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

Abstract

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.

1. Introduction

Tl₅Te₃ and its derivatives have attracted considerable attention as thermoelectric materials [1,2,3,4,5,6,7,8,9,10,11] and recently as topological materials with a superconducting phase below 2.4 K [12]. Binary Tl₅Te₃ is known to adopt the In₅Bi₃ type structure (space group I4/mcm, a = 893.0(2) pm, c = 1258.9(4) pm), with two distinct Tl positions (Tl1 on Wyckoff site 4c and Tl2 on 16l) and two Te positions (Te1 on 4a, Te2 on 8h) [12,13]. Several ternary derivatives of the types Tl₉MTe₆ (M = Sb, Bi), Tl₉RETe₆ (RE = rare earth metal) and Tl₄M’Te₃ (M’ = Cu, Sn, Pb, Mo) have been reported [1,2,3,4,5,6,7,8,9,10,11,14,15,16,17,18,19,20,21]. Substitutions have generally been found to occur on Wyckoff site 4c preferably. The composition Tl₄M’Te₃ could in principle be realized by complete substitution of Tl1 on Wyckoff site 4c, the composition Tl₉MTe₆ corresponds to a substitution of one-half of the Tl1 atoms. Mixed M/Tl occupancies on the 4c site were reported for Tl_10−xRE_xTe₆ (RE = La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho and Er, with 0 < x < 1.32), e.g., [6,9]. Magnetization data for the compounds Tl_10−xRE_xTe₆, RE = Ce, Pr, Tb, Sm point at paramagnetic behavior in low fields down to T = 2 K and the extracted effective paramagnetic moments indicate (with the exception of Ce) trivalent rare earth metals [10]. Therefore, a charge ordered formula for the composition Tl₉RETe₆ could be written as 9 Tl⁺ + RE³⁺ + 6 Te²⁻ in accordance with the semiconducting properties of these compounds [9]. Moreover, it may as well give rise to the formation of a two-fold superstructure with full ordering of M ³⁺ and Tl1⁺ atoms.

The progenitor of the series Tl₅Te₃ 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 Tl₉RETe₆ with RE = Ce, Sm, Gd on single crystals. Such compound in a magnetically ordered state would be a candidate magnetic topological semimetal. We aim to provide the crystallographic data of highest possible quality and precision for the first-principles calculations, since topological properties depend on the fine details of lattice symmetries. The results are presented in the following.

2. Materials and Methods

2.1. Synthesis

All preparation steps were carried out in an argon (99.996% Messer-Griesheim, Sulzbach, Germany) filled glovebox (MBraun, Garching, Germany). The title compounds were obtained by direct synthesis of the elements in stoichiometric amounts, typically aiming at a sample mass of 1.5 g per batch. The rare-earth metals (Ce, Gd, Sm: 99.9%, Strem, Kehl, Germany) were rasped from compact blocks and Tl (99.9% Alfa Aesar, Karlsruhe, Germany) was cut from a rod. The metal pieces were filled in silica ampoules with glassy carbon crucibles together with the calculated amount of Te (lump 99.999%, Alfa Aesar, Karlsruhe, Germany). The ampoules were flame sealed and placed in a furnace, heated to 1020 K for 24 h and cooled to ambient temperature with 5 K/h.

The resulting ingots are dark-grey with metallic luster. The materials are brittle and can easily be crushed. Some parts were further ground for powder X-ray and magnetic measurements. Crystals for structure determination could be selected from the crushed ingots.

2.2. X-ray Powder Diffraction

X-ray powder diagrams (powder diffractometer XPert Pro, PANalytical GmbH, Kassel, Germany; CuKα₁ 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].

2.3. 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].

2.4. 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].

2.5. 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 Tl₉GdTe₆ 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].

2.6. 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.

3. 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. Energy dispersive X-ray (EDX) derived composition of Tl₉RETe₆ (atom-%), stated are average values from different crystals of each sample.

Element	Tl9CeTe6	Tl9SmTe6	Tl9GdTe6	Theor.
RE	5.7(4)	5.9(4)	6.4(2)	6.2
Tl	56.0(3)	55.3(5)	55.1(3)	56.3
Te	38.3(3)	38.8(2)	38.5(4)	37.5

. 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. Crystallographic data and refinement parameters of Tl₉RETe_6.

Chemical Composition	Tl9CeTe6	Tl9SmTe6	Tl9GdTe6
Mr/g·mol−1, F(000)	2745.1, 2189	2755.4, 2206	2762.3, 2210
temperature/K	295(1)
diffractometer type	Kappa Apex II CCD (Bruker-AXS)
wavelength/Å	0.71069 (Mo Kα, graphite monochromator)
crystal system	tetragonal
space group (No.), Z	I4/m (no. 87), 2
cell parameters *, a/pm	890.48(2)	886.50(5)	887.00(3)
c/pm	1313.42(5)	1306.41(8)	1306.56(5)
cell volume/106 pm3	1041.48(5)	1026.7(1)	1027.96(6)
density/g·cm−3	8.75	8.91	8.92
Abs. coefficient/mm−1	79.69	81.48	81.75
absorption correction	multi-scan (SADABS [26])
-	0.289/0.749	0.292/0.746	0.499/0.747
crystal size / mm3	0.189 × 0.057 × 0.045	0.021 × 0.027 × 0.043	0.075 × 0.061 × 0.035
measurement range	2.8 ≤ θ ≤ 42.6 −13 ≤ h ≤ 15 −15 ≤ k ≤ 15 −15 ≤ l ≤ 24	2.8 ≤ θ ≤ 34.7 −11 ≤ h ≤ 14 −9 ≤ k ≤ 14 −20 ≤ l ≤ 20	2.8 ≤ θ ≤ 35.2 −14 ≤ h ≤ 13 −14 ≤ k ≤ 11 −17 ≤ l ≤ 19
Rint	0.0328	0.071	0.030
refinement	JANA2006, full-matrix least squares on F2 [23]
reflections, with I > 3σ(I), parameters	1693, 1458, 25	1153, 795, 24	1151, 830, 25
extinction parameter	0.118(2)	-	0.0059(7)
goodness-of-fit	1.5	1.1	1.2
R1(obs), wR2(obs)	0.031, 0.065	0.035, 0.062	0.026, 0.049
R1(all), wR2(all)	0.038, 0.066	0.059, 0.069	0.050, 0.055
twin matrix	0 1 0, 1 0 0, 0 0 −1
twin volume fraction	0.518(2)	0.672(2)	0.997(1)
Δρmin / Δρmax, e/106 pm3	2.57/−2.02	2.02/−3.38	2.29/−2.12

* from powder data

).

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 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 Tl₉SmTe₆). 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 RE³⁺ ions to reside on two crystallographically independent sites, as has been described for SbTl₉Te₆ in a similar way [20]. The symmetry and structure relations between Tl₅Te₃ in space group I4/mcm and those of the title compounds Tl₉RETe₆ (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 Table 2 and

Table 3. Fractional coordinates and isotropic displacement parameters of Tl₉RETe₆.

Atom	x	y	z	Ueq, pm2
Tl9CeTe6
Ce	0	0	0	170(1)
Tl1	0	0	½	252(1)
Tl2	0.1557(1)	0.6377(1)	0.1600(1)	335(1)
Te1	0	0	0.2403(1)	120(1)
Te2	0.3284(1)	0.8466(1)	0	180(1)
Tl9SmTe6
Sm	0	0	0	173(3)
Tl1	0	0	½	0273(3)
Tl2	0.1539(1)	0.6392(1)	0.1602(1)	339(1)
Te1	0	0	0.2372(1)	201(3)
Te2	0.3245(1)	0.8487(1)	0	185(2)
Tl9GdTe6
Gd	0	0	0	173(3)
Tl1	0	0	½	273(3)
Tl2	0.1539(1)	0.6392(1)	0.1602(1)	339(1)
Te1	0	0	0.2372(1)	201(3)
Te2	0.3245(1)	0.8487(1)	0	185(2)

U_eq is defined as 1/3 of the orthogonalized U_ij tensor.

, selected interatomic distances are listed in

Table 4. Selected interatomic distances (pm) of Tl₉RETe₆.

Tl9CeTe6
Ce–	Te1	315.7(1)	2×	Tl1–	Te1	341.1(1)	2×
	Te2	322.8(1)	4×		Te2	344.4(1)	4×
	Tl2	409.2(1)	8×		Tl2	391.4(1)	8×
Tl2–	Tl2	352.3(1)		Tl2–	Te2	320.0(1)
		352.8(1)	2×			346.4(1)
		370.2(1)				347.6(1)
	Te1	355.2(1)
		366.6(1)
Tl9SmTe6
Sm–	Te1	309.9(1)	2×	Tl1–	Te1	343.3(1)	2×
	Te2	317.5(1)	4×		Te2	346.0(1)	4×
	Tl2	405.9(1)	8×		Tl2	391.3(1)	8×
Tl2–	Tl2	350.2(1)		Tl2–	Te2	318.1(1)
		350.3(1)	2×			343.6(1)
		362.0(1)				348.7(1)
	Te1	356.8(1)
		362.0(1)
Tl9GdTe6
Gd–	Te1	309.4(1)	2×	Tl1–	Te1	343.9(1)	2×
	Te2	316.9(1)	4×		Te2	346.9(1)	4×
	Tl2	405.7(1)	8×		Tl2	392.0(1)	8×
Tl2–	Tl2	350.1(1)		Tl2–	Te2	318.2(1)
		350.4(1)	2×			343.1(1)
		368.2(1)				349.7(1)
	Te1	357.6(1)
		361.5(1)

. 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 (Tl₉CeTe₆), CSD-427737 (Tl₉GdTe₆) and CSD-427738 (Tl₉SmTe₆). 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 binary phase Tl₅Te₃ 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 Tl₉RETe₆ compounds, the average distances in the RE–Te and Tl1–Te octahedra are 320.4(1) pm and 343.3(1) pm for Tl₉CeTe₆ 314.4(1) pm and 345.9(1) pm for Tl₉GdTe₆, 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.

Looking for next nearest neighbors of the Sm and Tl1 atoms, eight Tl2 atoms forming a cuboid have to be considered. The distances to the central Sm and Tl1 atoms are 409.2(1) pm and 391.3(1) pm, respectively. The Te1 atoms are surrounded by a square antiprism of eight Tl2 atoms with both square faces capped by Tl1 or Sm atoms, Figure 5.

Tl₅Te₃, Tl₅Se₃ 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 Tl₉RETe₆, this would result in 9 Tl⁺ + RE³⁺ + 6 Te²⁻. The sizes of the metal coordination octahedra can then be rationalized according to the ionic radii of the respective Tl⁺ and RE³⁺ metal ions: 164 pm for Tl⁺, 115 pm for Ce³⁺, 110 pm for Sm³⁺ and 108 pm for Gd³⁺, 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⁺ + Tl²⁺ + 3 Te²⁻ [32]. However, the formulation as mixed-valent compound according to 9 Tl⁺ + Tl³⁺ + 6 Te²⁻ is conceivable, yet not supported by crystallographic evidence.

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 µ_B/Gd atom. This value is slightly lower than the theoretical moment of 7.98 μ_B for Gd³⁺ [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 μ_Β 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 Ce³⁺ (J = 5/2) system [33] and might point towards a small amount of Ce⁴⁺. For Tl₉GdTe₆, the Curie–Weis fit yields 8.12 μ_Β per Gd atom for the Gd compound in reasonable agreement with the expected value for a J = 7/2 system of 7.98 μ_Β [33]. Whereas binary Tl₅Te₃ turns superconducting at T_c = 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 T_c noticeably.

4. 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⁺)₉RE³⁺(Te²⁻)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 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 Ce⁴⁺ in Tl₉CeTe₆.