Order-disorder type of Peierls instability in ${\mathrm{BaVS}}_3$

Lattice dynamics of low-dimensional ${\mathrm{BaVS}}_3$ is reported across the metal-insulator Peierls transition occurring at $T_P=69$ K using a combination of the thermal diffuse scattering of x rays, inelastic x-ray scattering, and density-functional theory calculations. The nondetection of a Kohn anomaly points to a unique situation of an order-disorder Peierls instability with a quasielastic critical scattering which has been fully characterized. These observations are discussed in the scope of a Peierls instability dominated by strong electron-phonon coupling and/or nonadiabatic effects.

Figure 1

Room-temperature hexagonal structure of ${\mathrm{BaVS}}_3$, seen along the $c$ axis, presenting a top $\mathrm{Ba}{\mathrm{S}}_3$ plane, a middle V layer, and a bottom $\mathrm{Ba}{\mathrm{S}}_3$ layer. $a_H, b_H$ are for the hexagonal unit cell wave vectors. According to recent structural refinements [16] the Ba/S and V subsystems are not adjusted in terms of space group at RT.

Figure 2

Reconstruction of the ($h$, 0, $l$) plane at 114 K (a), and the ($h, k$, 3.5) plane at 300 K (b), 114 K (c), 74 K (d), and 69 K (e). Calculated TDS intensity, including only inelastic contribution and corresponding to the $\mathrm{Cmc}{2}_1$ space group is shown in (f). It should be compared to the diffuse scattering (DS) map in (c). The first Brillouin zone (BZ), six shifted first BZ covering a part of the second BZ (red lines), and a diffuse hexagon (green line) are schematically shown in (g). High-symmetry points A, H, L, are indicated in the first BZ. ${\mathrm{A}}^{\prime }$ and ${\mathrm{L}}^{\prime }$ are the equivalent points out of the first BZ. Black full (open) circles show the positions of the satellites in the first (shifted first) BZ, which are L (${\mathrm{L}}^{\prime }$) points, respectively. The first BZ and a diffuse hexagon are shown in (e), while solely a diffuse hexagon position is given in (c) and (f). Light blue lines in (a) and (c) indicate line scans in DS maps. Points ${\mathrm{A}}^{\prime }$ (diffuse hexagon corner) and L are scanned in the $c^{*}$ direction in (a), while ${\mathrm{L}}^{\prime }$ is scanned in the $a^{*}+b^{*}$ direction in (c). The analysis of the scans is presented in Fig. 4. Unit cell wave vectors are given in hexagonal settings.

Figure 3

Temperature dependence of the DS intensity at the ${\mathrm{A}}^{\prime }$ point. It is derived from two distinct measurements, performed on two different samples. Sample 1 (red points) is a pure ${\mathrm{BaVS}}_3$, studied in this work. Black points are revisited data from a slightly Al-doped sample, studied previously [39]. The intensity of the second measurements is normalized in order to obtain the same intensity at a common temperature of about 110 K.

Figure 4

(a) Momentum HWHM (in ${\mathrm{nm}}^{-1}$) and (b) $\mathrm{T}/{\mathrm{I}}_m$ (temperature over intensity maximum) of diffuse spots at satellite positions ${\mathrm{L}}^{\prime }$ point (3, $-1.5$, 3.5) and L point ($-0.5$, 0, $-4.5$), scanned, respectively, in the $a^{*}+b^{*}$ and $c^{*}$ directions. The HWHM and $\mathrm{T}/{\mathrm{I}}_m$ measured in the $c^{*}$ direction at the position of a diffuse hexagon corner ${\mathrm{A}}^{\prime }$ point, ($-1.0$, 0, $-4.5$), are shown for comparison. $T_P$ is for the temperature of the Peierls transition. $2k_F$ and 1/$a$ indicate, respectively, the CDW modulation wave vector and the inverse minimal distance between two V in the ($a,b$) plane.

Figure 5

(a) $q$ dependence of the energy of the two phonons along high-symmetry lines, measured at 75 K. High-symmetry points are indicated for the hexagonal (orthorhombic) BZ. (b) The first BZ with the explored high-symmetry lines, $\mathrm{\Gamma }$-A-L-M-K-H-A (red arrows). Additional path is explored out of the first BZ, ${\mathrm{A}}^{\prime }$-L-H-${\mathrm{L}}^{\prime }\text{−}{\mathrm{M}}^{\prime }$ (blue arrows), where edges of diffuse hexagons appear. Note that the positions of the points $\mathrm{\Gamma }$, M, K, ${\mathrm{M}}^{\prime }$ are not exact, but there is an error of 5% of the reduced wave vector in the $\mathit{h}$ and $\mathit{k}$ directions. Moreover, in the orthorhombic phase, at least 3 twins coexist. A general $q$ point in experimental data becomes a superposition of nonequivalent points of the reciprocal orthorhombic unit cell. For example, the L point in the hexagonal phase becomes a superposition of T and R points in the orthorhombic phase.

Figure 6

IXS scans at two satellite positions, (a) L point at (0, $-0.5$, 4.5), (b) ${\mathrm{L}}^{\prime }$ point at (0.5, 0.5, 4.5), and (c) at the hexagon-diffuse corner, ${\mathrm{A}}^{\prime }$ point at (0, $-1$, 4,5). They are fitted with three structures: a central peak (CP, black), a low-energy phonon (LE, red) and a high-energy phonon (HE, yellow).

Figure 7

Temperature evolution of the phonon (a) energy, (b) HWHM, measured at the two satellite positions. The error bars of the HWHM of the high-energy phonon being too large, the data are not shown.

Figure 8

IXS central pic (a) energy HWHM and (b) temperature over integrated intensity ($\mathrm{T}/{\mathrm{I}}_i$), measured at two satellite positions, L point at (0.0, $-0.5$, 4.5) (red circles), ${\mathrm{L}}^{\prime }$ point at (0.5, 0.5, 4.5) (black squares), and the position of the corner of a diffuse hexagon, ${\mathrm{A}}^{\prime }$ point at (0, $-1$, 4.5) (open black triangles). Horizontal arrow indicates the energy resolution of 1.325 meV (HWHM). The vertical arrow is for the temperature of the metal-insulator transition, as determined from the conductivity measurements. Dashed lines in (b) are guides for the eye. Data are extracted from the scans shown in Fig. 6.

Figure 9

(a) Calculated TDS intensity in the ($h, k$, 3.5) plane, corresponding to the $\mathrm{Cmc}{2}_1$ space group, indexed in hexagonal settings. The green hexagon, white dotted lines and particular points ${\mathrm{A}}_1^{\prime }, {\mathrm{L}}^{\prime }, {\mathrm{A}}_2^{\prime }$, A, indicate the portion of the momentum space where the phonon analysis was performed. (b) Reconstruction of the measured ($h, k$, 3.5) plane at 114 K. The green hexagon indicates the same region as in (a).

Figure 10

Dispersion of low-energy phonons along ${\mathrm{A}}_1^{\prime }\to {\mathrm{A}}_2^{\prime }$ (a) and ${\mathrm{A}}_1^{\prime }\to {\mathrm{A}}_3^{\prime }$ (b) directions in reciprocal space.

Figure 11

Reconstruction of the ($h, k$, 3.5) plane at 300 K, 114 K, 74 K, and 69 K, presented in the same intensity range.