Low-temperature crystal and magnetic structure of $\alpha -{\mathrm{RuCl}}_3$

Single crystals of the Kitaev spin-liquid candidate $\alpha -{\mathrm{RuCl}}_3$ have been studied to determine the low-temperature bulk properties, the structure, and the magnetic ground state. Refinements of x-ray diffraction data show that the low-temperature crystal structure is described by space group $C2/m$ with a nearly perfect honeycomb lattice exhibiting less than 0.2% in-plane distortion. The as-grown single crystals exhibit only one sharp magnetic transition at $T_N=7$ K. The magnetic order below this temperature exhibits a propagation vector of $k=(0,1,1/3)$, which coincides with a three-layer stacking of the $C2/m$ unit cells. Magnetic transitions at higher temperatures up to 14 K can be introduced by deformations of the crystal that result in regions in the crystal with a two-layer stacking sequence. The best-fit symmetry-allowed magnetic structure of the as-grown crystals shows that the spins lie in the $ac$ plane, with a zigzag configuration in each honeycomb layer. The three-layer repeat out-of-plane structure can be refined as a ${120}^{\circ }$ spiral order or a collinear structure with a spin direction of ${35}^{\circ }$ away from the $a$ axis. The collinear spin configuration yields a slightly better fit and also is physically preferred. The average ordered moment in either structure is less than 0.45(5) ${\mu }_B$ per ${\mathrm{Ru}}^{3+}$ ion.

Figure 1

(a) The in-plane structure of layered compound $\alpha -{\mathrm{RuCl}}_3$ viewed perpendicular to the layers along the $c^{*}$ axis showing the positions of the ${\mathrm{Ru}}^{3+}$ ions (red) and ${\mathrm{Cl}}^{-}$ ions (blue) in $C2/m$ space group symmetry. Two types of ${\mathrm{Ru}}^{3+}–{\mathrm{Ru}}^{3+}$ distances are highlighted with blue [3.454(1) Å] and green [3.449(2) Å] lines (b) ABC stacking: the out-of-plane structure viewed along the $b$ axis, showing the layered structure as well as the octahedra tilted along $c$. Every layer is translated by $a$/3, such that every fourth layer falls on top of the first layer when viewed along $c^{*}$ (dotted line). The blue dashed line along the $c$ axis indicates the perfect stacking for this ABC stacking. Details of the monoclinic structure are in the text as well as in Table 1. (c) ABAB stacking viewed in the same orientation as that in (b), with the top two layers twinned ${120}^{\circ }$ with respect to the bottom two layers. The neighboring layer is translated back and forth by $a$/3, guided by the dotted grey line (details in text). The blue dashed line along the $c$ axis indicates the ABAB stacking is faulty stacking (orange dashed line showing the layer at which the fault occurs). (d) $\left[0KL\right]$ cut of the reciprocal space measured by single-crystal x-ray diffraction at 60 K. (e) The observed squared structure factors vs the calculated ones from the single-crystal x-ray data refinement.

Figure 2

(a) The heat capacity of an as-grown single crystal of $\alpha -{\mathrm{RuCl}}_3$ from 2–20 K shows the low-temperature region exhibiting one sharp Néel transition at $T_{N1}=7$ K. As determined by the neutron diffraction reported here, the in-plane magnetic order is zigzag with out of plane order corresponding to ABC stacking of the layers. The inset shows the data in the large temperature range of 2–200 K. The data excluding the 5–10 K transition region can be fit to a 2D Debye expression $C_p\left(T\right)=ANk{\left(\frac{T}{{\theta }_D}\right)}^2{\int }_0^{\frac{{\theta }_D}{T}}\frac{x^2}{e^x-1}dx$ with ${\theta }_D=209\left(2\right)$ K, similar to powder [21]. (b) The thermal evolution of the intensity of the magnetic peak (0, 1, 1/3) [trigonal ${(1/2,0,1)}_T$] as measured at HB-3A shows a rapid fall-off near $T_{N1}=7$ K. A crystal from the same batch as shown in (c)-inset with similar dimensions was used for the single-crystal neutron diffraction at HB-3A. (c) The heat capacity data on the same single crystal when subject to artificial deformation. The violet curve 1 represents the marginally deformed crystal and shows a rather suppressed anomaly at $T_{N1}$ as compared to an as-grown crystal. When this crystal is manually deformed, the green curve 2 is obtained. Additional transitions, most prominently at $T_{N2}=14$ K, appear, while the anomaly at the $T_{N1}$ transition loses strength. When deformed further, the anomaly at $T_{N1}$ completely vanishes leaving behind a broad anomaly $T_{N2}$ as the only strong feature (brown curve 3). The heat-capacity of the deformed crystal resembles that of powder $\alpha -{\mathrm{RuCl}}_3$ (blue curve 4). The inset is a picture of the as-grown crystal against a grid of 1 ${\mathrm{mm}}^2$.

Figure 3

(a) $L$ scans of (1, 1, ${L)}_T$, (2, 0, $L/3$) in monoclinic notation, measured by single-crystal neutron diffraction at 5 K (black solid squares) and 10 K (red open circles) at HB-3A. The reflections can be indexed in a trigonal lattice but the intensities are incompatible with a trigonal lattice symmetry. No structural change was observed from 5 to 10 K. The inset shows a close-up at (1, 1, 3)${}_T$. (b) Three monoclinic structure domains form in the crystal measured by neutron diffraction. Each domain has the honeycomb layer shifted by $a$/3 along the direction perpendicular to one of honeycomb edges from one layer to the next, which yields a pseudo trigonal pattern in the neutron diffraction measurement. (c) Rocking curve scan at (0, 0, 3) measured by neutron diffraction exhibits a resolution limited width of $0.5^{\circ }$ along the stacking direction, indicating a high quality crystal with only a few stacking faults. (d) Observed squared structure factors vs the calculated ones from the neutron data refinement.

Figure 4

Single-crystal neutron diffraction measured on $\alpha -{\mathrm{RuCl}}_3$ at 4.2 K. (a) $2\theta$ scan at (0, 1, 2/3). (b) The $2\theta$ scan at (0, 1, 1/2) does not show a peak signal, i.e., no magnetic order related to the wave vector $k=(0,1,1/2)$ exists in the measured crystal. (c) and (d) Rocking curve scans at the magnetic peaks (0, 1, 1/3) and (0, 1, 2/3) indicating a magnetic order with the propagation vector $k=(0,1,1/3)$. The magnetic signal was obtained by subtracting the corresponding scan above $T_N$ at 10 K.

Figure 5

Magnetic structures of $\alpha -{\mathrm{RuCl}}_3$ at 4.2 K. Large red balls represent Ru atoms. (a) Spiral zigzag magnetic structure. The spins rotate ${120}^{\circ }$ from one layer to the next but the spin direction in each layer is not able to be determined by the neutron diffraction data. (b) and (c) Modulated zigzag magnetic structures showing the spins tilting $\varphi ={35}^{\circ }$ and $-{35}^{\circ }$ out of the $ab$ plane. The special case with $\mathrm{\Psi }=0$ yields a zero-moment layer flanked by two layers with moments of magnitude 0.52 ${\mu }_B$. Small white balls represent Cl atoms. (d) The observed squared magnetic structure factors vs the calculated ones for the magnetic structure refinement with the spiral (red) and modulated (blue) zigzag models. (e) The goodness of the fit ${\chi }^2$ vs the spin tilting angle $\varphi$ out of the $ab$ plane for the spiral (red) and modulated (blue) zigzag models. The inset shows the minimum near $\varphi ={35}^{\circ }$, the other minimum near $\varphi =-{35}^{\circ }$ has the same ${\chi }^2$.