Syntheses, Crystal Structure and Magnetic Properties of Tl9RETe6 (RE = Ce, Sm, Gd)

The three compounds Tl9RETe6 with RE = Ce, Sm, Gd were synthesized from the elements at 1020 K. Their isostructural crystal structures are ordered derivatives of the Tl5Te3 type with rare-earth metal and thallium occupying different Wyckoff positions. The structures can be understood as charge-ordered in accordance with the Zintl-Klemm concept: 9 Tl+ + RE3+ + 6 Te2−. DFT calculations for Tl9GdTe6, however, result in a low, but finite density of states at the Fermi level. Magnetic data confirm trivalent Gd, but indicate a small amount of Ce4+ in Tl9CeTe6; no indications for long-range magnetic order was found down to T = 2 K.

The progenitor of the series Tl 5 Te 3 has a non-trivial topology of the electronic band structure due to a band inversion between the Tl2 and Te states of opposite parity at the Z point of the 3D Brillouin zone [12]. Given the current interest in quantum materials that combine non-trivial topology and intrinsic magnetic order [22], we re-investigated the crystal structures and magnetic properties of Tl 9 RETe 6 with RE = Ce, Sm, Gd on single crystals. Such compound in a magnetically ordered state

X-ray Powder Diffraction
X-ray powder diagrams (powder diffractometer XPert Pro, PANalytical GmbH, Kassel, Germany; CuKα 1 radiation, Bragg-Brentano setup) were recorded to check for phase purity and to determine the lattice parameters. Moreover, Rietveld fits were performed to refine the lattice parameters and to check the structure model derived from single crystal data for consistency [23].

Energy Dispersive X-ray Spectroscopy (EDX)
Energy dispersive X-ray (EDX) analyses were performed in a SEM SU 8020 (Hitachi High-Technologies Europe GmbH, Krefeld, Germany) equipped with a silicon drift EDX detector XMAX N (Oxford Instruments, Wiesbaden, Germany) at 30 kV acceleration voltage. Crystals of the phase pure samples were embedded in a conductive polymer matrix, cut and polished to provide a plane and clean surface. Analyses were made by averaging on several points and line scans of different crystals for each sample according to the fundamental parameter method applying a PAP matrix correction [24].

Crystal Structure Determination
Single crystal experiments were performed on a Kappa Apex II CCD diffractometer (Bruker-AXS GmbH, Karlsruhe, Germany) with Mo Kα radiation using the software package Apex Suite [25]. A multi-scan absorption correction was employed [26]. Atom parameters and atom designations for structure refinement with Jana 2006 [23] were derived by the symmetry reduction stated in the Discussion, see below. Diamond 4 was used for structure visualization [27].

Electronic Structure Calculations
Density functional theory (DFT) calculations within the local density approximation with Hubbard correction (LDA+U) using the around mean field (AFM) double counting were performed for Tl 9 GdTe 6 in the full-potential full-electron linear augmented plane-wave (FP-LAPW) code [28]. Spin-orbit coupling was taken into account fully-relativistically. The values of Hubbard U = 6.7 eV and J = 0.7 eV were chosen to treat the Gd d-orbitals. These optimized parameters were reported for the electronic structure of pure gadolinium metal and we tested them to reproduce the magnetic moments on Gd atoms with our program code [29]. Formal charges were calculated according to the Bader partitioning scheme [30].

Magnetic Measurements
Magnetization measurements on sample of Tl 9 CeTe 6 and Tl 9 GdTe 6 were carried out with a commercial superconducting quantum interference device (SQUID) magnetometer MPMS (Quantum Design Europe, Darmstadt, Germany) in a temperature range of 300 K ≤ T ≤ 2 K.

Results and Discussion
EDX analyses performed on several of the as-grown crystals of each sample confirm the composition of the compounds within the limit of the method, although a slight excess of Te was observed for all samples, Table 1. No hints for contaminations or defects were obtained. According to the X-ray powder patterns and the respective Rietveld fits, phase-pure samples of Tl 9 CeTe 6 , Tl 9 SmTe 6 and Tl 9 GdTe 6 were obtained, cf. Figure 1 as an example and also Figure S1. The tetragonal lattice parameters derived from powder X-ray data are in good agreement with those from single crystal experiments (Table 2). Crystals 2020, 10, x FOR PEER REVIEW 3 of 11

Magnetic Measurements
Magnetization measurements on sample of Tl9CeTe6 and Tl9GdTe6 were carried out with a commercial superconducting quantum interference device (SQUID) magnetometer MPMS (Quantum Design Europe, Darmstadt, Germany) in a temperature range of 300 K ≤ T ≤ 2 K.

Results and Discussion
EDX analyses performed on several of the as-grown crystals of each sample confirm the composition of the compounds within the limit of the method, although a slight excess of Te was observed for all samples, Table 1. No hints for contaminations or defects were obtained. According to the X-ray powder patterns and the respective Rietveld fits, phase-pure samples of Tl9CeTe6, Tl9SmTe6 and Tl9GdTe6 were obtained, cf. Figure 1 as an example and also Figure S1. The tetragonal lattice parameters derived from powder X-ray data are in good agreement with those from single crystal experiments (Table 2). Analyses of the single-crystal data sets of the compounds Tl9CeTe6, Tl9SmTe6 and Tl9GdTe6 indicated body-centered tetragonal unit cells each. For all three compounds, a considerable number of reflections with intensities well above a threshold of 3σ(Ι) were found to contradict glide planes and screw axes. Moreover, depending on the twin volume ratio (cf. below), the Rint value for symmetry averaging was found to be significantly lower for Laue class 4/m as compared to Laue class Analyses of the single-crystal data sets of the compounds Tl 9 CeTe 6 , Tl 9 SmTe 6 and Tl 9 GdTe 6 indicated body-centered tetragonal unit cells each. For all three compounds, a considerable number of reflections with intensities well above a threshold of 3σ(I) were found to contradict glide planes and screw axes. Moreover, depending on the twin volume ratio (cf. below), the R int value for symmetry averaging was found to be significantly lower for Laue class 4/m as compared to Laue class 4/mmm (e.g., 0.071 vs. 0.125, respectively, for Tl 9 SmTe 6 ). These findings refute space group I4/mcm and point towards I4/m instead.
Structure solutions were hence made in I4/m and refinements proceeded smoothly to the results and residuals stated in Table 2. Space group I4/m provides a possibility for Tl + and RE 3+ ions to reside on two crystallographically independent sites, as has been described for SbTl 9 Te 6 in a similar way [20]. The symmetry and structure relations between Tl 5 Te 3 in space group I4/mcm and those of the title compounds Tl 9 RETe 6 (RE = Ce, Sm, Gd) is depicted in the Bärnighausen diagram in Figure 2. The occupancies of the Tl1 (Wyckoff site 2a) and the RE atoms (2b) were found to be unity within an uncertainty interval of 3σ in the refinements. No experimental evidence for a mixed occupancy on the 2a and 2b sites was found, as for any other Wyckoff site. The main crystallographic data and refinement details are stated in Tables 2 and 3, selected interatomic distances are listed in Table 4. Crystallographic data have been deposited with the Fachinformationszentrum Karlsruhe, D-76344 Eggenstein-Leopoldshafen (Germany) and can be obtained on quoting the depository number CSD-427736 (Tl 9 CeTe 6 ), CSD-427737 (Tl 9 GdTe 6 ) and CSD-427738 (Tl 9 SmTe 6 ). Note, that despite the evidence of the reflection conditions refuting the higher symmetric space group I4/mcm, refinements in this space group were performed for reasons of comparison with previously published data. These refinements, as can be seen from Table S1, Supporting Information, resulted in unsatisfactory R-values and much higher difference Fourier peaks in all three cases and underline the correct choice of space group I4/m additionally.  As the three title compounds Tl9CeTe6, Tl9SmTe6 and Tl9GdTe6 are isotypic, the structure description and discussion are exemplified by Tl9SmTe6. The structures of Tl5Te3 and some of its derivatives have been discussed in several publications; however, authors have emphasized different structural details. Focus was laid on the stacking of two different sets of interpenetrating nets [14], equidistant linear Tl1-Te1 chains running along [001] [14], coordination polyhedra around Tl1 and Te1 [15][16][17][18][19][20][21] or a perovskite-like arrangement of Tl1Te6-octahedra in which the large voids are occupied by Tl4-tetrahedra [12]. Figure 3 shows projections of the unit cells of Tl9SmTe6 and Tl5Te3 next to each other for comparison. As can be seen, the major difference is in the decoration of the metal sites (Tl1 and RE), other structural differences are hardly noticeable from this image.
A more detailed view on the structures, especially on the Tl1Te6 and SmTe6 octahedra, however, reveals further differences. The Tl1Te6 octahedra are defined by two apical Tl-Te distances of 343.3(1) pm and four basal ones of 346.0(1) pm. The Sm atom does also reside in a slightly compressed octahedron with two apical Sm-Te distances of 302.9(1) pm and four basal ones of 317.5(1) pm. The average Sm-Te distances in the octahedra is 312.6(1) pm and thus about 10% shorter than the average Tl1-Te distance of 345.1(1) pm for the Tl1Te6 octahedra. For comparison: the Tl1Te6 octahedron in the  [14] and the Tl 9 RETe 6 title compounds.
As the three title compounds Tl 9 CeTe 6 , Tl 9 SmTe 6 and Tl 9 GdTe 6 are isotypic, the structure description and discussion are exemplified by Tl 9 SmTe 6 . The structures of Tl 5 Te 3 and some of its derivatives have been discussed in several publications; however, authors have emphasized different structural details. Focus was laid on the stacking of two different sets of interpenetrating nets [14], equidistant linear Tl1-Te1 chains running along [001] [14], coordination polyhedra around Tl1 and Te1 [15][16][17][18][19][20][21] or a perovskite-like arrangement of Tl1Te 6 -octahedra in which the large voids are occupied by Tl 4 -tetrahedra [12]. Figure 3 shows projections of the unit cells of Tl 9 SmTe 6 and Tl 5 Te 3 next to each other for comparison. As can be seen, the major difference is in the decoration of the metal sites (Tl1 and RE), other structural differences are hardly noticeable from this image. U eq is defined as 1/3 of the orthogonalized U ij tensor.
A more detailed view on the structures, especially on the Tl1Te 6 and SmTe 6 octahedra, however, reveals further differences. The Tl1Te 6 octahedra are defined by two apical Tl-Te distances of 343.3(1) pm and four basal ones of 346.0(1) pm. The Sm atom does also reside in a slightly compressed octahedron with two apical Sm-Te distances of 302.9(1) pm and four basal ones of 317.5(1) pm. The average Sm-Te distances in the octahedra is 312.6(1) pm and thus about 10% shorter than the average Tl1-Te distance of 345.1(1) pm for the Tl1Te 6 octahedra. For comparison: the Tl1Te 6 octahedron in the binary phase Tl 5 Te 3 consists of two apical Tl-Te distances of 314.7 pm and four basal ones of 336.1 pm, resulting in an average value of 329.0 pm; for the Tl 9 RETe 6 compounds, the average distances in the RE-Te and Tl1-Te octahedra are 320.4(1) pm and 343.3(1) pm for Tl 9 CeTe 6 314.4(1) pm and 345.9(1) pm for Tl 9 GdTe 6 , respectively. Figure 4 illustrates the size difference by enfolding the octahedra with a sphere of the radius of the average Sm-Te and Tl1-Te distances. This spherical representation clearly evidences why the ternary compounds preferably adopt the lower symmetric structure in I4/m. In this context, the term "charge-ordered structure" does not reflect the whole truth as size-order is at least a comparable driving force.  Figure 4 illustrates the size difference by enfolding the octahedra with a sphere of the radius of the average Sm-Te and Tl1-Te distances. This spherical representation clearly evidences why the ternary compounds preferably adopt the lower symmetric structure in I4/m. In this context, the term "charge-ordered structure" does not reflect the whole truth as size-order is at least a comparable driving force.     Figure 4 illustrates the size difference by enfolding the octahedra with a sphere of the radius of the average Sm-Te and Tl1-Te distances. This spherical representation clearly evidences why the ternary compounds preferably adopt the lower symmetric structure in I4/m. In this context, the term "charge-ordered structure" does not reflect the whole truth as size-order is at least a comparable driving force.    Tl 5 Te 3 , Tl 5 Se 3 and their ternary derivatives can, at least formally, be written on the basis of a Zintl-like charge-ordered formula in the first approach. For the rare-earth metal substituted compounds Tl 9 RETe 6 , this would result in 9 Tl + + RE 3+ + 6 Te 2− . The sizes of the metal coordination octahedra can then be rationalized according to the ionic radii of the respective Tl + and RE 3+ metal ions: 164 pm for Tl + , 115 pm for Ce 3+ , 110 pm for Sm 3+ and 108 pm for Gd 3+ , all for octahedral coordination [31]. The smaller TlTe 6 coordination polyhedron in Tl 5 Te 3 as compared to those in Tl 9 RETe 6 is also understandable: In Tl 5 Te 3 one fifth of the Tl atoms (i.e., the Tl atoms on 4c in space group I4/mcm) can be considered to be in an intermediate 2+ valence state: 4 Tl + + Tl 2+ + 3 Te 2− [32]. However, the formulation as mixed-valent compound according to 9 Tl + + Tl 3+ + 6 Te 2− is conceivable, yet not supported by crystallographic evidence.  Tl5Te3, Tl5Se3 and their ternary derivatives can, at least formally, be written on the basis of a Zintllike charge-ordered formula in the first approach. For the rare-earth metal substituted compounds Tl9RETe6, this would result in 9 Tl + + RE 3+ + 6 Te 2− . The sizes of the metal coordination octahedra can then be rationalized according to the ionic radii of the respective Tl + and RE 3+ metal ions: 164 pm for Tl + , 115 pm for Ce 3+ , 110 pm for Sm 3+ and 108 pm for Gd 3+ , all for octahedral coordination [31]. The smaller TlTe6 coordination polyhedron in Tl5Te3 as compared to those in Tl9RETe6 is also understandable: In Tl5Te3 one fifth of the Tl atoms (i.e., the Tl atoms on 4c in space group I4/mcm) can be considered to be in an intermediate 2+ valence state: 4 Tl + + Tl 2+ + 3 Te 2− [32]. However, the formulation as mixed-valent compound according to 9 Tl + + Tl 3+ + 6 Te 2− is conceivable, yet not supported by crystallographic evidence.  Based on the crystallographic data, we perform preliminary spin-polarized band-structure calculations for Tl 9 GdTe 6 and find that a ferromagnetically ordered state is more energetically favorable than a non-magnetic configuration. Figure 6 shows the full-relativistic bulk electronic spectrum, which is metallic with low yet finite electron density at the Fermi energy. This is in line with the experimentally observed electronic conductivity [8]. At about 0.2 eV below the Fermi level the electron density drops to almost zero and there is an (avoided) band crossing at the Γ point. This feature is constituted by Tl and Te states, while the majority of Gd f -states reside at ca. −10 eV. These spin-polarized bands may either hybridize and open a tiny gap or form a protected crossing. In both cases, Tl 9 GdTe 6 could be a candidate topological material: either a topological insulator or a topological semimetal. These scenarios call for further in-depth elucidation. The calculated effective magnetic moment amounts to 7.4 µ B /Gd atom. This value is slightly lower than the theoretical moment of 7.98 µ B for Gd 3+ [33], the discrepancy likely pointing towards a certain degree of electron delocalization in a metallic system. The computed formal charges are: Tl1: +0.3, Tl2: +0.3, Gd: +0.55, Te1: −0.5, Te2: −0.5. Based on the crystallographic data, we perform preliminary spin-polarized band-structure calculations for Tl9GdTe6 and find that a ferromagnetically ordered state is more energetically favorable than a non-magnetic configuration. Figure 6 shows the full-relativistic bulk electronic spectrum, which is metallic with low yet finite electron density at the Fermi energy. This is in line with the experimentally observed electronic conductivity [8]. At about 0.2 eV below the Fermi level the electron density drops to almost zero and there is an (avoided) band crossing at the Γ point. This feature is constituted by Tl and Te states, while the majority of Gd f-states reside at ca. −10 eV. These spin-polarized bands may either hybridize and open a tiny gap or form a protected crossing. In both cases, Tl9GdTe6 could be a candidate topological material: either a topological insulator or a topological semimetal. These scenarios call for further in-depth elucidation. The calculated effective magnetic moment amounts to 7.4 µB/Gd atom. This value is slightly lower than the theoretical moment of 7.98 μB for Gd 3+ [33], the discrepancy likely pointing towards a certain degree of electron delocalization in a metallic system. The computed formal charges are: Tl1: +0.3, Tl2: +0.3, Gd: +0.55, Te1: −0.5, Te2: −0.5. Magnetic measurements performed on samples of Tl9CeTe6 ( Figure S2) and Tl9GdTe6 (Figure 7) demonstrate that both compounds are paramagnetic in the temperature interval 2 K < T < 300 K and no long-range magnetic order was established. The Curie-Weis fit for Tl9CeTe6 results in a magnetic moment of 2.18 μΒ per Ce-atom, in accordance with [10]. The values are slightly reduced with respect to the expected value of 2.51 μB for a pure Ce 3+ (J = 5/2) system [33] and might point towards a small amount of Ce 4+ . For Tl9GdTe6, the Curie-Weis fit yields 8.12 μΒ per Gd atom for the Gd compound in reasonable agreement with the expected value for a J = 7/2 system of 7.98 μΒ [33]. Whereas binary Tl5Te3 turns superconducting at Tc = 2.4 K [12], we find no indication for superconductivity for the Ce-and Gd-substituted samples. The RE substitution seems at least to lower the Tc noticeably. Magnetic measurements performed on samples of Tl 9 CeTe 6 ( Figure S2) and Tl 9 GdTe 6 ( Figure 7) demonstrate that both compounds are paramagnetic in the temperature interval 2 K < T < 300 K and no long-range magnetic order was established. The Curie-Weis fit for Tl 9 CeTe 6 results in a magnetic moment of 2.18 µ B per Ce-atom, in accordance with [10]. The values are slightly reduced with respect to the expected value of 2.51 µ B for a pure Ce 3+ (J = 5/2) system [33] and might point towards a small amount of Ce 4+ . For Tl 9 GdTe 6 , the Curie-Weis fit yields 8.12 µ B per Gd atom for the Gd compound in reasonable agreement with the expected value for a J = 7/2 system of 7.98 µ B [33]. Whereas binary Tl 5 Te 3 turns superconducting at T c = 2.4 K [12], we find no indication for superconductivity for the Ceand Gd-substituted samples. The RE substitution seems at least to lower the T c noticeably.

Conclusions
In contrast to previous investigations, the stoichiometrically substituted tellurides Tl9CeTe6, Tl9SmTe6 and Tl9GdTe6 were found to adopt an ordered variant of the In5Bi3 type, which allows for an adaption of the different metal atom sizes. The compounds crystallize in space group I4/m (no. 87) and the structures can be understood as charge-ordered in accordance with a Zintl-type formula (Tl + )9RE 3+ (Te 2− )6. Spin-polarized DFT calculations for Tl9GdTe6 result in a low, but finite density of states at the Fermi level. The experimental transport behavior determined on hot-pressed powder samples points towards p-type semiconductors for the Tl9RETe6 compounds with relatively high conductivity values at ambient temperature. Our preliminary calculations also indicate a possibility for non-trivial topology of the electronic structure, which will be studied in full detail elsewhere. There is an (avoided) band crossing at the Γ point of the 3D Brillouin zone at ca. 0.2 eV below the Fermi level. Thus, Tl9GdTe6 may become a candidate topological material upon p-doping and given a ferromagnetic ordering. The calculated ground state is ferromagnetic with 7.4 µB/Gd-atom, however, magnetization measurements reveal paramagnetic behavior down to 2 K with a moment of 8.12 µB/Gd atom. As reported previously, the experimentally derived moment of 2.18 µB/Ce atom points to a certain amount of Ce 4+ in Tl9CeTe6.

Supplementary Materials:
The following are available online at www.mdpi.com/xxx/s1, Table S1: Crystallographic data and refinement parameters of Tl9RETe6 in space group I4/mcm with Tl1/RE mixed occupancy on Wyckoff site 4c of the for reasons of comparison, Figure S1: Profile plots for Tl9CeTe6, and Tl9SmTe6 (exp. data and Rietveld fits), Figure S2: Magnetic data for Tl9CeTe6.
Author Contributions: A.I. performed and analyzed the electronic structure calculations. R. S. performed and analyzed the magnetic measurements. T.D. performed and analyzed the powder and single-crystal X-ray data collections, elucidated the crystal structures and supervised the project. All three authors contributed to writing of the manuscript.
Funding: This research was funded by the Deutsche Forschungsgemeinschaft (grants Do 590/5 and IS 250/1) in the framework of the priority program 1666 "Topological Insulators".

Conclusions
In contrast to previous investigations, the stoichiometrically substituted tellurides Tl 9 CeTe 6 , Tl 9 SmTe 6 and Tl 9 GdTe 6 were found to adopt an ordered variant of the In 5 Bi 3 type, which allows for an adaption of the different metal atom sizes. The compounds crystallize in space group I4/m (no. 87) and the structures can be understood as charge-ordered in accordance with a Zintl-type formula (Tl + ) 9 RE 3+ (Te 2− ) 6 . Spin-polarized DFT calculations for Tl 9 GdTe 6 result in a low, but finite density of states at the Fermi level. The experimental transport behavior determined on hot-pressed powder samples points towards p-type semiconductors for the Tl 9 RETe 6 compounds with relatively high conductivity values at ambient temperature. Our preliminary calculations also indicate a possibility for non-trivial topology of the electronic structure, which will be studied in full detail elsewhere. There is an (avoided) band crossing at the Γ point of the 3D Brillouin zone at ca. 0.2 eV below the Fermi level. Thus, Tl 9 GdTe 6 may become a candidate topological material upon p-doping and given a ferromagnetic ordering. The calculated ground state is ferromagnetic with 7.4 µ B /Gd-atom, however, magnetization measurements reveal paramagnetic behavior down to 2 K with a moment of 8.12 µ B /Gd atom. As reported previously, the experimentally derived moment of 2.18 µ B /Ce atom points to a certain amount of Ce 4+ in Tl 9 CeTe 6 .
Author Contributions: A.I. performed and analyzed the electronic structure calculations. R.S. performed and analyzed the magnetic measurements. T.D. performed and analyzed the powder and single-crystal X-ray data collections, elucidated the crystal structures and supervised the project. All three authors contributed to writing of the manuscript. All authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by the Deutsche Forschungsgemeinschaft (grants Do 590/5 and IS 250/1) in the framework of the priority program 1666 "Topological Insulators".