Superstructures arising from V trimers with orbital ordering in ${\mathbf{BaV}}_{10}{\mathbf{O}}_{15}$

In ${\mathrm{BaV}}_{10}{\mathrm{O}}_{15}$ with quasitriangular V lattices, we found unique superstructures characterized by $\left(qq0\right)$-type peaks in the momentum space, where $q$ varies continuously with temperature between $q=0$ and $1/3$ and locks at $1/3$. Such a threefold superstructure is likely caused by the dense arrangement of the V trimers associated with the orbital ordering of V. The results indicate that the superstructure of the V trimers, each of which is also a superstructure, gives rise to the ordered phases with peculiar characteristics.

Figure 1

Arrangement of the V ions in ${\mathrm{BaV}}_{10}{\mathrm{O}}_{15}$ along the $ab$ plane for (a) one layer above $T_s$, (b) two layers (red and blue for each layer) above $T_s$, and (c) two layers below $T_s$. Figures were drawn using VESTA [36]. The yellow triangles in (c) represent the V trimers. The dashed-line rectangle in (b) indicates the unit cell. The solid-line rectangles in (b) and (c) indicate the zigzag double chains of V.

Figure 2

(a) Orbital states ($\sigma$ bonds of the $t_{2g}$ orbitals $xy$, $yz$, $zx$) in the V trimer for ${\mathrm{BaV}}_{10}{\mathrm{O}}_{15}$. (b) Two units of the V double chain in a parallelogram, each of which is composed of four V triangles. V ions exist on the corners of the triangles. Three different colors (red, blue, and magenta) of the edges depict the bonds composed of three different $t_{2g}$ orbitals: $xy$, $yx$, and $zx$ shown in (a). (c) V double chain with V trimerization. The shaded triangle corresponds to a V trimer, and the corner that does not belong to the shaded triangle corresponds to the lone V ion. (d) Flattened picture of the V double chain. Different colors (red and blue) correspond to the two types of parallelogram with different normal vectors shown in (b) and (c). The arrows in (c) and (d) indicate the period of the structure.

Figure 3

(a) Resistivity along the $b$ axis for ${\mathrm{BaV}}_{10}{\mathrm{O}}_{15}$ with $T_s=135\mathrm{K}$ (red), 128 K (green) and 123 K (blue). (b) Enlarged figure of the resistivity above $T_s$ along the $a$ and $b$ axes for the sample with $T_s=135\mathrm{K}$. The blue and red lines correspond to the data in the cooling and warming runs, respectively. The dashed-line rectangle in (a) corresponds to the drawing range of (b).

Figure 4

(a) Magnetic susceptibility with the magnetic field of 0.1 T applied along the $c$ axis for ${\mathrm{BaV}}_{10}{\mathrm{O}}_{15}$ with $T_s=135\mathrm{K}$ (red), 128 K (green), and $T_s=123\mathrm{K}$ (blue). (b) Enlarged figure of the magnetic susceptibility above $T_s$ along the $a$, $b$, and $c$ axes for the sample with $T_s=135\mathrm{K}$. The three data sets are offset for clarity. The blue and red lines correspond to the data in the cooling and warming runs, respectively. The dashed-line rectangle in (a) corresponds to the drawing range of (b).

Figure 5

(a) Strain along the $a$, $b$, and $c$ axes for ${\mathrm{BaV}}_{10}{\mathrm{O}}_{15}$ with $T_s=135\mathrm{K}$ (solid lines) and ${\mathrm{SrV}}_{10}{\mathrm{O}}_{15}$ (dashed lines). (b) Difference between strain for ${\mathrm{BaV}}_{10}{\mathrm{O}}_{15}$ and that for ${\mathrm{SrV}}_{10}{\mathrm{O}}_{15}$ above $T_s$ along the $a$, $b$, and $c$ axes. The blue and red lines correspond to the data in the cooling and warming runs, respectively.

Figure 6

Specific heat of ${\mathrm{BaV}}_{10}{\mathrm{O}}_{15}$ with $T_s=135\mathrm{K}$. The dots correspond to the experimental data and they are connected by a solid line for clarity. The inset is the enlargement around $T_{\mathrm{triple}}=175\mathrm{K}$.

Figure 7

(a) X-ray diffraction along $(4+q,q,3)$ for ${\mathrm{BaV}}_{10}{\mathrm{O}}_{15}$ with decreasing $T$ from 240 K to 142 K in 2 K steps (except for the data between 240 K and 220 K in 2.5 K steps). (b) $T$ dependence of the position of the superlattice peak $q$.

Figure 8

Electron diffraction patterns of ${\mathrm{BaV}}_{10}{\mathrm{O}}_{15}$ taken from the $\left[1\overline{1}0\right]$ direction at 150 K and 117 K.

Figure 9

X-ray diffraction along $(4,0,3+q^{\prime })$ for ${\mathrm{BaV}}_{10}{\mathrm{O}}_{15}$ at various $T$ values.

Figure 10

Schematic pictures of the V trimers in the V double chain (a) with a commensurate structure for $T<T_s$, (b) with a threefold superstructure for $T_s<T<T_{\mathrm{triple}}$, and (c) the flattened picture for the threefold superstructure in (b). Each arrow indicates the period of the structure.

Figure 11

Schematic of the V trimers (yellow triangles) along the $ab$ plane, which is consistent with superlattice peaks at $(h\pm 1/3,k\pm 1/3,l)$ for ${\mathrm{BaV}}_{10}{\mathrm{O}}_{15}$. The dashed rectangle represents a unit cell with the superstructure.

Figure 12

Schematic of the V trimers in the V double chain in the flattened depiction for (a) a commensurate structure, (b) threefold superstructure, (c) fivefold superstructure, and (d) sevenfold superstructure. Each arrow indicates the period of the structure.

Figure 13

Arrangement of the V ions in ${\mathrm{BaV}}_{10}{\mathrm{O}}_{15}$ along the $ab$ plane in neighboring bilayers (light and dark colors), and the two ${\mathrm{VO}}_6$ octahedra along the $c$ axis, drawn using VESTA [36].