Modulated crystal structure of the atypical charge density wave state of single-crystal ${\mathrm{Lu}}_2{\mathrm{Ir}}_3{\mathrm{Si}}_5$

The three-dimensional charge density wave (CDW) compound ${\mathrm{Lu}}_2{\mathrm{Ir}}_3{\mathrm{Si}}_5$ undergoes a first-order CDW phase transition at around 200 K. An atypical CDW state is found, that is characterized by an incommensurate CDW with $\mathbf{q}=\left[0.2499\right(3),0.4843(4),0.2386(2\left)\right]$ at 60 K, and a large orthorhombic-to-triclinic lattice distortion with $\beta =91.945{\left(2\right)}^{\circ }$. We present the modulated crystal structure of the incommensurate CDW state. Structural analysis shows that the CDW resides on the zigzag chains of iridium atoms along $\mathbf{c}$. The structural distortions are completely similar between nonmagnetic ${\mathrm{Lu}}_2{\mathrm{Ir}}_3{\mathrm{Si}}_5$ and previously studied isostructural magnetic ${\mathrm{Er}}_2{\mathrm{Ir}}_3{\mathrm{Si}}_5$ with the small differences explained by the different values of the atomic radii of Lu and Er. Such a similarity is unique to $R_2{\mathrm{Ir}}_3{\mathrm{Si}}_5$ $(R=\mathrm{rare}\mathrm{earth})$. It differs from, for example, the rare-earth CDW compounds $R_5{\mathrm{Ir}}_4{\mathrm{Si}}_{10}$ for which ${\mathrm{Lu}}_5{\mathrm{Ir}}_4{\mathrm{Si}}_{10}$ and ${\mathrm{Er}}_5{\mathrm{Ir}}_4{\mathrm{Si}}_{10}$ possess entirely different CDW states. We argue that the mechanism of CDW formation, thus, is different for $R_2{\mathrm{Ir}}_3{\mathrm{Si}}_5$ and $R_5{\mathrm{Ir}}_4{\mathrm{Si}}_{10}$.

Figure 1

$\left(h0l\right)$ section of reciprocal space, reconstructed from the SXRD data measured at: (a) 298, (b) 200, and (c) 60 K. Splitting of reflections due to the pseudomonoclinic lattice distortion increases with an increasing magnitude of the index $h$. The black bands are due to bands of insensitive pixels between individual modules of the Pilatus 1M CdTe detector.

Figure 2

Temperature dependence of the lattice parameters. (a) Values of the lattice parameters relative to their values at $T=298\mathrm{K}$: $\frac{a}{a\left(298\right)}$ (red circles), $\frac{b}{b\left(298\right)}$ (triangles), and $\frac{c}{c\left(298\right)}$ (diamonds) with $a\left(298\right)=9.9021\left(4\right),b\left(298\right)=11.3131\left(5\right)$, and $c\left(298\right)=5.7279\left(3\right)\AA$. (b) Values of the lattice parameters $\alpha$ (red circles), $\beta$ (diamonds), and $\gamma$ (triangles). Open symbols are for the orthorhombic phase at $T>200\mathrm{K}$; full symbols are for the triclinic phase at $T<200\mathrm{K}$. At 200 K both phases coexist. Two regimes are clearly visible as discontinuities of the temperature dependences of the lattice parameters $a,b,c$, and $\beta$.

Figure 3

Flow chart depicting the loss of symmetry from orthorhombic $Ibam$ to triclinic $I\overline{1}$ resulting in the formation of triclinic twin domains of four different orientations. See Nespolo [38] for a formal description of the symmetries of twinned crystals.

Figure 4

Projections of the crystal structure of ${\mathrm{Lu}}_2{\mathrm{Ir}}_3{\mathrm{Si}}_5$ at 60 K. (a) Projection of one unit cell onto the $(\mathbf{a},\mathbf{c})$ plane. Ir1a-Ir1b atoms are at a basic-structure distance of $3.376\left(5\right)\AA$ for full lines and of $3.753\left(5\right)\AA$ for dashed lines. (b) Projection of one slab (half a unit cell along $\mathbf{c}$) onto the $(\mathbf{a},\mathbf{b})$ plane. Atoms Lu1, Ir1, and Si3 are on the $z=0.5$ plane; atoms Si1, Si2, and Ir2 are at $z=0.5\pm \frac{1}{4}$. Zigzag chains ${\left(\mathrm{Ir}1\mathrm{a},\mathrm{Ir}1\mathrm{b}\right)}_{\infty }$ run along $\mathbf{c}$ with the displacement parallel to $\mathbf{a}$.

Figure 5

$t$ plot of the interatomic distances between atoms Ir1a and Ir1b $(x,y,z)$ and between Ir1a and Ir1b at $(x,y,z-1)$ for the crystal structure at $T=60\mathrm{K}$. Dashed lines give the distances in the basic structure with values of 3.376 (5) and $3.753\left(5\right)\AA$.