Phase Separation Prevents the Synthesis of VBi2Te4 by Molecular Beam Epitaxy

Intrinsic magnetic topological insulators (IMTIs) have a non-trivial band topology in combination with magnetic order. This potentially leads to fascinating states of matter, such as quantum anomalous Hall (QAH) insulators and axion insulators. One of the theoretically predicted IMTIs is VBi2Te4, but experimental evidence of this material is lacking so far. Here, we report on our attempts to synthesise VBi2Te4 by molecular beam epitaxy (MBE). X-ray diffraction reveals that in the thermodynamic phase space reachable by MBE, there is no region where VBi2Te4 is stably synthesised. Moreover, scanning transmission electron microscopy shows a clear phase separation to Bi2Te3 and VTe2 instead of the formation of VBi2Te4. We suggest the phase instability to be due to either the large lattice mismatch between VTe2 and Bi2Te3 or the unfavourable valence state of vanadium.

To introduce magnetism into TIs, the following methods are currently used [16]: doping magnetic ions into the TI [6,7,11,17], bringing the TI in proximity with ferromagnetic materials [10,16,[18][19][20] and incorporating intrinsic magnetic moments in the crystal structure, which results in an intrinsic magnetic topological insulator (IMTI) [8,9,14,21,22].All three methods are successful in realising the QAH state; however, with the former two methods the temperatures at which this state arises is very low in the light of applications.It is interesting to compare the temperature at which the QAH effect is observed to the Curie temperature (T C ) of the materials.Remarkably, the temperatures for observing the QAH effect are an order of magnitude smaller than T C [16].The explanation for this difference in temperature depends on the method used to introduce the magnetism.In the magnetically doped system, the the high level of disorder caused by the random distribution of magnetic dopants may reduce the effective exchange gap [16], form a conducting bulk or create regions without ferromagnetic ordering [11].In the magnetic proximity system, the sensitivity to the interface between the TI and the magnetic material is the main problem [14].
These challenges are overcome in IMTIs because in these materials the magnetic moment is intrinsically embedded in the unit cell.In 2019, Li et al. [9] theoretically predicted a class of materials acting as IMTIs, called the MBT family (M = transition-metal or rare-earth element, B = Bi or Sb and T = Te or Se).The materials in the MBT family have the same crystal structure, but their behaviour differs depending on the magnetic element (transition-metal or rare-earth element, M) in the MBT structure.The unit cell of the MBT family can be viewed as the unit cell of the well studied family of Bi 2 Te 3 TIs, with a structural intercalated layer containing a magnetic element.The addition of magnetism within the unit cell results in periodic magnetic layers, which results in a large magnetic exchange gap [9,21].A representative material of the MBT family is MnBi 2 Te 4 , for which the crystal structure is shown in Figure 1a.Like other materials in the MBT family, it crystallises in the R3m space group with a rhombohedral structure.Each monolayer has a triangular lattice with ABC stacking along the out-of-plane direction.A monolayer is structured as a septuple layer (SL) with T-B-T-M-T-B-T stacking and a Van der Waals (VdW) gap separates consecutive SLs.The Mn atoms introduce a magnetic moment of 5 µB per atom with an out-of-plane easy axis [9].The exchange coupling within a single SL (J || ) is ferromagnetic (FM), while the coupling between consecutive SLs (J ⊥ ) is antiferromagnetic (AFM) [9,[23][24][25].In these VdW materials, the J || is much stronger than J ⊥ [23,26].
Another potential member of the MBT family of IMTIs is the theoretically predicted VBi 2 Te 4 [9].In contrast to MnBi 2 Te 4 , VBi 2 Te 4 has a predicted in-plane easy axis (Figure 1b), the V-atoms introduce a magnetic moment of 3 µB per atom [9,26] and a stronger J ⊥ is expected in VBi 2 Te 4 leading to a higher T C [26].The latter could potentially result in a higher temperature at which topological phases such as QAH can be observed, opening up possibilities for applications.However, to the best of our knowledge, no experimental evidence of VBi 2 Te 4 has been published so far.
In this work, we report on a structural MBE study to synthesise VBi 2 Te 4 .The crystal structure of the films was analysed by X-ray diffraction (XRD), scanning transmission electron microscopy (STEM) and energy dispersive diffraction (EDX), which are suitable techniques to detect the presence of the SL structure of VBi 2 Te 4 .The surface morphology of the films was characterised by reflective high energy electron diffraction (RHEED) and atomic force microscopy (AFM).The analysis of the crystal structure indicates a phase separation to Bi 2 Te 3 and VTe 2 instead of the SL structure of VBi 2 Te 4 .This observation suggests VBi 2 Te 4 to be unstable in the deposition conditions of MBE.

Materials and Methods
The deposition of VBi 2 Te 4 is performed on (0001)-Al 2 O 3 substrates in an ultrahigh vacuum Octoplus 300 MBE system from Dr. Eberl MBE Komponenten with a base pressure of 5.0 × 10 −11 mbar.High-purity (6N) bismuth (Bi) and tellurium (Te) are evaporated from standard Knudsen effusion cells and their fluxes are calibrated by a quartz crystal monitor.The Bi-and Te-flux are kept constant during the depositions at ϕ Bi = 0.0027 Å/s and ϕ Te = 0.072 Å/s.ϕ Te is set to a high flux to prevent Te vacancies.High-purity (5N) vanadium (V) is evaporated from a custom high-temperature Knudsen effusion cell.The flux, ϕ V , is indicated by the heating temperature of the Knudsen cell and is varied from 1750 • C to 1900 • C. The combination of the V-pocket size and the high evaporation temperature result in a large flux instability measured with the quartz crystal monitor, and therefore the pocket temperature will be kept as a reference for ϕ V .An estimate for the flux variation in this temperature range is from 0.001 Å/s to 0.0080 Å/s.The substrate temperature T sub was kept constant at 150 • C. Before the deposition of VBi 2 Te 4 , a buffer layer of Bi 2 Te 3 was deposited of ≈1 nm.The samples discussed in this article are deposited using the co-evaporation method, meaning all elemental beams are opened simultaneously during the full deposition.In addition to these results, some attempts were made to use a beamshuttering method to interrupt the V-and Bi-beams during the deposition.First, Bi and Te are opened to deposit a monolayer of Bi 2 Te 3 .Second, V and Te are opened to deposit a monolayer of VTe on top of the Bi 2 Te 3 layer.Third, an annealing step is applied during which the VTe layer should diffuse into Bi 2 Te 3 to form the SL of VBi 2 Te 4 .These three steps were repeated to form a multilayered VBi 2 Te 4 film.This method was previously used to successfully deposit MnBi 2 Te 4 by MBE [27], but for VBi 2 Te 4 the beam-shuttered method resulted in the same observations discussed here for the co-evaporation method showing a phase separation to VTe 2 and Bi 2 Te 3 .Right after deposition, a RHEED image of the diffraction pattern is taken.From the RHEED image the in-plane lattice constant can be deduced by comparing the diffraction pattern of the film to a known substrate.
The crystal structure of the films is measured with XRD, STEM and EDX.The XRD measurements are performed with a Bruker D8 Discover system (Bruker, Billerica, MA, USA) with a two-dimensional Eiger2 500K detector and a two-bounce channel-cut germanium monochromator.Symmetric 2θ-ω scans were performed along the surface normal direction.The STEM measurements are made with a Thermo Scientific Spectra 300 STEM (Thermo Fisher Scientific, Waltham, MA, USA) with an electron beam voltage of 300 kV and a high-angle annular dark-field (HAADF) detector.

Results
The crystal structure of the films is analysed with STEM, EDX and XRD.STEM is performed on a sample deposited with ϕ V = 1800 • C (Figure 2a).The image shows the V-Bi-Te film and the Al 2 O 3 substrate.These STEM results clearly indicate two regions by looking at the contrast.These variations are caused by the Z-contrast related to the atomic weight of the present elements.For a V-Bi-Te sample, the atomic weights are arranged as m Bi > m Te > m V .Therefore, the bright areas in Figure 2a are Bi-rich regions.These results clearly indicate a phase separation between a Bi-compound and a non-Bi compound.EDX (Figure 2b) shows a clear separation between a Bi/Te region and a V/Te region.Figure 2c shows a detailed STEM scan of the sample.The atoms in the bright areas are structured as a QL separated by a VdW-gap.This structure is consistent with Bi 2 Te 3 (Figure 1c).In the darker area the bright atoms form the typical Te octahedra of VTe 2 which are separated by a VdW gap as shown in Figure 1d.The in-plane lattice constant a is related to the distance between the atoms in the x-direction, dx. Figure 2d shows the distribution of dx as extracted from Figure 2c.This distribution indicates two clearly separated regions.The in-plane lattice constants related to these two regions are calculated from the dx value with maximum intensity as a = 2dx for both Bi 2 Te 3 and VTe 2 .This calculation results in the lattice constants a 1 = 3.82 Å, corresponding to VTe 2 , and a 2 = 4.65 Å, corresponding to Bi 2 Te 3 .
Figure 2e presents the 2θ-ω scans of films deposited with different ϕ V .The peaks in the 2θ-ω scans can be identified as the (00l)-Bi 2 Te 3 and (00l)-VTe 2 peaks.The dotted arrow at the (006)-Bi 2 Te 3 peak indicates the dominance of Bi 2 Te 3 at low ϕ V , but the intensity of this phase decreases as ϕ V increases.The dashed arrow at the (001)-VTe 2 peak indicates the dominance of VTe 2 at high ϕ V , but this phase disappears as ϕ V decreases.VBi 2 Te 4 is absent in all 2θ-ω scans.The surface of the films is analysed with RHEED and AFM. Figure 3a presents the in situ RHEED pattern of a film deposited with ϕ V = 1750 • C. The RHEED pattern consists of a double streak pattern as indicated by the blue and white arrows.This doubled pattern indicates the presence of two separate crystal phases at the surface.The in-plane lattice constants related to these streaks are a 1 = 4.31 Å (white arrows) and a 2 = 3.59 Å (blue arrows).These values correspond well with the lattice constants of Bi 2 Te 3 and VTe 2 , respectively.
The surface morphology is measured by AFM. Figure 3b shows the height distribution as measured with AFM for films deposited with different ϕ V .The insets show the surface morphology of the films with ϕ V = 1750 • C and ϕ V = 1900 • C. At low ϕ V , the morphology shows strong island formation and the triangular crystals typically observed for Bi 2 Te 3 .The results at high ϕ V show a relative flat film without any sharp crystals.The height distributions indicate a strong influence of the ϕ V on the distribution spread.With an increasing ϕ V , the height variation becomes smaller, indicating a flatter surface.

Discussion
VBi 2 Te 4 is a SL structure requiring the embedding of VTe within the QL structure of Bi 2 Te 3 .According to our results, the formation of VBi 2 Te 4 is unstable with respect to phase separated Bi 2 Te 3 and VTe 2 within the thermodynamic conditions of the MBE.The instability of VBi 2 Te 4 can have various causes.
First, a large in-plane lattice mismatch, ∆ a , between VTe 2 and Bi 2 Te 3 might prohibit the formation of VBi 2 Te 4 [28].Our STEM results indicate ∆ a = 0.83 Å between the two phases.The theoretically predicted lattice constant of VBi 2 Te 4 , a = 4.37 Å, is close to the lattice constant of Bi 2 Te 3 , a = 4.65 Å.Therefore, the VTe 2 lattice has to overcome ∆ a to form VBi 2 Te 4 .Table 1 gives an overview of different materials structured as a SL with the relevant lattice constants and whether the material was successfully observed in experiments.The intercalated layer is presented as XTe or XTe 2 , depending on the experimental stability of the phases.The experimentally successful materials match ∆ a < 0.6 Å, while the experimentally unsuccessful materials match ∆ a > 0.5 Å.This difference can indicate a limit to the maximum allowed ∆ a of 0.5 Å to 0.6 Å between the SL material and the intercalated layer, possibly explaining the phase separation in VBi 2 Te 4 .However, this observation does not match with the stability of PbBi 2 Te 4 and SnBi 2 Te 4 [29].Therefore, the lattice mismatch between the intercalated layer and Bi 2 Te 3 does not completely explain the instability of the SL structure in general, and another factor should be considered.
Second, the elemental valence states in the intercalated layer might prohibit the formation of the SL.In the SL, the preferred valence states are M (+2) Bi 2 (+3) Te 4 (−2) (M = transition metal or rare-earth element), which matches well with the valence states of an intercalated layer structure of M (+2) Te (−2) [30].However, when the stable compound of the intercalated layer is structured as M (+4) Te 2 (−2) the valence states of the intercalated layer and the SL do not match.A mismatch between the preferred valence state of the intercalated layer and the SL indicates the instability of the SL.Table 1 reflects this instability, showing that every experimentally observed intercalated layer bulk compound with a valence structure of M (+2) Te (−2) also has a stable SL counterpart, but a valence structure of M (+4) Te 2 (−2) does not.This is in agreement with our study on VBi 2 Te 4 , because VTe 2 is thermodynamically more stable than VTe [31].
Furthermore, ref. [32] studied the preferred valence states of V, Cr, Mn and Fe in Bi 2 Te 3 .In Te-rich conditions, only V 3+ and Cr 3+ can substitute neutrally for Bi +3 atoms in Bi 2 Te 3 .In contrast, Mn and Fe mostly form Mn 2+ and Fe 2+ , which create energetically unfavourable states when mixed with Bi 3+ [9,32].This additionally shows the unfavourable V 2+ valence state.Therefore, Mn and Fe can more easily form a neutral SL structure with respect to V and Cr.
Table 1.Overview of materials with a unit cell structured as a SL.The table presents whether the material is successfully synthesised experimentally, the lattice constants found in the literature for these materials (either experimental or theoretical values), the intercalated layer with the corresponding lattice constant and the lattice mismatch between the SL and the intercalated layer.The intercalated layer is presented as XTe or XTe 2 , depending on the experimental stability of the phases.In conclusion, the influence of the ϕ V during MBE depositions was investigated on the synthesis of the VBi 2 Te 4 phase.The resulting films do not show any indication of VBi 2 Te 4 but rather a phase separation into Bi 2 Te 3 and VTe 2 .These results show VBi 2 Te 4 is unstable within the deposition conditions of MBE.

Figure 1 .
Figure 1.(a) MnBi 2 Te 4 and (b) VBi 2 Te 4 have a unit cell structured as SLs separated by a VdW gap.The dashed boxes indicate the relative intercalated layers of MnTe and VTe in Bi 2 Te 3 .J || is FM with either an (a) out-of-plane or (b) in-plane easy axis.J ⊥ is AFM.(c) Bi 2 Te 3 structured in QLs separated by a VdW gap.(d) VTe 2 .

Figure 2 .
Figure 2. (a) STEM image of a V-Bi-Te sample.The image is taken with a HAADF detector at 300 keV.A clear phase separation between bright and dark areas can be observed.(b) EDX scan of the V-Bi-Te sample.A strong separation between V-regions and Bi-regions can be observed.(c) STEM image of a smaller region on a V-Bi-Te sample.The bright areas (blue) show the QL structure of Bi 2 Te 3 and the dark areas (orange) the VTe 2 structure.(d) Histogram of the atomic distance in the x-direction.(e) 2θ-ω scans indicating (00l)-Bi 2 Te 3 being dominant at low ϕ V , while (00l)-VTe 2 is dominant at high ϕ V .The arrows indicate the disappearance of the respective phases as a function of ϕ V .* indicates the Al 2 O 3 substrate peak.

Figure 3 .
Figure 3. (a) RHEED pattern for ϕ V = 1750 • C showing a double streak pattern related to the phases Bi 2 Te 3 with a 1 = 4.31 Å and VTe 2 with a 2 = 3.59 Å, indicated by the blue and white arrows, respectively.(b) Height distribution at the surface as a function of the ϕ V .The insets show the surface morphology of the samples with ϕ V = 1750 • C and ϕ V = 1900 • C.

Author Contributions:
Conceptualization, T.J. and A.B.; methodology, M.A. and T.J.; validation, M.A. and T.J.; formal analysis, M.A., T.J. and M.T.; investigation, M.A. and T.J.; resources, M.T. and A.B.; data curation, M.A., T.J. and A.B.; writing-original draft preparation, M.A.; writing-review and editing, M.A., T.J., M.T. and A.B.; visualization, M.A. and T.J.; supervision, A.B.; project administration, M.A. and T.J.; funding acquisition, A.B.All authors have read and agreed to the published version of the manuscript.Funding: This research was funded by the research program "Materials for the Quantum Age" (QuMat) and the Dutch Research Council (NWO).QuMat (registration number 024.005.006) is part of the Gravitation program financed by the Dutch Ministry of Education, Culture and Science (OCW).The NWO supports this research via the TOPCORE project (registration number OCENW.GROOT.2019.048).