Site-Selective Mott Transition in a Quasi-One-Dimensional Vanadate ${\mathrm{V}}_6{\mathrm{O}}_{13}$

The microscopic mechanism of the metal-insulator transition is studied by orbital-resolved ${}^{51}\mathrm{V}$ NMR spectroscopy in a prototype of the quasi-one-dimensional system ${\mathrm{V}}_6{\mathrm{O}}_{13}$. We uncover that the transition involves a site-selective $d$ orbital order lifting twofold orbital degeneracy in one of the two ${\mathrm{VO}}_6$ chains. The other chain leaves paramagnetic moments on the singly occupied $d_{xy}$ orbital across the transition. The two chains respectively stabilize an orbital-assisted spin-Peierls state and an antiferromagnetic long-range order in the ground state. The site-selective Mott transition may be a source of the anomalous metal and the Mott-Peierls duality.

Figure 1

Magnetic susceptibility $\chi$ measured with a SQUID magnetometer for a single crystal of ${\mathrm{V}}_6{\mathrm{O}}_{13}$ ($H_0=1\mathrm{T}\parallel b$ and $b^{\prime }$). The lower and upper insets show crystal structures in the metallic (monoclinic $C2/m$) and insulating (monoclinic $Pc$) phases, respectively [22].

Figure 2

(a) ${}^{51}\mathrm{V}$ NMR spectra of ${\mathrm{V}}_6{\mathrm{O}}_{13}$ [$H_0=9.401\mathrm{T}\parallel c^{*}(a^{\prime *})$ for the metallic (insulating) phase], measured with $\tau =6$ and $10–30\mu \mathrm{s}$ for the lower and higher frequency parts, respectively. The red, blue, green, and gray lines are assigned to V(1) [V(1a)], V(2) [V(2a), V(2b)], V(3) [V(3a), V(3b)], and V(1b) based on the angle dependent profiles (Fig. 4). (b) $K$ and (c) $\delta \nu$ obtained from the ${}^{51}\mathrm{V}$ NMR spectra.

Figure 3

(a) Site-dependent local susceptibility obtained from the isotropic ${}^{51}\mathrm{V}$ Knight shifts and (b) $1/T_{1}T$ in ${\mathrm{V}}_6{\mathrm{O}}_{13}$. Solid curves are fitting results of the 1D Heisenberg model, whereas the dashed one is an average of ${\chi }^{\mathrm{V}(3\mathrm{a})}$ and ${\chi }^{\mathrm{V}(3\mathrm{b})}$.

Figure 4

(a) Calculated ${\mathsf{q}}_{ij}$ proportional to the on-site dipole hyperfine coupling and EFG for $d_{xy}$, $d_{yz}$, and $d_{zx}$ orbitals. The orthogonal coordinate axes $(x,y,z)$ are taken on the ${\mathrm{VO}}_6$ octahedron and parallel to $(a,b,c^{*})$ or $(c^{\prime },b^{\prime },a^{\prime *})$ in Fig. 1. [(b)–(e)] Angular dependence of the ${}^{51}\mathrm{V}$ Knight shift $K$ and the nuclear quadrupole splitting frequency $\delta \nu$ at 170 and 100 K in ${\mathrm{V}}_6{\mathrm{O}}_{13}$. The curves are fitted results with the sinusoidal functions of Volkov’s formula [34].

Figure 5

Configurations of the predominant orbital occupations in the (a) metallic and (b) insulating phases of ${\mathrm{V}}_6{\mathrm{O}}_{13}$. The bold lines indicate spin-singlet pairs. The arrows on $\mathrm{V}(3\mathrm{a})/\mathrm{V}(3\mathrm{b})$ denote antiferromagnetically ordered spins below 50 K [24].