Trimerization and orbital ordering in ${\mathrm{Ba}}_{1-x}{\mathrm{Sr}}_x{\mathrm{V}}_{13}{\mathrm{O}}_{18}$

We studied the physical properties of ${\mathrm{Ba}}_{1-x}{\mathrm{Sr}}_x{\mathrm{V}}_{13}{\mathrm{O}}_{18}$ single crystals, which exhibit three different phases caused by the orbital and charge degrees of freedom in V $t_{2g}$ states. We found from the magnetic susceptibility and the NMR measurement that the low-temperature phase of this series of compounds is characterized by the spin-singlet state. We also found from the electrical resistivity and optical conductivity spectra that these compounds become heavily anisotropic in the low-temperature phase with V trimerization, indicating that the orbital ordering of V $t_{2g}$ states causes the anisotropy of the electronic structure of this series of compounds.

Figure 1

Schematic illustrations of orbital ordering in (a) the V trimer and (b) V tetramer. (c) Arrangement of V ions in HT and IT phases viewed along the $c$ axis (left) and the $ab$ plane (right). (d) Arrangement of V ions in the LT phase viewed along the $c$ axis (left) and the $ab$ plane (right). (c) and (d) were drawn using vesta [13].

Figure 2

Phase diagram of the ${\mathrm{Ba}}_{1-x}{\mathrm{Sr}}_x{\mathrm{V}}_{13}{\mathrm{O}}_{18}$ single crystals. The closed squares correspond to the transition temperatures between the HT phase and the IT phase. The circles correspond to the transition temperatures between the IT phase and LT phase ($x\le 0.3$) or between the HT phase and LT phase ($x>0.3$). The solid and open circles correspond to that in the warming and cooling runs, respectively.

Figure 3

Temperature dependence of the resistivity for ${\mathrm{Ba}}_{1-x}{\mathrm{Sr}}_x{\mathrm{V}}_{13}{\mathrm{O}}_{18}$ with (a) $x=0$, (b) $x=0.1$, (c) $x=0.2$, and (d) $x=1$. (e) Temperature dependence of the magnetic susceptibility for ${\mathrm{Ba}}_{1-x}{\mathrm{Sr}}_x{\mathrm{V}}_{13}{\mathrm{O}}_{18}$. The data are offset for clarity. (f) Sr concentration dependences of $E_g/k_B$ and $T_{\mathrm{co}}$.

Figure 4

Temperature dependence of the Hall coefficient for ${\mathrm{BaV}}_{13}{\mathrm{O}}_{18}$.

Figure 5

(a) ${}^{51}\mathrm{V}$ NMR spectra of ${\mathrm{BaV}}_{13}{\mathrm{O}}_{18}$ for $H\parallel c$. The intensity of the spectra is normalized using the peak value. The Knight shift origin ($K=0$) is located at 68.264 MHz for $H=6.10$ T. The green inverse triangles represent the electric quadrupole splitting. (b) Temperature $T$ dependence of integrated spin-echo intensity $I$ multiplied by $T$, where $I$ is extrapolated to $\tau =0$ by measuring the spin-echo decay rate $T_2^{-1}$ using the pulse sequence of ($\pi /2$)-$\tau$-($\pi /2$)-$\tau$, and (c) nuclear spin-lattice relaxation rate $T_1^{-1}$ divided by $T$ for $x=0$ and $x=0.1$.

Figure 6

Optical conductivity spectra along the $ab$ plane $\left[{\sigma }_a\left(\omega \right)\right]$ and $c$ axis $\left[{\sigma }_c\left(\omega \right)\right]$ at 300 K for (a) ${\mathrm{Ba}}_{0.9}{\mathrm{Sr}}_{0.1}{\mathrm{V}}_{13}{\mathrm{O}}_{18}$ and (b) ${\mathrm{SrV}}_{13}{\mathrm{O}}_{18}$.

Figure 7

Optical conductivity spectra along (a) the $ab$ plane $\left[{\sigma }_a\left(\omega \right)\right]$ and (b) the $c$ axis $\left[{\sigma }_c\left(\omega \right)\right]$ for ${\mathrm{Ba}}_{0.9}{\mathrm{Sr}}_{0.1}{\mathrm{V}}_{13}{\mathrm{O}}_{18}$ at various temperatures.

Figure 8

Temperature dependence of the spectral weight (a) between 0.1 and 0.2 eV and (b) between 0.1 and 0.5 eV.

Figure 9

The ${\sigma }_a\left(\omega \right)$ and ${\sigma }_c\left(\omega \right)$ spectra at (a) 300 K (HT phase), (b) 160 K (IT phase), and (c) 30 K (LT phase).

Figure 10

(a) The ${\sigma }_a\left(\omega \right)$ and (b) ${\sigma }_c\left(\omega \right)$ spectra for ${\mathrm{SrV}}_{13}{\mathrm{O}}_{18}$ at various temperatures.

Figure 11

Temperature dependence of spectral weight for ${\sigma }_a\left(\omega \right)$ (red circles) and ${\sigma }_c\left(\omega \right)$ (blue circles) between 0.1 and 1 eV.

Figure 12

The ${\sigma }_a\left(\omega \right)$ and ${\sigma }_c\left(\omega \right)$ spectra at (a) 300 K (HT phase) and (b) 50 K (LT phase) for ${\mathrm{SrV}}_{13}{\mathrm{O}}_{18}$.

Figure 13

Comparison of (a) ${\sigma }_a\left(\omega \right)$ and (b) ${\sigma }_c\left(\omega \right)$ at the lowest temperature between ${\mathrm{Ba}}_{0.9}{\mathrm{Sr}}_{0.1}{\mathrm{V}}_{13}{\mathrm{O}}_{18}$ and ${\mathrm{SrV}}_{13}{\mathrm{O}}_{18}$.