Introduction

The peculiar interplay between spin-orbit effects, electron–electron interaction, and subtle lattice distortions is expected to produce an elaborate phase diagram for the 4d5 transition metal layered compound α-RuCl3, which to date remains inadequately understood1,2,3,4. The proposed state of an electron on the honeycomb lattice of edge-shared RuCl6 octahedra is described by a spin-orbit entangled Jeff=1/2 Mott state1,4,5 that can potentially host novel exotic quantum phases, such as a room temperature Quantum Spin Hall Effect6 and Kitaev quantum spin liquid (QSL) behaviour3,4,7,8. The elementary excitations associated with the Kitaev QSL model include Majorana fermions9,10,11,12, which are relevant in the context of a topological quantum computer13. Recent identification of a magnetic phase proximate to the Kitaev QSL in neutron scattering experiments3 have further fueled an excitement over a breakdown of the putative classical physics in the α-RuCl3 system.

As the nearest-neighbour coupling between Jeff=1/2 moments in 4d5 and 5d5 honeycomb compounds is highly sensitive to a small distortion of the 90° metal-ligand-metal bond14,15,16, a rigorous understanding of the local structural properties of the α-RuCl3 compound is required for exploring a potential departure from the Kitaev QSL phase and realization of a spatially inhomogeneous magnetic ground state in the presence of lattice disorder. An equally important factor in establishing the atomic scale phenomenology for the α-RuCl3 system is a study of its local electronic behaviour. Whereas most of the experiments have so far focused on bulk magnetic properties of α-RuCl3, the experimental research on its nanoscale electronic properties, including a potential role of unit-cell scale charge (re)distribution in determining the final ground state and the associated exotic phenomena in the Kitaev limit, is scarce. In addition, exploring properties of thin films, the surface effects in α-RuCl3, and their relationship to the bulk parent compound can provide important clues for potential applications of ‘Kitaev materials’ in next generation of 2D nanoscale quantum electronic devices for the post-silicon era.

While, most of the studies in the material have concentrated on reciprocal space and bulk properties2,3,17,18,19, to explore the many complexities of this system, it is important to be able to visualize directly its local structural and electronic orders in real space.

In the following, we employ a combination of in-situ scanning transmission electron microscopy (STEM) and in-situ scanning tunnelling microscopy (STM) on exfoliated/cleaved α-RuCl3 samples as ideal tools for detailed evaluation of structural and electronic parameters of the system with a sub-nanometre precision. To date the only existing in literature atomically resolved STM study on α-RuCl3 reported an apparently strong lattice distortions on the surface of the sample20. However, as those STM measurements were performed in the ambient environment and the samples were not cleaved in situ, it remains unclear whether the observed structure peculiarities were the intrinsic properties of the material or caused by some extrinsic effects, such of sample and/or STM tip contamination. The STM and STEM measurements performed here are further supported by neutron scattering, first principles calculations, and a multivariate statistical analysis. This combination of both reciprocal space and real space tools, together with a computational effort, provides an excellent starting point in establishing the structure-property relationship in α-RuCl3 system. In this study, we find that the exfoliated thin films (thickness ≈15∼30 layers) can be characterized by P3-type space group, which is explained with a help of neutron diffraction data as due to transition from C2/m to P31 type stacking order at above ∼150 K. For each individual α-RuCl3 layer we found that in addition to a uniform octahedral distortion reported earlier for bulk α-RuCl3 crystals, there is a persistent local inhomogeneity in the ligand geometries. Such nanometre scale perturbations in structural order, inferred from the STEM data with a subpixel precision and not typically accounted for by theory, can have an important role for determining collective spin-orbital state of the system in Kitaev-Heisenberg model. The STM spectroscopic measurements in the paramagnetic phase of the in-situ cleaved α-RuCl3 samples demonstrated a presence of ≈0.25 eV gap in density of states of the individual surface layer, which is explained by a realization of Jeff=1/2 Mott state. Furthermore, our STM probe into the atomic-scale surface electronic structure revealed a striking anisotropy in a charge distribution along the Ru–Cl–Ru hopping paths, indicating that the bond-dependent behaviour in this system may appear at the temperatures considerably higher than the estimated strength of the Kitaev coupling. In addition, we observed a fine structure of the corresponding charge ordered state characterized by a coexistence of trigonal-like and dimer-like patterns of charge disproportionation at the Cl-terminated surface.

Results

Structure (neutron and STEM)

We start with a real-space characterization of α-RuCl3 films using high-resolution annular dark field STEM measurements. A representative Z-contrast STEM image (Z is atomic number) of α-RuCl3 film (thickness≈30 layers) taken perpendicular to the sample’s c*-axis at T=295 K is shown in Fig. 1a. The image consists of a periodic repetition of an effective unit cell containing six brighter columns and three less bright columns. The registration of higher and lower Z atom columns with the P3112 structural model for α-RuCl3 proposed in ref. 3 provides a good initial match to the entire image (see Supplementary Note 1 and Supplementary Fig. 1). As intensity in these STEM images is proportional roughly to the square of Z, the six brightest spots in the image are assigned to overlapping atomic columns of Ru and Cl atoms (Ru/Cl), whereas the three less bright spots are the Cl atomic columns (see inset in Fig. 1a). It is worth noting that for the C2/m phase, reported recently in bulk α-RuCl3 crystals21, one would expect a STEM image consisting of a well-defined line-like features with every third line substantially darker than the two others (see Supplementary Fig. 1), which is not the case in Fig. 1a. In this regard, we point out that stacking order in quasi-2D exfoliated films may not necessarily resemble the stacking order of bulk as-grown crystals, which themselves may be subject to faults that modify the layer stacking under particular crystal growth conditions. However, our neutron measurements on bulk crystals does confirm a more general possibility of P3-type space group scenario in α-RuCl3 system as described below.

Figure 1: Scanning transmission electron microscopy data on α-RuCl3 films.
figure 1

(a) Z-contrast STEM image of α-RuCl3 film (raw data). Inset shows filtered data, where brown and blue crosses correspond to the centers of Ru/Cl columns and Cl columns, respectively. (b,c) Histogram-based visualization of inter-column distances for six nearest neighbours of Ru/Cl columns (b) and Cl columns (c). Dotted red vertical lines show the value of inter-column distances expected for perfect trigonal symmetry. The red arrow in c indicates the presence of a well-defined shoulder originating from an increase in nearest neighbour distances of Cl columns. (d) Line profile illustrating a modulation of inter-column distances for Cl and Ru/Cl columns with respect to the value of 198 pm for ideal trigonal symmetry.

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The larger single crystals which were exfoliated for this study are consistently C2/m structure at low temperatures21,22, however, at high temperatures they comply with the P31 structure. The two structures are connected by a first-order phase transition at T∼150 K with a ∼30 K hysteresis region (Fig. 2a), which explain the kinks observed in past susceptibility measurements19. This structural transition is characterized by the (1,0,L=3n) and (1,1,L≠3n) peaks appearing, while (1,1,L=3n) (n=integer) peaks disappearing above 150 K, as shown in Fig. 2b (see Supplementary Table 1 for the refined parameters, and methods section for details of the measurement). Indeed, the C2/m, P3112 and P31 type space groups are polytypes22 of each other with similar in-plane honeycomb morphology. The difference is the out-of-plane stacking arrangement. All the analysis in the following sections will be based on the P31-type space group assuming that the in-layer structural properties discussed in the text are applicable to both C2 and P3 stacks of weakly coupled α-RuCl3 layers.

Figure 2: Neutron diffraction data on single crystals of α-RuCl3.
figure 2

(a) Temperature dependence of the (1,1,3) and (1,1,4) peak intensities. The hysteresis of the (1,1,3) and (1,1,4) orders is clearly observed (shaded area). The structural transition temperature between monoclinic and trigonal lattices is Ts=165 K for warming up and Ts=140 K for cooling down. (b) L-scans at several selected values of temperature.

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The statistical analysis of the inter-column distances distribution performed for six nearest neighbours of Ru/Cl and Cl columns (Fig. 1b,c, respectively) shows a significant distortion from ideal trigonal symmetry (that is, the symmetry expected from a 2D-projection of atomic columns in ABC-stacked α-RuCl3 with undistorted RuCl6 octahedra), in which all inter-column distances are expected to be 0.198 nm. This is particularly clear from the non-symmetric nearest neighbours distance distribution for Cl columns that has a well-defined shoulder at around 215 pm (red arrow in Fig. 1c). The pairwise analysis of inter-column distances shows that the shoulder is associated with an increase in the Cl–Cl inter-column distances by ΔDCl–Cl≳15 pm. (Fig. 1d). This indicates a presence of a lattice distortion in the film system that is addressed below.

To gain further insight into the details of structural distortions found above we performed density functional theory (DFT)-based first-principles calculations on α-RuCl3 (see Methods section for computational details) and compared them to the STEM results. Our starting point is the P3112 unit cell with nearly perfect local cubic symmetry in which all Cl–Ru–Cl bonds in the Ru-centered Cl octahedra are equal to (90±1)° (refs 17, 23). The DFT calculated relaxed structure shows that Cl atoms from opposite sublayers in each RuCl3 ‘sandwich’ become displaced towards each other (Fig. 3a). This result is consistent with the findings reported in ref. 24. From additional simulations we have found that it is robust against changing the stacking and the inclusion of spin-orbit coupling, interactions and magnetism. The resultant compression of the Cl ligand cage along Ru–Ru ‘bonds’ (C3 symmetry axis for threefold rotation) leads to a deviation from its original perfectly octahedral symmetry. Notably the lattice distortion is limited mainly to the Cl sublattice, leaving the Ru honeycomb lattice close to a distortion-free state within the resolution of available experimental structure methods. In Fig. 3c we show the DFT calculated structure of atomic columns superimposed on to the STEM experimental image of α-RuCl3 film (top-view). One can immediately see that the direction and magnitude of a lateral component of Cl cage deformation matches well with the Cl columns displacement found from the STEM experimental image. Particularly, we found that a distance between centers of mass of Cl columns in theoretical structure is expanded by 12 pm, which is very close to an average experimental value of 15 pm (see Fig. 3b). While the presence of distortion in the bulk α-RuCl3 crystals was known from earlier papers (see also Supplementary Note 2 and Supplementary Fig. 2), the STEM measurements presented here provide the first real-space evidence for octahedral distortion in thin films of α-RuCl3.

Figure 3: Analysis of structural distortions in α-RuCl3 films.
figure 3

(a) DFT-calculated relaxed structure of α-RuCl3 unit cell. The equilibrium length of Ru–Cl bonds found in DFT is 236 pm. The Cl–Ru–Cl bond angle at the shared octahedral edges in the relaxed structure is ≈86.3°, whereas the rest of Cl–Ru–Cl angles are approximately 91.3°. (b) Cl–Cl inter-column distances in unperturbed lattice (D0)17,23, DFT calculations (DDFT), and experimental STEM data (DSTEM). (c) DFT-based coordinates of ABC-stacked α-RuCl3 cell superimposed on experimental STEM image. The white arrows schematically show the displacements of Cl columns. (d) Principal component analysis of normal modes of displacement for M=90 unit cells (810 atomic columns); the center of the mass of the entire effective unit cell is chosen as origin. The principal component analysis-derived first three eigenmodes are presented as vectors of deformation from columns position in the averaged cell. Colouring scheme: first three displacement modes are described by blue, red and green arrows, respectively. The length of the arrows is magnified by a factor of 20. The dashed rhombus in c,d schematically denotes the effective unit cell.

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The average STEM unit cell of α-RuCl3 films derived above agrees well with neutron data and DFT calculations providing us a good understanding of a long range atomic order in the α-RuCl3 system. We now use information contained in microscopic degrees of freedom available from STEM images to characterize atomic structure on a local scale25,26,27,28. Particularly, we employ a principal component analysis to search for statistically significant distortions of an average unit cell structure of STEM observations in Fig. 1a26. This issue is important because unit-cell scale variations in order parameters, usually not seen in spatially averaged, or reciprocal space measurements of bulk crystals, may have powerful and non-random effects on the macroscopic observables in strongly-correlated systems29,30. Interestingly, we found only relatively small displacements from average structure in the Ru/Cl columns (see also Supplementary Fig. 3 and Supplementary Fig. 4). As the location of Ru/Cl column centers is determined largely by a contribution from the Ru core electrons (due to the large difference in atomic numbers (Z) between Cl and Ru), the results in Fig. 3d suggests that the positions of Ru atoms in a honeycomb lattice remain nearly intact in a symmetric fashion. On the other hand, relatively large variations from average were observed in the positions of Cl columns. The detected local inhomogeneity in a ligand sublattice can originate from a presence of distortion nanodomains (‘patches’), whose local structure, such as bond length and bond angles, deviates from the average lattice structure (see also Supplementary Note 3). A resultant interplay between local inhomogeneity and ‘regular’ lattice structure may lead to alternation of relative strength (and, in principle, sings) of terms in the spin-1/2 Hamiltonian. It will be interesting to see its implications for the quantum Heisenberg-Kitaev model, where a large number of phases can be generated from the pure Kitaev limit31 by using perturbations that are highly sensitive to the local ligand environment32,33. One intriguing consequence of such local perturbations is a potential realization of a spatially inhomogeneous ground magnetic state in the system. Furthermore, we suggest that our observation of the local variations in lattice structure can provide a lacking ingredient for matching theory models to the results of magnetic measurements on α-RuCl3 (refs 34, 35).

Local density of states

Having analysed in detail the local structural properties of α-RuCl3 crystals, we turn to a real-space characterization of its electronic structure by virtue of ultra-high-vacuum STM imaging and spectroscopic tools. The representative STM topographic image of in situ cleaved α-RuCl3 surface shown in Fig. 4a reveals a hexagonal lattice associated with Cl-terminated surface layer. A typical scanning tunnelling spectroscopy (STS) probe of the density of states on such surface over a wide energy region at T=295 K (Fig. 4b) shows a particle-hole asymmetric dI/dU curve with two well-defined peaks centered at about ±0.7 eV. The presence of a pronounced STS peak at ≈−0.7 eV is in a good agreement with early angle-resolved photoemission spectroscopy (ARPES) measurements of α-RuCl3, in which the author observed a quasi-flat band at 0.7 eV below the Fermi level associated with localized Ru 4d states36. Zooming in to a narrower energy range in Fig. 4c, we found persistent peaks in LDOS at about ±0.12eV, as well as a strong suppression of density of states in the energy window of ≈0.1 eV around the Fermi level. These observations demonstrate a presence of a charge excitation gap at the Fermi level. The formation of an energy gap well above the temperature of a magnetically ordered phase indicates that α-RuCl3 is a Mott-type insulator37. Recent DFT calculations38 have shown that the α-RuCl3 single layer remains metallic if the spin-orbit coupling and electron–electron interactions are not accounted for. The inclusion of spin-orbit coupling and electron correlations leads to an insulating character of density of states with unambiguous charge gap due to a Mott-Hubbard splitting of Jeff=1/2 states. Therefore, our STS observations support a theory view of a monolayer α-RuCl3 as a spin-orbit assisted Mott insulator38. To the best of our knowledge, this is the first observation of Jeff=1/2 state in an individual surface layer of α-RuCl3.

Figure 4: Scanning tunnelling microscopy data on in-situ cleaved α-RuCl3 surface.
figure 4

(a) Representative STM constant current image of the RuCl3 surface layer (tunnelling conditions: Utip=300 mV, Isetpoint=60 pA). Insets: 2D fast Fourier transform of the image (top left), STM cross-sectional profile along the yellow line (bottom right). (b) Averaged STS spectra over a wide energy window; U=−Utip (c) STS spectra in the narrower energy window around the Fermi level showing peaks at ≈±0.12 V (denoted by red arrows). The spectra were averaged over 40 individual dI/dU curves. Setpoint parameters: Utip=−500 mV (b), Utip=−400 mV (c); junction resistance RJ=25 GΩ (b), 20 GΩ (c). (d) Zoomed-in area from white rectangular in a; coexistence of trigonal CO and dimer-like CO shown by red circles and green ovals, respectively. (e) Three-dimensional rendered high-resolution STM image highlighting a crossover between two different phases of CO at Utip=−1.0 V, Isetpoint=100 pA.

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Interestingly, the ≈0.25 eV surface charge gap found in our STS experiment (measured as an inter-peak separation in Fig. 4c) is much smaller than the gap of ≈1.2 eV observed in recent ARPES measurements39, which was also explained as the correlation induced Mott gap. On the other hand, the presence of ≈0.25 eV gap in the STS experiment agrees well with observations of a peak at about 0.3 eV in X-ray adsorption measurements17,40 and of a 0.2 eV gap in neutron measurements of bulk α-RuCl3 crystals3. The origin of the current discrepancy between STM and ARPES measurements of the gapped state of α-RuCl3 must be carefully addressed in future studies of this material.

Charge density modulation

To further explore details of the real-space electronic behaviour on a local scale it is crucial to be able to identify positions of electron density peaks associated with an underlying Cl atomic sublattice in the STM image in automated fashion. For this purpose, we first create a template unit cell from fast Fourier transform-filtered image data, and then perform normalized cross-correlation analysis coupled with position based and intensity based refinement in order to extract maximal electron densities associated with Cl sublattice (see Supplementary Note 4 for details). The resultant lattice of electronic densities is shown in Fig. 5a (see also Supplementary Note 5 and Supplementary Fig. 5 for analysis of the nearest neighbour distances in the constructed lattice).

Figure 5: Analysis of scanning tunnelling microscopy data on α-RuCl3 surface.
figure 5

(a) Colour-coded binary lattice overlay. The red lattice spots correspond to the normalized intensity above the threshold of 0.5 and form a superlattice of a periodicity. (b) Histogram-based visualization of distribution of STM intensities at Cl atoms in a; the two peaks are approximated by Gaussian curves. The green arrow indicates admixture of a competing CO into charge density distribution. Inset in b shows a three-dimensional rendered experimental image of Cl triangular unit with a non-uniform distribution of STM intensities. (c) Schematic model showing anisotropy of charge density at Cl atoms along Ru–Cl–Ru electron hopping pathways (double-end blue and red arrows). The three ‘top’ Cl atoms in the unit cell are labelled in the same way in b,c.

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Once the construction of electron densities lattice is completed (that is, all the positions of electron density peaks are identified), one can clearly see a modulation of STM intensity associated with an intra-unit cell symmetry breaking in a charge density distribution at three ‘top’ Cl atoms in the α-RuCl3 layer unit cell. This can be confirmed by looking at the histogram-based visualization of the STM intensities distribution (Fig. 5b) for all the ‘lattice’ points associated with Fig. 4a. The two well-defined peaks in the histogram, whose height differs by roughly a factor of 2, reflect the enhancement of the STM intensity on every third Cl atom. On a larger scale, this leads to a formation of a charge ordered pattern (CO) with a (R3) surface symmetry (R is a translational vector of an unperturbed Cl surface lattice). Noteworthy, an emergence of a qualitatively similar R3 electronic superlattice has been recently reported in the STM experiment on the honeycomb iridates, where it was explained as purely due to the structural reconstructions41. Since STM cannot always distinguish between electronic and structural contributions, one may argue that the non-uniform distribution of STM intensity on α-RuCl3 surface is in fact due to the geometrical tilts/rotations of Ru-centered Cl octahedral cage. However, a presence of such octahedral tilts with long range order does not follow from the detailed structural analysis described in the first part of the paper. Indeed, all Cl surface atoms remained confined to a two-dimensional plane in our structural analysis. This confirms that the formation of the R3 superlattice is due to the electronic symmetry breaking at Cl-terminated surface of α-RuCl3 crystals. The superlattice and regular Cl lattice form the inner and outer hexagons, respectively, rotated by 30° with respect to each other in the 2D fast Fourier transform of the STM image (inset in Fig. 4a). The R3 pattern was observed up to relatively high energies with respect to Fermi level (Utip≈|1.5 V|), at both positive and negative bias polarities.

To elucidate a possible physical origin of the CO we start with discussing a potential relation between CO and lattice degrees of freedom in α-RuCl3. The trigonal component of RuCl6 octahedral distortion found in DFT results in a well-defined periodic modulation of Cl interatomic distances that breaks the hexagonal symmetry of 2D surface layer. The resultant distorted hexagonal pattern features alternating short and long Cl–Cl interatomic distances of 337 pm and 359 pm, respectively (see Supplementary Note 6 and Supplementary Fig. 6). The symmetry of atomic distortions at the surface plane matches well with the symmetry of the R3 superlattice formed by the brightest spots in the STM image, implying a direct relation between Cl atomic displacements and CO. However, our DFT-based STM simulations did not reveal any imbalance in the distribution of charge density despite finding the distortion of Cl cage (see Supplementary Fig. 6), indicating that the Cl displacements are not the primary cause of the observed CO. We have also investigated the possible role of surface relaxation effects (see Supplementary Note 7, as well as Supplementary Figs 7–9) and found these to be negligible reflecting the fact that α-RuCl3 is a quasi-2D system.

Another argument explaining the emergence of a CO phase stems from the possible non-equivalence of the three ‘bond axes’ (that is, the nearest neighbour Ru–Ru distances within a layer, which hereafter are referred as ‘bonds’) in the sample. We note that the intra-unit cell symmetry breaking in the STM experiments persists at the energies as high as +1.5 eV above the Fermi level suggesting involvement of both t2g-derived and eg-derived electronic states in a formation of the CO pattern17. This observation is important because a hopping process between t2g and eg orbital via ligand atom is vital in determining a ground state of Kitaev-Heisenberg model on the honeycomb lattice42 (see also Supplementary Note 8).

The experimentally observed anisotropy in a charge density distribution along Ru–Cl–Ru hopping pathways, schematically denoted by red and blue arrows in Fig. 5c, indicates that the bond-dependent behaviour in α-RuCl3 may appear at temperatures ∼3 times higher than an estimated strength of the Kitaev coupling (∼100 K) (refs 3, 19). Since the STEM and neutron measurements suggest that the high-temperature lattice structure primarily complies with a trigonal P31 type space group and that the Ru sublattice is isotropic (see for example, Fig. 1b), which agrees with DFT calculations, we argue that it is the anisotropic exchange pathways via the Cl sublattice that imparts additional bond-directional anisotropy along the Ru–Ru bond axes. It results in an overall anisotropic energy distribution, that could explain why the RuCl3 layers rearrange and form a C2/m structure at temperatures below 154 K (ref. 22). Arguably, this would also determine the direction of the ‘a’ and ‘b’ axes of the C2/m structure. This, in turn, would determine the direction of the zig-zag ordering, where the blue ‘bonds’ in Fig. 5c have aligned spins, and the red ‘bonds’ have anti-aligned spins. This anisotropy in the chlorine position will directly affect the Kitaev Hamiltonian and has to be included in the calculations to simulate both the anisotropic susceptibility and the spin-wave gap of 2 meV observe in this material3.

We next discuss a fine structure of the CO state at the Cl-terminated surface, in which the clusters of dimer-like electronic superlattice are admixed into the trigonal R3 CO electronic superlattice discussed above (see Fig. 4d,e). These two types of superlattices were persistently found in various areas of the sample at different bias voltages. The admixture of the dimer-like superlattice into CO produces an additional weaker peak in the histogram in Fig. 5b (denoted by a green arrow), as confirmed by the inspection of absolute values of the normalized STM intensities extracted from Fig. 4a. This effectively turns the surface of α-RuCl3 into a competing CO heterogeneous system. The peculiar switching between two surface electronic superlattices at nanometre length scales can be related to a subtle crystalline disorder, such as occurrence of vacancies in the bottom Cl layer of RuCl3 ‘sandwich’ which cannot be directly seen in the STM, as well as due to the presence of defects in the second RuCl3 ‘sandwich’ layer. Furthermore, the variations of an average unit cell structure in the Cl sublattice have been routinely seen in our analysis of the STEM data. The nanoscale strain fields associated with competing structural orders can induce a transition of a purely electronic nature between different CO phases as was recently reported for NbSe2 (ref. 43). Another interesting possibility is that the observed fine structure of CO is a reflection of magnetic short-range correlation persisting above TN (ref. 35). It remains to be seen in the future, if magnetic patches could couple via the strong spin-orbit coupling to the orbital occupation in the Ru atoms, which in turn would alter the hybridization with the Cl-p orbitals and thus the tunnelling current in the STM tips. In addition, it will be educational to measure the anisotropy of the in-plane susceptibility signal, as such will also be affected by these magnetic patches. Finally, the spatial fluctuations of CO may produce an additional scattering potential for electrons in α-RuCl3 and associated contribution to the resistivity of the individual α-RuCl3 layers.

Discussion

To summarize, we have presented the first comprehensive study of the local electronic and lattice degrees of freedom in α-RuCl3. We expect that the findings reported here will have significant ramifications in several areas of research on spin-orbit coupled Mott insulators with possible Kitaev QSL state. First, our finding of a charge gap at EF in a surface monolayer of α-RuCl3 well-above a temperature of a magnetically ordered phase supports the theoretical view of a Jeff=1/2 Mott insulator produced by an interplay of electron correlations and spin-orbit coupling. Second, we observed the emergence of a charge-ordered pattern originating from anisotropy in the charge distribution along Ru–Cl–Ru hopping pathways. The charge order appears to have a fine structure, in which two types of the electronic superlattices, dimer-like and R3 trigonal, coexist at the nanometre length scale. One of the intriguing questions for future studies is: What are the exact implications of the charge distribution at the Cl- ligands on the spin degrees of freedom in the Kitaev limit? Third, our finding of a structural inhomogeneity in the ligand sublattice is significant as it may result in a unit-cell scale inhomogeneity of the magnetic ground state. Finally, our discussion on potential interplay between charge, lattice and spin degrees of freedom hinted at the possibility of nanoscale strain engineering of magnetic and electronic properties in α-RuCl3, which would enable applications in hybrid spintronics and straintronics devices. In the future, we expect that extensions of this work using heterojunction techniques, as well as thin films with mis-oriented RuCl3 layers44, may provide a pathway to drive α-RuCl3 or related materials towards the pure Kitaev limit where the true quantum-spin-liquid ground state flourishes.

Methods

Sample preparation (bulk crystals)

Commercial-RuCl3 powder was purified in-house to a mixture of α-RuCl3 and β-RuCl3, and converted to 99.9% phase pure α-RuCl3 after annealing at 500 °C. Single crystals of α-RuCl3 were grown by vapour transport with TeCl4 as the transport agent.

Neutron scattering

Neutron scattering experiments and the data in Fig. 2 were obtained using the HB-3A Four-Circle neutron diffractometer at High Flux Isotope Reactor at ORNL using an incident energy Ei=14.7 meV on a large single crystal (1 cm × 1 cm × 0.3 mm) mounted on the top of the Goniometer head on a 4 K displex. The data has been analysed using FullProf structural refinement routine, and further confirmed using X-ray diffraction measurements refined using ShelX program. Above 200 K, the structure is consistent with the P31 space group, while at low temperatures the structures are consistent with C2/m proposed in ref. 21. Interestingly enough, the phase transition was not observed in powder and smaller samples which remain in the same space group at all temperatures.

STEM experiment

The films of α-RuCl3 for STEM measurements were exfoliated by sonication of bulk samples. STEM-annular dark field imaging was performed on an aberration-corrected Nion UltraSTEM-100 microscope operated at 60 kV. Only the images without noticeable electron beam induced structural damage were used for analysis. The STEM images used in analysis were summed over 30 frames after cross-correlation.

STM experiment

The STM experiments were performed using an Omicron VT-STM equipped with a Nanonis controller in an operating pressure of 2 × 10−10 Torr. The samples for the STM experiments were cleaved in the ultra-high vacuum (∼10−10 Torr). The STM images were obtained with mechanically cut Pt/Ir alloy tips with electrically biased tips and grounded samples. Due to the insulating nature of α-RuCl3, the STS measurements were performed at T=295 K, using a standard lock-in technique, with high-tunnelling junction resistance RJ=20–25 Ω. To ensure a reproducibility of the high-temperature STM spectroscopic measurements, the dI/dU curves were recorded at clean surface areas (that is, with no apparent defects) in several macroscopically different regions of each sample and the resultant averaged data was compared across the samples from three different batches.

DFT calculations

The DFT calculations were performed within the generalized gradient approximation using the Perdew–Burke–Ernzerhof exchange correlation scheme45 and projector augmented wave potentials46 as implemented in VASP47,48. We used a 400 eV kinetic energy cutoff and 7 × 7 × 3 Monkhorst-Pack type k-point grid49 to calculate the relaxed atomic geometries. The internal forces were relaxed to <10 meV Å−1 without enforcing any symmetry. The external lattice parameters were fixed to the experimental values reported in ref. 23.

Statistical and image analysis

The principal component analysis of STEM data, construction of electron densities lattice from STM image, and analysis of atomic distances were performed using MATLAB software.

Data availability

The data that support the findings of this study are available from the corresponding authors upon request.

Additional information

How to cite this article: Ziatdinov, M. et al. Atomic-scale observation of structural and electronic orders in the layered compound α-RuCl3. Nat. Commun. 7, 13774 doi: 10.1038/ncomms13774 (2016).

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