Spin Dynamics and Charge Order in $\beta -\mathrm{N}{\mathrm{a}}_{\mathrm{1}\mathrm{/}\mathrm{3}}{\mathrm{V}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$

We present detailed electron-spin resonance investigations on single crystals of the one-dimensional vanadium-oxide bronze $\beta -\mathrm{N}{\mathrm{a}}_{\mathrm{1}\mathrm{/}\mathrm{3}}{\mathrm{V}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$. From the angular dependence of the $g$ value it can be concluded that the electrons are primarily located on the V1 zigzag chains. The anisotropy of the linewidth, which is determined by the intrachain symmetric anisotropic exchange interaction, favors statistic electron distribution in the metallic and blockwise charge-order in the insulating phase. The temperature dependence of the linewidth indicates the opening of a charge gap at the metal-to-insulator transition at $T_{\mathrm{M}\mathrm{I}}=132\mathrm{K}$.

Figure 1

Crystal structure of $\beta -\mathrm{N}{\mathrm{a}}_{\mathrm{1}\mathrm{/}\mathrm{3}}{\mathrm{V}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$ and plot of V1 zigzag chain and V2 ladder. Black spheres denote electronically occupied V sites ($3d^1$) as derived from our ESR results. Stars indicate positions at $b/2$ above the $ac$ plane.

Figure 2

Temperature dependence of ESR linewidth $\Delta H$ (Inset: reduced contribution $\Delta H_{\sigma }$ compared to $b$-axis conductivity as Arrhenius plot) and $g$ value of a $\beta -\mathrm{N}{\mathrm{a}}_{\mathrm{1}\mathrm{/}\mathrm{3}}{\mathrm{V}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$ single-crystal at Q-band frequency with the external magnetic field parallel to different crystallographic axes.

Figure 3

Angular dependence of ESR linewidth $\Delta H$ and $g$ value of a $\beta -\mathrm{N}{\mathrm{a}}_{\mathrm{1}\mathrm{/}\mathrm{3}}{\mathrm{V}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$ single-crystal at 200 K and 50 K (X band). Solid lines: simulations (see text).