Break of symmetry at the surface of IrTe₂ upon phase transition measured by x-ray photoelectron diffraction

By focusing on a particular core level in XPS, it is possible to choose the specific emission intensity of a given atom. The selected outgoing photoemitted electrons have a strong anisotropic distribution of angular intensity related to the local geometry around the target atom. The analysis of the obtained XPD patterns is simplified for electron kinetic energies above about 500 eV. Above this energy the strong anisotropy in the individual electron–atom scattering leads to a forward focusing of electron flux along directions pointing from the photoemitter to the scatterer [29]. The so-called forward focusing effect consists of a strong increase in intensity along the emitter–scatterer direction and more generally along densely packed atomic planes (giving so-called Kikuchi bands) and rows of atoms (corresponding to low-index crystallographic directions) [5, 30].

In order to anticipate the main intensity peaks in the XPD measurements, we describe below specific patterns that can be observed from a diffractogram emitted from an iridium atom, later called Ir emitter. Figure 2(a) shows in-plane and out of plane cuts of the 1T-IrTe₂ crystal structure, where Ir atoms are represented with blue markers and Te atoms with red markers. The Te atoms closest to the Ir emitter, in gray, will lead to major intensity peaks, with the forward-focusing effect, in the XPD diffractograms. There are six Ir atoms near the emitter, highlighted with a red hexagon, which will result in high intensities in the XPD diffractograms. In addition, these Ir atoms are also located on the Kikuchi bands {101}, the black dashed lines. The crossings of the Kikuchi bands, on a batch of Ir atoms, reflect the orientation of the unit cell as well as three-fold symmetry and are therefore sensitive to modifications of the structure during phase transitions. This crossing is highlighted by an orange quadrilateral. The next closest Ir atoms, highlighted with light blue arrows, will also cause distinctive intensities in the XPD diffractograms.

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To simulate, in a simple way, the diffraction patterns expected from the structure above, we adopt the following strategy. We construct a cluster of atoms centered on an Ir atom, chosen to be an emitter. For the (1 × 1) phase, the cluster is developed for the 1T crystallographic structure (space group $P\bar{3}m1$) with the lattice parameters a = b = 3.93 Å and c = 5.40 Å and a trigonal unit cell, as presented in figure 1(a). The Ir emitters are distributed, one per sandwich, down to 13 Å below the surface which corresponds to three layers, obtained from the electrons IMFP [31]. The in-plane size of the cluster consists of 13 × 13 unit cells. For the (5 × 1) phase, we take a cluster size similar to the (1 × 1) phase cluster (in terms of number of atoms as the unit cell in the (5 × 1) phase is very large), with the lattice parameters from the literature a^⋆ = 3.95 Å, b^⋆ = 6.65 Å and c^⋆ = 14.45 Å in a monoclinic unit cell $(P\bar{1})$ [8, 17]. Due to the symmetry break induced by the phase transition (the three fold symmetry switching to an one fold symmetry), there are then five Ir atoms per unit cell. According to the Wyckoff classification system, we have one Ir atom (monomer) at (1a) site, two Ir atoms (monomer) at (2i) sites and two Ir (dimer) at (2i) sites. We attribute these different sites to five inequivalent Ir atoms, based on a local view. We then discriminate these inequivalent atoms in the calculations to be able to construct the different diffractograms representing the structure from the perspective of a monomer or dimer emitter.

For a cluster centered on an Ir emitter, as described above, we build a simulated diffractogram as follows. For all scattering atoms above this emitter, we calculate the relative position in polar coordinates. We display in figure 2(b) in stereographic projection these relative positions in order to simulate the XPD diffractograms. For this purpose, we calculate the relative distance of these scattering atoms k to the emitter L_k , while noting the atomic mass Z, in addition to the distance of the emitters i to the surface d_i , in order to determine their respective sizes. The size of the scattering intensities D_k,i in the stimulated diffractograms is then established from the following formula, knowing that for neighboring atoms of the same type (angular distances less than 0.01) we sum their respective sizes,

$$\begin{equation*}{D}_{k,i}=Z{e}^{\frac{-{L}_{k}-{d}_{i}}{\lambda }},\end{equation*}$$

where λ is a proportional factor related to the IMFP (λ = 13 Å). The scattering contributions of all three layers and all inequivalent emitters are finally summed to generate simulated diffractograms. All the features highlighted in figure 2(a) are also present in the simulated diffractogram in figure 2(b) with the same color code. An additional effect is the refraction that occurs as the electron wave passes from the solid to the vacuum. We therefore introduce a correction θ^cor on the polar angle θ in proportion to the kinetic energy (E_kin) and the inner potential (V₀ = 13 eV [6, 24]) which is defined as

$$\begin{equation*}{\theta }^{\text{cor}}=\mathrm{arcsin}\left(\mathrm{sin}(\theta )\sqrt{\frac{{E}_{\text{kin}}}{{E}_{\text{kin}}-{V}_{0}}}\right).\end{equation*}$$

The contributions of each type of scatterer [Ir (monomer), Te and Ir (dimer)] have been differentiated by color in the simulated diffractograms. This enables the precise identification of the origin of the intensities in the XPD measurements, but reduces the agreement with the XPD measurements. Indeed, the bullets therefore appear smaller and denser in the simulated diffractograms in the (5 × 1) phase, as 2/5 of the Ir atoms are dimerised with a strongly modified structure compared to the RT structure, see figure 1.

In figure 3(a), we recall schematically the structure of the basic building blocks for the Ir plane in two different phases of IrTe₂. The (1 × 1) phase is composed only of equivalent Ir atoms represented with blue bullets (as seen also in figures 1(a) and (b)), leading to a single Ir 4f_7/2 core level at 60.6 eV. In the (5 × 1) phase, five atoms split in two dimerized Ir atoms represented with light blue bullets (one dimer) and three undimerized atoms (figures 3(a) and 1(c), (d)) ⁵ . This leads to a splitting of the Ir 4f_7/2 core level into a contribution due to the dimerized Ir atoms [6, 14, 27, 32], at higher binding energy, and a contribution due to the three undimerized Ir atoms. These different contributions in XPS are used to acquire XPD diffractograms specific to the local environment of the monomer (undimerised) and dimer Ir atoms. We present the corresponding XPS spectra and detailed fit of the Ir 4f core levels in figure 3(b) with a zoom on the Ir 4f_7/2 core levels measured at different temperature upon cooling. A clear splitting occurs below ${T}_{{c}_{1}}$ between the peak at 60.6 eV binding energy, which is attributed to the monomer states, and a new peak appearing at 61.2 eV binding energy corresponding to the dimer states. The intensity ratio measured by XPS has been interpreted as a measure of the density of dimers in the different phases observed in IrTe₂ [6, 14, 32]. Below ${T}_{{c}_{1}}$, in the (5 × 1) phase, the dimerized Ir atom ratio is 0.4 and this is also in good agreement with the relative peak intensities in our XPS data at normal emission.

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Figure 3(b) displays also the fit components used in the data processing. The panels show an exemplary spectrum of the full XPD data at two different temperatures. In the first panel, the raw data (in blue) at RT in the (1 × 1) phase are fitted with two Voigt functions, one is attributed to the main core level and the second to a shake-up satellite ⁶ (in light blue), composing the total fit (in orange). The Voigt functions have a fixed position, at 60.6 eV and 61.0 eV respectively, and their relative amplitudes are fixed. The second panel displays an exemplary spectrum of the full XPD data taken at 250 K in the (5 × 1) phase (in blue) along with the fit components. Since IrTe₂ has undergone a phase transition expressed in a splitting of the Ir 4f_7/2 core level, we then chose to use four Voigt functions with fixed position and with their relative amplitudes fixed two by two. Thanks to this fitting procedure, out of a full XPD data set we obtain two XPD diffractograms of IrTe₂ in the (5 × 1) phase. An XPD diffractogram for the emitter in the monomer state and the second one for the emitter in the dimer state are then generated. In order to simplify the language, we will use the term monomer emitter for an Ir emitter atom in monomer state and dimer emitter for an Ir emitter atom in the dimer state.

Figures 4(a)–(c) displays the XPD diffractograms (top row) and their respective simulated diffractograms (bottom row) for an Ir 4f_7/2 core level emitter in the (1 × 1) phase at 295 K from a monomer emitter, in the (5 × 1) phase from a monomer emitter and in the (5 × 1) phase from a dimer emitter at 250 K, acquired using 500 eV photon energy. These measurements and simulations probe the local environment in real space for both monomer and dimer emitters. Normal emission intensity is at the center and grazing angle emission is at the edge of the diffractogram. The XPD measurements present the high intensities in white and the low intensities in black. The simulated diffractograms are constructed according to the procedure detailed in section 3.2, where the Te scatterer atoms are represented with red bullets, the Ir monomer scatterer atoms with dark blue bullets and the Ir dimer scatterer atoms with light blue bullets.

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The diffractograms in the (1 × 1) phase show the typical three-fold symmetry of the IrTe₂ space group. In the experimental data from figure 4(a), the forward focusing peaks, present since electrons have a kinetic energy of 500 eV, are dominant and define intensity patterns that reflect the emitter local environment. These peaks are located along low-index directions, as well as on the Kikuchi bands connecting these directions. The patterns at the crossing of the Kikuchi bands are highlighted in orange. The particular patterns anticipated in section 3.2 can be recognized in the XPD diffractograms, see figure 2, from the signatures of the closest Ir atoms close to 30° in polar angle θ (red hexagon) to the next closest Ir atoms below 60° in polar angle θ at 90°, 210° and 330° in azimuth angle ϕ (light blue) and in particular the crossings of the Kikuchi bands, as already mentioned. The simulated diffractogram in figure 4(a) contains only fingerprints originating from Ir monomer and Te atoms, since the crystal is in the (1 × 1) phase. Globally, the simulation is comparable to the experimental measurement.

Now we focus on the main pattern modifications in XPD diffractograms for a monomer emitter in the (5 × 1) phase, see figure 4(b). Although the experimental XPD diffractogram for a monomer emitter in the (5 × 1) phase have similarities with the experimental XPD diffractogram for a monomer emitter in the (1 × 1) phase, we observe a symmetry break from the trigonal to the monoclinic unit cell that occurs in particular at the intersection of the Kikuchi bands at about 150° in azimuth angle ϕ. This change is pointed out with a blue quadrilateral. The Kikuchi bands crossing is shifted by a few degrees in azimuth angle ϕ toward 180°. In contrast, the Ir atoms plane on the Kikuchi band at the opposite side of this crossing is not much affected by the phase transition. The respective local environments of the different inequivalent Ir atoms ⁷ are affected by the phase transition which explains the changes in the simulation. This is the result of structural modifications by the emergence of dimerised Ir atoms in the structure as shown in the top view of figure 1(d). For example, the dimerised Ir atoms in the layer above the inequivalent monomer emitters are located more on the left side rather than the other and this results in a higher concentration of dimer signatures in upper left part of the simulated diffractogram. Moreover, in the simulated diffractogram, the stripes of dimerised Ir atoms are arranged along the one-dimensional axis from 60° to 240° in azimuth angle ϕ, in the same direction as in figure 1(d). These split signatures in the simulated diffractogram are expressed as shifts in intensity, in the experimental XPD diffractogram, and are in good agreement. This suggests then that the experimental measurement shows a preferential direction of dimerisation.

The experimental XPD diffractogram for dimer emitters, in the (5 × 1) phase in figure 4(c), displays broader intensities. Although some of the patterns strongly remind those of the monomer XPD diffractograms such as the Kikuchi bands and the highlighted quadrilaterals, they are more difficult to identify. The simulated diffractogram, in figure 4(c), shows the same perturbation of the Kikuchi band crossing as well as a stronger splitting of the Ir monomer scatterer, Ir dimer scatterer and Te scatterer signatures as in the simulated diffractogram for the monomer emitter in figure 4(b). The signatures of Te atoms at 90°, 210° and 330° in azimuth angle ϕ near 77° in polar angle θ are significantly perturbed. The structure of the figure 1(c) provides a better understanding of the local environment of the dimer emitters. The dimerised Ir atom local environment changes are then enhanced in the simulation as well as the diffraction measurement since the dimerised Ir atom moved by 0.8 Å [16] from its original RT position, with staircase-like stacking. Dimerised Ir atoms therefore have an apparent disordered local environment, see figure 1(d). The resulting patterns in the experimental and simulated diffractograms, in the (5 × 1) phase, for a dimer emitter, are then broader than the other experimental and simulated diffractograms.

To emphasise the intensity changes undergone across the first phase transition, figure 5(a) displays a diffractogram ⁸ constructed with the experimental XPD diffractogram for an monomer emitter in the (5 × 1) phase minus the experimental XPD diffractogram for a monomer emitter in the (1 × 1) phase. The azimuthal cuts at three different polar angles θ shown in figure 5(b) display the gains (in red) and losses (in blue) of intensities caused by the phase transition. We see that the main variation is at the crossing of the Kikuchi bands near 150° in azimuth angle ϕ near 52° in polar angle θ, as observed in figure 4. Intensity from below 150° in azimuth angle ϕ is transferred to higher azimuthal angle. This is due again to the breaking of the three-fold symmetry across the phase transition. A significant gain is observed at 90°, 210° and 330° in azimuth angle ϕ near 77° in polar angle θ. This effect can be observed in the simulated diffractograms in figures 4(a) and (b). Te atoms, located in the lower plane of the Te–Ir–Te sandwich immediately above the emitter in figure 1, move toward the normal emission in the (5 × 1) phase during the phase transition and cause this red signature in the diffractogram in figure 5. Finally, the lower central part of the diffractogram remains white indicating that minimal changes occurred in this region, as already pointed out earlier in the discussion of figure 4(b). Figure 5(c) shows a diffractogram composed of the experimental XPD diffractogram for a dimer emitter in the (5 × 1) phase at 250 K minus the experimental XPD diffractogram for a monomer emitter in the (1 × 1) phase with azimuthal cuts (d) similarly to (a) and (b). A pronounced shift in intensity of a few degrees close to 150° in azimuth near 52° in polar angle θ occurs, as observed before. We note that the differences between XPD diffractogram for a monomer emitter in the (1 × 1) phase and XPD diffractogram for a dimer emitter in the (5 × 1) phase are globally larger (with greater amplitudes) than the diffractogram in figure 5(a) due to the huge displacement of the dimerized Ir atoms emitter with respect to the RT structure. An unaffected domain, in white, lies in the center of the lower part of the XPD diffractogram difference, but considerably smaller than that in figure 5(a), supporting the greater amount of changes in the local environment of the dimer emitter. In addition to these difference plots, animations, presenting the XPD diffractograms one after the other, are available in supplementary materials (https://stacks.iop.org/JPCM/34/075001/mmedia) to this paper. These animations highlight the differences between the XPD diffractograms of the different emitters in a very visible way.

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In our study we can confirm, within the limit of the surface local environment sensitivity of our measurement, the bulk-sensitive observations made with XRD for the (1 × 1) phase [6, 8] and the (5 × 1) phase [6, 17, 34] as well as the surface-sensitive observations made with STM [6, 15, 18, 22, 23]. We further contribute by probing the local real space of Ir atoms down to three layers, giving access to the surface as well as to the subsurface region. We observe the break of the three fold symmetry induced by the phase transition, using the crossing of the Kikuchi bands as reference. We investigated this effect on both experimental XPD diffractograms for a monomer emitter and dimer emitter in the (5 × 1) phase. Qualitatively our results are consistent with the atomic positions obtained from the bulk structure of both the (1 × 1) and (5 × 1) phases and therefore the stacking in a staircase scheme [8, 17] of the dimerised Ir atoms near the surface, see figure 1. In particular, the XPD patterns evolution through the phase transitions confirm the displacements of the Ir atoms. This displacement leads to an apparent local disordered environment for the dimerised Ir atoms, resulting in XPD diffractograms with broad intensities. In addition, our XPD measurements confirm that Te atoms also undergo large displacements relative to the Ir emitter, suggesting their participation in the stabilisation of the Ir dimers, as also established using DFT calculations [21, 35] and experimental investigations [19, 35]. The simulated diffractograms permit to estimate these displacements with an accuracy of about 5% of the lattice parameters. Beyond this limit, the simulated diffractograms no longer display any clear similarity with the experimental diffractograms.

Given the complexity of the IrTe₂ structure at low temperature, with multiple inequivalent emitters arranged in staircase-like scheme, XPD calculations are challenging to achieve using codes such as multiple scattering package for spectroscopies using electrons to probe materials (MsSpec) code [36] or electron diffraction in atomic clusters code [37]. Therefore, we leave this effort for future studies.

Furthermore, we were able to measure a crystal of IrTe₂ at low temperature in a preferential orientation, although the photon beam size and the method of XPD acquisition implies that we probed likely a region of several 100 micrometres, much larger than domains observed in the literature [15, 22, 38]. This very large region of the (5 × 1) phase in a preferential orientation suggests that our crystal is locally under strain possibly due to the silver epoxy glue used, as was already observed for the (6 × 1) phase on a strain induced sample holder [27].

The following abbreviations are used in this manuscript: