Triangular Zn₃ and Ga₃ units in Sr₂Au₆Zn₃, Eu₂Au₆Zn₃, Sr₂Au₆Ga₃, and Eu₂Au₆Ga₃ – structure, magnetism, ¹⁵¹Eu Mössbauer and ^69;71Ga solid state NMR spectroscopy

2.1 Synthesis

Starting materials for the syntheses of Sr₂Au₆Zn₃, Eu₂Au₆Zn₃, Sr₂Au₆Ga₃ and Eu₂Au₆Ga₃ were sublimed ingots of strontium (Aldrich, >99 %), europium pieces (Alfa Aesar, >99.9 %), pieces of a gold bar (Heraeus, >99.9 %), zinc granules (Merck, >99.9 %) and gallium lumps (Johnson Matthey, >99.9 %). Suitable pieces of strontium were prepared under paraffin oil (the oxidized cusp was removed mechanically), washed with n-hexane and kept in Schlenk tubes under argon prior to the reactions. Europium pieces were arc-melted [39] to buttons under argon and kept in Schlenk tubes. Argon was purified with titanium sponge (900 K), silica gel, and molecular sieves. The elements were then weighed in the ideal atomic ratio of 2:6:3 and arc-welded in small tantalum tubes under an argon pressure of ca. 800 mbar. The filled containers were subsequently placed in water-cooled sample chambers of induction furnaces (Hüttinger Elektronik, Freiburg, Germany, Typ TIG 2.5/300 or Kontron Rotomelt) [40, 41].

The annealing sequence (Hüttinger furnace) for the Sr₂Au₆Ga₃ and Eu₂Au₆Zn₃ samples was rapid heating to 1273 K, keeping this temperature for 3 min and subsequent cooling to 873 K at a rate of 40 K h^–1. The samples were kept at 873 K for another 2 h followed by quenching through switching off the power supply of the furnace. The temperature was controlled by a Sensor Therm Methis MS09 pyrometer with an accuracy of ±30 K. The Eu₂Au₆Ga₃ sample was annealed in the Kontron furnace: (i) rapid heating to 1300 K, (ii) 10 min at 1300 K, (iii) cooling to ambient temperature at a rate of ca. 35 K min^–1.

For phase-pure synthesis, the Eu₂Au₆Zn₃ sample was crushed, cold-pressed to a pellet and annealed for 5 d at 773 K in a sealed evacuated silica tube. The Sr₂Au₆Zn₃ sample used for the susceptibility measurements was synthesized with the annealing sequence given in [18].

All four samples could mechanically be separated from the crucible material. There was no visible attack of the container material. The samples showed metallic luster and were stable in air over weeks.

2.2 X-ray diffraction

The purity of the polycrystalline Sr₂Au₆Zn₃, Eu₂Au₆Zn₃, Sr₂Au₆Ga₃, and Eu₂Au₆Ga₃ samples was characterized by X-ray powder diffraction using the Guinier technique: Enraf-Nonius camera, type FR 552, imaging plate detector, Fujifilm BAS-1800, CuK_α1 radiation, and α-quartz (a = 491.30, c = 540.46 pm) as an internal standard. The lattice parameters (Table 1) were calculated by a least-squares routine and the correct indexing was ensured through a comparison with calculated patterns [42].

Small irregularly shaped single crystals of Eu₂Au₆Zn₃ and Eu₂Au₆Ga₃ were selected from the crushed samples and glued to thin quartz fibers using bees wax. The crystals were studied on a Buerger camera (using white Mo radiation) to check their quality. Intensity data of Eu₂Au₆Ga₃ were collected at room temperature on a Stoe IPDS-II image plate system (graphite monochromatized Mo radiation; λ = 71.073 pm) in oscillation mode. A numerical absorption correction was applied to the data set. The Eu₂Au₆Zn₃ data set was measured on a Stoe StadiVari diffractometer equipped with a Mo micro focus source and a Pilatus detection system. Due to a Gaussian-shaped profile of the X-ray source scaling was applied along with a numerical absorption correction. Details of the data collections and the crystallographic parameters are summarized in Table 2.

2.3 Structure refinements

Isotypism of Eu₂Au₆Zn₃ and Eu₂Au₆Ga₃ with the corresponding strontium compounds [18] was already evident from the Guinier powder patterns. The systematic extinctions were compatible with space group R3̅c. The atomic positions of the strontium compounds were taken as starting values and both structures were refined using Shelxl-97 [43] (full-matrix least-squares on F²) with anisotropic atomic displacement parameters for all atoms. Refinement of the occupancy parameters revealed a small degree of Au/Zn, respectively Au/Ga mixing for the 18e sites, as previously observed also for Sr₂Au_6.52Zn_2.48 [18] and Sr₂Au_6.18Al_2.82 [20]. These mixed occupancies were refined as an additional variable in the final cycles. The last difference Fourier syntheses revealed no residual peaks. The refined atomic positions, displacement parameters, and interatomic distances are given in Tables 3 and 4.

Further details of the crystal structure investigation may be obtained from Fachinformationszentrum Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: +49-7247-808-666; e-mail: crysdata@fiz-karlsruhe.de, http://www.fiz-karlsruhe.de/request_for_deposited_data.html) on quoting the deposition number CSD-430836 (Eu₂Au_6.07Ga_2.93) and CSD-430835 (Eu₂Au_6.04Zn_2.96).

2.4 EDX data

The crystals of Eu₂Au_6.07Ga_2.93 and Eu₂Au_6.04Zn_2.96 studied on the diffractometer were semiquantitatively analyzed by EDX using a Zeiss EVO^® MA10 scanning electron microscope in variable pressure mode. EuF₃, Au, Zn and GaP were used as standards. The experimentally observed compositions (18±3 at% Eu:55±3 at% Au:27±3 at% Ga and 15±3 at% Eu:62±3 at% Au:23±3 at% Zn) were close to the ones refined from the single crystal X-ray data. The standard deviations result from the irregular surface of the crystals (conchoidal fracture). No impurity elements (especially from the container material) were detected.

2.5 Magnetic characterization

Magnetic susceptibility investigations have been performed with a Quantum Design Physical-Property-Measurement-System (PPMS) using the VSM (Vibrating Sample Magnetometer) option. The powdered samples were packed in polypropylene capsules and attached to the sample holder rod. The samples were investigated in the temperature range of 2.5–300 K with magnetic flux densities up to 80 kOe (1 kOe = 7.96 × 10⁴ A m^–1).

2.6 ¹⁵¹Eu Mössbauer spectroscopy

The 21.53 keV transition of ¹⁵¹Eu with an activity of 130 MBq (2 % of the total activity of a ¹⁵¹Sm:EuF₃ source) was used for the Mössbauer spectroscopic experiments, which were conducted in transmission geometry. The temperature of the absorber was varied with a commercial helium-flow cryostat, while the source was kept at room temperature. The samples were enclosed in small PMMA containers at a thickness corresponding to about 10 mg Eu per cm². Fitting of the spectra was performed with the Normos-90 program system [44].

2.7 ^69;71Ga solid state NMR spectroscopy

NMR spectroscopic experiments were performed on a Bruker Avance III spectrometer at ambient temperature. The magnetic flux density of 9.40 T yields ⁶⁹Ga and ⁷¹Ga resonance frequencies of 96.044 and 120.036 MHz, respectively. The signals were referenced to a solution of Ga(NO₃)₃ in D₂O. All spectra were measured in a custom-made automatic tuning, matching, and goniometer (ATMG) probe [45]. It was developed in cooperation with NMR Service GmbH, Erfurt (Germany).

The sample was ground in an agate mortar, embedded in two-component glue and filled into two quartz glass tubes of 5 mm diameter. The first sample was immediately fixed in the probe and brought inside the orienting magnetic field (B_or). The glue was allowed to set there for 12 h, fixing the preferred crystallite orientation caused by magnetically induced alignment. Another sample was treated correspondingly but cured in the absence of magnetic fields. They are referred to as oriented and regular powders, respectively. Since the NMR line shapes of oriented powders are highly sensitive towards the sample orientation with respect to the direction of the external field (B₀) [46–49], a series of ten orientation dependent NMR experiments was performed in steps of ten degrees.

Both regular and oriented powders were measured using a solid-echo pulse sequence with pulses of equal duration. The main transition signals spanning a frequency range of <200 kHz were investigated by single frequency excitation with hard pulses of 1.5 μs. Signals with larger frequency distributions were recorded using the frequency sweep technique. Throughout the entire frequency range individual measurements were performed in steps of 25 kHz and excitation pulses of 20 μs.

The relevant experimental quadrupole and signal shift NMR parameters were obtained by performing least-squares analysis using the SIMPSON simulation package [50].

Quadrupole coupling is characterized by the largest principal axis of the electric field gradient (EFG) and the asymmetry parameter η_Q = (|V_XX| – |V_YY|)/|V_ZZ| with the principal axes defined in the sequence |V_ZZ| > |V_XX| ≥ |V_YY|. The signal shift is characterized by the isotropic shift (Δ_iso), the anisotropy of the signal shift (Δ_aniso) as well as the asymmetry parameter (η_Δ) [46]. For the sake of simplicity, the principal axis systems (PAS) for both interactions were assumed to coincide.

The powder averaging for the simulation of regular powder signals was performed using the Repulsion method [51]. The crystal files for oriented powders were created considering the EFG tensor orientation of the Ga atoms obtained by quantum mechanical (QM) calculations and an alignment of the crystallites with their c axis parallel to the external magnetic field.

2.8 Quantum mechanical calculations

All electron first principle calculations were performed with density functional theory (DFT). The main component of the electric field gradient (EFG) tensor V_ZZ, the asymmetry parameter η_Q as well as the tensor orientations with respect to the crystal frame were calculated using the full-potential Linearized Augmented Plane Wave plus local orbital (LAPW + lo) method implemented in Wien2k [52]. The atomic-sphere radii R_MT were chosen as 2.31 a.u. for Ga and 2.50 a.u. for both Sr and Au. The separation energy for core and valence states was set to the default value of –6.0 Ry. The plane-wave cut-off, defined as R_MT × K_max, was set to a value of 6. The PBE exchange-correlation functional was employed within the generalized gradient approximation (GGA).

The lattice parameters used for the calculations were adopted from the X-ray diffraction experiments. EFG calculations were performed with full symmetry (space group R3̅c) and without any symmetry restraints (space group P1). 8 × 8 × 8 and 10 × 10 × 3 k grids were employed for the space groups R3̅c and P1, respectively.

3.1 Crystal chemistry

The structural chemistry of the prototype Sr₂Au₆Zn₃ [18] and several isotypic compounds [17, 19–21] has been discussed in detail in the original contributions. Herein we focus only briefly on the crystal chemical details of Eu₂Au₆Zn₃. As already mentioned in the introduction, all these structures derive from the aristotype AlB₂ and the gold atoms build a three-dimensional substructure that consists of puckered hexagons. The Au–Au distances in Eu₂Au₆Zn₃ range from 285 to 303 pm, close to the Au–Au distance of 288 pm in fcc gold [53]. The cavities within this network (which correspond to the Al sites of the aristotype) are filled in an ordered manner by europium atoms and Zn₃ triangles in 2:1 ratio. The local coordination is presented in Fig. 2. The different geometry of the Zn₃ triangles as compared to the spherical europium atoms leads to significant distortions within the gold substructure. This is readily evident from the course of the Eu–Au distances which range from 321 to 365 pm. In EuAu₂ [54], a slightly puckered AlB₂ variant with KHg₂ type structure, the europium coordination is more regular with 6 × 321 and 6 × 339 pm Eu–Au.

Fig. 2:

Coordination of the europium atoms (top) and the Zn₃ triangles (bottom) in the structure of Eu₂Au₆Zn₃. Relevant interatomic distances are given.

The Zn₃ triangles in Eu₂Au₆Zn₃ show Zn–Zn distances of 281 pm, which compare well with the distances in hcp zinc of 6 × 266 and 6 × 291 pm [53]. The triangles bind to the surrounding gold network through Au–Zn interactions. The Au–Zn distances range from 261 to 279 pm, slightly longer than the sum of the covalent radii [55] for Zn + Au of 259 pm. In view of the Au–Zn distances in CeAu₄Zn₂ (272 pm [56]) and EuAuZn (271–283 pm [57]), we can assume significant Au–Zn bonding in Eu₂Au₆Zn₃. Chemical bonding in these phases is addressed in more detail by ^69;71Ga solid state NMR spectroscopy in combination with QM calculations on the diamagnetic representative Sr₂Au₆Ga₃ (vide infra).

3.2 Magnetic properties and ¹⁵¹Eu Mössbauer spectroscopy

The magnetic behavior of the earlier reported strontium compounds Sr₂Au₆Ga₃ and Sr₂Au₆Zn₃ [18] was studied first. The temperature dependence of the magnetic susceptibility is shown in Fig. 3. Both samples show negative susceptibilities down to 10 K. The slight increase of the susceptibilities in the low-temperature regime is due to traces of paramagnetic impurities. Above 100 K we observe almost constant susceptibilities with a room temperature value of ca. –3.5 × 10^–4 emu mol^–1, at first sight pointing to diamagnetism. Electronic structure calculations [17, 19] showed a small residual density-of-states at the Fermi level for different valence electron counts. This is compatible with metallic behavior. The Pauli contribution to the total susceptibility is small and overcompensated by the stronger intrinsic diamagnetism, leading to overall negative susceptibility values.

Fig. 3:

Temperature dependence of the magnetic susceptibility of Sr₂Au₆Ga₃ and Sr₂Au₆Zn₃ measured at 10 kOe.

The temperature dependence of the magnetic susceptibility of Eu₂Au₆Zn₃ is presented in Fig. 4. Eu₂Au₆Zn₃ shows Curie–Weiss behavior in the temperature range from 22 to 300 K. A fit of this range results in a paramagnetic Curie temperature of θ_P = 8.2(5) K and an experimental magnetic moment of μ_eff = 7.56(1) μ_B Eu atom^–1, slightly lower than the theoretical value of 7.94 μ_B of the free Eu²⁺ ion. The positive value of θ_P indicates ferromagnetic interactions in the paramagnetic range and the experimental magnetic moment points to a stable divalent state for the europium atoms. The low-temperature behavior was studied in more detail by zero-field-cooling (ZFC) and field-cooling (FC) measurements at an external field strength of 100 Oe (inset of Fig. 4). The europium magnetic moments show antiferromagnetic ordering below a Néel temperature of T_N = 16.3(2) K. The magnetization behavior of Eu₂Au₆Zn₃ was studied through magnetization isotherms at 3, 14, 25, and 50 K (Fig. 4, bottom). At 50 K, well above the magnetic ordering temperature, we observe a linear increase of the magnetization with increasing field, usually observed for a paramagnetic material. The isotherm at 25 K already shows a weak curvature, indicating saturation effects. This becomes more pronounced in the 14 K isotherm, slightly below the Néel temperature. The 3 K isotherm shows a pronounced metamagnetic transition at a critical field of ca. 25 kOe, clearly manifesting the antiferromagnetic ground state. The saturation moment at 3 K and 80 kOe is 6.4(1) μ_B per Eu atom, close to the theoretical saturation magnetization of 7 μ_B according to g × J. Thus almost all europium moments are aligned in parallel. The slight reduction of the moment in the ordered state might be a consequence of the polycrystalline character of the sample and has frequently been observed for related europium intermetallics, e.g. 6.0 μ_B in EuAuGe [58] and 5.9 μ_B in EuAuIn [59].

Eu₂Au₆Ga₃ shows very similar magnetic behavior. The experimental magnetic moment of 7.98 μ_B Eu atom^–1 underlines the divalent nature of europium and the paramagnetic Curie temperature is also positive (13.7(5) K). The gallide shows a slightly lower Néel temperature of T_N = 12.1(1) K. The saturation magnetization at 3 K and 80 kOe is 6.9(1) μ_B Eu atom^–1.

Fig. 4:

Magnetic properties of Eu₂Au₆Zn₃. (top) Temperature dependence of the magnetic susceptibility (χ and χ⁻¹ data) measured at 10 kOe. The low-temperature behavior in zero-field-cooling and field-cooling mode (100 Oe data) is given in the inset; (bottom) magnetization isotherms at 3, 14, 25, and 50 K.

In addition to the magnetic data we also characterized Eu₂Au₆Zn₃ and Eu₂Au₆Ga₃ through their ¹⁵¹Eu Mössbauer spectra (Fig. 5). The 78 K spectra of both compounds show signals with isomer shifts of δ = –10.28(2) mm s^–1 (Eu₂Au₆Zn₃) and –10.69 mm s^–1 (Eu₂Au₆Ga₃), clearly pointing to divalent europium. In comparison with many other intermetallic europium compounds [60], the isomer shifts are indicative of almost fully ionized europium. The zinc compound shows a small second signal around 0 mm s^–1. This corresponds to a small Eu(III) impurity phase, most likely resulting from surface oxidation, and was included as a Lorentzian curve in the fit.

Fig. 5:

Experimental and simulated ¹⁵¹Eu Mössbauer spectra of Eu₂Au₆Zn₃ and Eu₂Au₆Ga₃ at 78 and 5 K.

The quadrupole splitting parameters of ΔE_Q = 4.2(2) mm s^–1 (Eu₂Au₆Zn₃) and 4.0(3) mm s^–1 (Eu₂Au₆Ga₃) reflect the non-cubic site symmetry of the europium atoms. These values are in good agreement with the ΔE_Q values of EuAgZn (4.4 mm s^–1 [61]) and EuAuZn (3.9 mm s^–1 [57]) which show similar europium coordination. The experimentally observed line width parameters of 2.2(1) mm s^–1 (Eu₂Au₆Zn₃) and 2.1(1) mm s^–1 (Eu₂Au₆Ga₃) are in the usual range.

The low-temperature behavior was exemplarily studied for the gallium compound. At 5 K, in the antiferromagnetically ordered regime, we observe full magnetic hyperfine field splitting with a large hyperfine field of 25.0(1) T. The latter value manifests complete magnetic ordering [60].

3.3 ^69;71Ga solid state NMR spectroscopy and quantum mechanical calculations

In order to investigate the peculiar Ga bonding situation in the Ga₃ units, Sr₂Au₆Ga₃ was chosen for ^69;71Ga solid state NMR spectroscopy. Both nuclei possess a nuclear spin I = 3/2 and are therefore sensitive towards quadrupole coupling. The interaction of the nuclear quadrupole moment and the electric field gradient (EFG) is a measure for the anisotropic charge distribution at the nuclear sites [62, 63]. Thus it is well suited for the investigation of chemical bonding in intermetallic compounds [46, 49, 64]. The EFG of the Ga atoms is dominated by the p-like valence electrons as shown for the di- and tetragallides of the alkaline earth metals [47, 48].

^69;71Ga-NMR spectroscopic experiments on a regular powder of randomly distributed crystallites show line shapes typical for atoms located on crystallographic sites of low symmetry, in agreement with the .2 point symmetry of the Ga atoms in the crystals. The signals result mainly from second order quadrupole coupling as indicated by their large frequency distributions (Fig. 6, left).

Fig. 6:

Left: ⁶⁹Ga (top) and ⁷¹Ga (bottom) NMR signals of a regular powder. Right: Angle-dependent ⁶⁹Ga measurements of an oriented powder. χ is the angle between the magnetic fields used for alignment of the crystallites and the NMR measurements. Black lines represent the experimental data. Each dot symbolizes an individual sweep measurement; simulations are shown in gray.

Magnetically induced alignment of the crystallites results in characteristic, orientation dependent NMR signals (Fig. 6, right). The alignment of the crystallites in a magnetic field is in agreement with the anisotropic electrical conductivity of Sr₂Au₆Ga₃ [46]. In addition to NMR experiments a quantum mechanical (QM) approach was pursued in order to determine the EFG tensor orientations and their corresponding eigenvalues. These are required for a quantitative analysis of the orientation dependent experiments.

The QM calculated quadrupole coupling parameters are in good agreement with those obtained by simultaneous least-squares analysis of the entire experimental data (Table 5, and section 2.7 ^69;71Ga solid state NMR spectroscopy). They are almost identical for calculations with and without symmetry restraints. The difference between experimental and QM values is <8 % for V_ZZ and negligible for η_Q, being in perfect agreement with our previous observations obtained for the di- and tetragallides of the alkaline earth metals [47, 48]. It is significantly smaller than the typical confidence interval for calculations of quadrupole coupling parameters of about ±15 % for V_ZZ and ±0.1 for η_Q [47].

The negative sign of V_ZZ indicates an elongated, prolate charge distribution of the Ga atoms. The large asymmetry parameter suggests an electron distribution far off from axial symmetry, in good agreement with the low Ga site symmetry. The large isotropic signal shift of more than 2000 ppm is considerably outside the regime of chemical shifts of Ga atoms typically found in nonmagnetic insulators (±700 ppm) [65]. Consequently, the isotropic signal shift is dominated by the Knight shift induced through the conduction electrons in Sr₂Au₆Ga₃. Comparing the bonding situation in Sr₂Au₆Ga₃ with previous studies, the EFG and NMR signal shift are in the region found for the four-bonded rather than the five-bonded Ga atoms in alkaline earth metal tetragallides or the corresponding three-bonded Ga atoms in the digallides [47, 48].

Fig. 7 shows the EFG tensor orientation of a Ga atom with respect to its closest neighboring atoms. V_ZZ, representing the largest contribution of the anisotropic charge distribution, points almost into the middle of two neighboring gold atoms with distances of 259.1 and 279.9 pm. It is tilted by about 31° with respect to the c axis of the unit cell. V_XX aims right towards the geometric center of the Ga₃ triangle as required by the presence of a twofold rotation axis along the diagonal of the ab plane of the unit cell. In a first approximation, the smallest principal axis V_YY points towards a gold atom at a distance of 261.9 pm. Currently, ongoing analyses of the band structure of Sr₂Au₆Ga₃ will hopefully show whether the orientation of the Ga EFG is related to Ga–Au and/or Ga–Sr interactions.

Fig. 7:

Ga₃ triangle and its corresponding EFG tensor orientation. The surrounding atoms, the EFG tensor, and the main directions are shown for one gallium atom. The principal axes are defined as: |V_ZZ| > |V_XX| ≥ |V_YY|.

The accuracy of the calculated tensor orientation is confirmed by the good agreement between the experimental and the simulated orientation dependent ^69;71Ga NMR signals. The characteristic signal evolution is extremely sensitive with respect to the orientation of the EFG. A maximum uncertainty of ±5° results from a conservative estimation of the agreement of measured and simulated NMR signals. According to the evaluation of QM calculations and orientation dependent NMR experiments the c axis turned out to align parallel to the external magnetic field and is thus the axis of highest Fermi velocity of the electrons.