels of ions are named following Ref. 24. The distance between Pb(1) and O(1)b ions is longer than $3\mathrm{\AA }$, which is almost negligible as a chemical bond. The $6s^2$ lone pair is located at the open space between Pb(1) and O(1)b. The $6s^2$ lone pair on Pb(2) is directed to the open space within the Pb(2)-O(3)b-O(3)b-O(2)a-O(3)a pentahedra.

Figure 9

Schematic model to explain how the impurity ion terminates the magnetic chain. There are two ways to terminate the spin chain: along interdimer and intradimer paths.