Synthesis, crystal and electronic structures, physical properties and ¹²¹Sb and ¹⁵¹Eu Mössbauer spectroscopy of the alumo-antimonide Zintl-phase Eu₅Al₂Sb₆

Abstract

Eu₅Al₂Sb₆ was synthesized from the elements in niobium ampoules. It crystallizes in the orthorhombic crystal system (a = 1027.55(7), b = 1200.28(6), c = 1324.22(7) pm) with space group Pnma (no. 62), isostructural to Sr₅Al₂Sb₆, and can be described as a Zintl phase. The Al atoms are tetrahedrally surrounded by Sb atoms, forming branched strands. Besides Sb³⁻ anions, antimony Sb₂⁴⁻ dumbbells can also be found in the crystal structure. Eu₅Al₂Sb₆ [≡(Eu²⁺)₅(Al³⁺)₂(Sb³⁻)₄(Sb₂⁴⁻)] exhibits three magnetic ordering phenomena at T₁ = 12.3(1), T₂ = 10.6(1) and T₃ = 3.0(1) K, obtained by heat capacity measurements. While T₃ is of antiferromagnetic nature, T₁ and T₂ correspond to canted antiferromagnetic transitions. Resistivity investigations indicate that the title compound is a semiconductor, in line with the band structure calculations. Spin exchange parameters, calculated using mapping analysis, confirm that the magnetic phase transition at T_N = 3.5(1) is associated with the ordering of Eu1 atoms. The divalent character has been confirmed by ¹⁵¹Eu Mössbauer spectroscopic studies. Measurements conducted at 5 K show a hyperfine field splitting for two of the three Eu sites, underlining the magnetic data. Additionally, ¹²¹Sb Mössbauer spectroscopic studies have been conducted on Eu₅Al₂Sb₆ and isostructural Sr₅Al₂Sb₆.

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Introduction

Zintl phases are a class of materials that can be positioned between intermetallic compounds and insulating valence compounds from an electronic perspective.¹ Usually they contain an electropositive element from group 1 or 2 which, in a formal sense, transfers its electrons to an electronegative element from group 13, 14, or 15. A more concise definition of a Zintl compound is that they are materials in which both ionic and covalent bonding is found. If the anionic component of the structure has sufficient electrons, they will form isolated anions, isoelectronic to the noble gases. An example would be Mg₂Si, which adopts an anti-CaF₂ type structure with isolated Si⁴⁻ anions.² In cases of insufficient electrons, the main group elements form regular covalent bonds (2c–2e bonds), e.g. CaSi₂ where the Si₂²⁻ anion forms corrugated layers analogous to grey As.³ Besides the ‘classical’ binary Zintl phases numerous ternary compounds, also transition metal containing ones, have been found.⁴ Usually Zintl compounds are considered to be semiconductors, although compounds that are metallic in nature have also been found. The semiconducting properties make Zintl compounds an important class of materials for, as an example, thermoelectric applications.⁵ The aforementioned Mg₂Si is a good candidate for automotive waste heat recovery systems due to the low density and abundance of the constituent elements.^6,7 Yb₁₄MnSb₁₁^8,9 and Yb₉Mn_4.2Sb₉¹⁰ are examples of antimony-containing high ZT thermoelectric materials. While in the ternary system Sr–Al–Sb three compounds are known (Sr₅Al₂Sb₆,^11,12 Sr₁₄AlSb₁₁¹³ and Sr₃AlSb₃¹⁴) and have been characterized with respect to their properties, no compounds have been reported for the related system Eu–Al–Sb. Due to the comparable ionic radii of Eu²⁺ (117 pm) and Sr²⁺ (127 pm)¹⁵ known strontium representatives are a good starting point for the synthesis and characterization of isostructural europium compounds. Amongst the alkaline-earth metal group 13 antimonides several compounds with 5–2–6 composition are found. They can be grouped with respect to their prototypes, the Ca₅Ga₂As₆ (Pnma, no. 62) or Ca₅Al₂Bi₆ (Pbam, no. 55) type structures. For the latter one, the Yb₅M₂Sb₆^16–20 (M = Al, Ga, In) series is found, while for the Ca₅Ga₂As₆ type structure, e.g. Ca₅Al₂Sb₆,²¹ Ca₅Ga₂Sb₆,^22,23 Ca₅In₂Sb₆,²² Ca₅Al_2−xIn_xSb₆,²⁴ Sr₅In₂Sb₆,^22,25 Eu₅In₂Sb₆^26,27 and Ba₅In₂Sb₆¹¹ have been reported. Both compounds exhibit [MSb₄] tetrahedra and Sb₂⁴⁻ units; only the packing of the structural elements is slightly different. All of the aforementioned compounds exhibit intriguing thermoelectric properties. Here we report on the first compound in the Eu–Al–Sb system, Eu₅Al₂Sb₆. We have investigated its crystal structure, the physical properties (magnetism and electrical resistivity) along with ¹²¹Sb and ¹⁵¹Eu Mössbauer spectroscopic investigations of the bulk material. Theoretical calculations have been used to elucidate the electronic and magnetic structures of Eu₅Al₂Sb₆ and Bader charges in comparison with the isotypic strontium compound.

Experimental

Synthesis

The starting materials for the syntheses of the Eu₅Al₂Sb₆ and Sr₅Al₂Sb₆ samples were europium ingots (Alfa Aesar, 99.9%), strontium pieces (Sigma Aldrich, 99.0%), aluminium turnings (Koch Chemicals, 99.99%) and antimony pieces (ChemPur, 99.999%). The europium ingots and strontium pieces were stored under argon; the surface oxides were removed prior to the synthesis. The argon was purified over molecular sieves, silica gel and a titanium sponge (873 K). The elements were weighed in the ideal atomic ratio and arc-welded²⁸ in niobium tubes in a dried argon atmosphere of about 800 mbar. The metal tubes were subsequently placed in the water-cooled sample chamber of a high-frequency furnace (Hüttinger Elektronik, Freiburg, type TIG 1.5/300) under flowing argon.²⁹ The temperature was controlled by a Sensor Therm Methis MS09 pyrometer with an accuracy of ±50 K. The samples were rapidly heated to 1273 K, after 10 min the temperature was reduced to 1123 K and the samples were annealed for two hours. After the annealing step, the samples were cooled to room temperature within two hours. The samples were obtained as brittle polycrystalline pieces with metallic lustre and could easily be separated from the crucible material. No reaction with the containers was observed. The compounds showed moderate sensitivity to moisture and were therefore stored under dry argon atmosphere.

EDX data

Semiquantitative EDX analysis of the single crystal that has been investigated on the diffractometer was carried out by use of a Zeiss EVO® MA10 scanning electron microscope in variable pressure mode with EuF₃, Al₂O₃ and Sb as standards. The experimentally observed composition (39(2) at% Eu: 12(2) at% Al: 49(2) at% Sb) was close to the theoretical (38.5 at% Eu: 15.4 at% Al: 46.1 at% Sb) and refined one and no impurity elements heavier than sodium (detection limit of the instrument) were detected.

Powder X-ray diffraction

The polycrystalline sample was characterized by the Guinier powder pattern using CuK_α1 radiation and α-quartz (a = 491.30 and c = 540.46 pm) as an internal standard. The Guinier camera was equipped with an imaging plate (Fuji film, BAS-READER 1800). Least-squares refinements led to the lattice parameters listed in Table 1. To ensure correct indexing, the experimental pattern was compared to the calculated one using the refined atomic positions (vide infra) obtained from single crystal X-ray diffraction.³⁰ The diffraction pattern is depicted in Fig. S1 (ESI†).

Table 1 Crystallographic data and details of the room temperature single crystal structure refinement of Eu₅Al₂Sb₆ (Sr₅Al₂Sb₆ type, Pnma, no. 62, Z = 4)

Lattice parameter, (pm)	a = 1027.55(7)
	b = 1200.28(6)
	c = 1324.22(7)
Volume, V (nm^3)	1.628(1)
Molar mass (g mol^−1)	1544.3
Calc. density, Dx (g cm^−3)	6.30
Abs. coeff. μ (mm^−1)	28.8
F(000) (e)	2588
Crystal size (μm^3)	90 × 50 × 45
Transmission ratio (min/max)	0.074/0.292
Detector distance (mm)	70
Exposure time (min)	10
Integr. parameters A/B/EMS	13.0/2.7/0.015
θ range (deg)	2.3–36.3
Range in hkl	±17; ±14; ±18
Total no. reflections	26 749
Independent reflections/Rint	2570 (0.0626)
Reflections with I ≥ 3σ(I)/Rσ	2192 (0.0112)
Data/parameters	2570/71
Goodness-of-fit on F^2	1.68
R 1/wR2 for I ≥ 3σ(I)	0.0244/0.0514
R 1/wR2 for all data	0.0330/0.0531
Extinction coefficient	124(10)
Largest diff. peak/hole (e Å^−3)	+1.52/−1.88

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Single crystal X-ray diffraction

Single crystals were isolated from the crushed samples. The crystal fragments were glued to thin quartz fibres using beeswax and investigated by Laue photographs on a Buerger camera (white Mo radiation, Fujifilm imaging plate, BAS-1800) in order to check their quality for intensity data collection. The intensity data set was collected at room temperature by using a Stoe IPDS II (graphite-monochromatized MoKα radiation; oscillation mode) diffractometer. Numerical absorption correction was applied to the data set. Details about the data collection and the crystallographic parameters are summarized in Tables 1–3.

Table 2 Atomic coordinates and isotropic displacement parameters U_eq (pm²) for Eu₅Al₂Sb₆ (Sr₅Al₂Sb₆ type, space group Pnma, Z = 4). Standard deviations are given in parentheses

	Wyckoff site	x	y	z	U eq
Eu1	4c	0.16073(4)	1/4	0.68713(3)	165(1)
Eu2	8d	0.08106(2)	0.02636(3)	0.26332(2)	161(1)
Eu3	8d	0.33297(3)	0.52005(3)	0.46349(2)	192(1)
Al1	4c	0.4226(2)	1/4	0.0655(2)	152(6)
Al2	4c	0.3128(2)	1/4	0.2982(2)	141(6)
Sb1	4c	0.35383(5)	1/4	0.87598(4)	158(1)
Sb2	8d	0.32703(3)	0.05337(4)	0.16923(3)	144(1)
Sb3	4c	0.15063(5)	1/4	0.43721(4)	158(1)
Sb4	4c	0.45364(5)	1/4	0.62173(4)	157(1)
Sb5	4c	0.00550(5)	1/4	0.09135(4)	145(1)

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Table 3 Interatomic distances (in pm) in the structure of Eu₅Al₂Sb₆ (Sr₅Al₂Sb₆ type, space group Pnma, Z = 4). Standard deviations are smaller or equal to ±0.1 pm. All distances <400 pm are listed

Eu1	1	Sb4	313.0	Eu2	1	Sb2	277.6	Eu3	1	Sb2	320.5	Al1	1	Sb3	234.2
	1	Sb1	319.0		1	Sb2	283.4		1	Sb1	355.2		1	Sb1	260.5
	1	Sb1	326.0		1	Sb5	360.1		1	Eu3	359.6		2	Sb2	289.9
	1	Sb4	330.4		1	Sb3	360.5		1	Sb5	363.5		1	Al2	327.9
	1	Sb3	330.8		1	Al2	361.4		1	Sb4	369.8		2	Eu2	386.9
	2	Sb2	364.7		1	Sb1	369.4		1	Eu2	374.4
					1	Eu3	374.4		1	Sb3	375.6
					1	Sb4	382.3		1	Sb5	376.1
					1	Al1	386.9		1	Al2	391.3
					1	Al2	392.9		1	Eu2	397.6
					1	Eu3	397.6		1	Sb2	399.2
Al2	1	Sb5	246.0	Sb1	1	Al1	260.5	Sb2	1	Eu2	277.6	Sb3	1	Al1	234.2
	1	Sb3	248.2		1	Eu1	319.0		1	Eu2	283.4		1	Al2	248.2
	2	Sb2	291.4		1	Eu1	326.0		1	Al1	289.9		1	Eu1	330.8
	1	Al1	327.9		1	Sb4	351.7		1	Al2	291.4		2	Eu2	360.5
	2	Eu2	361.4		2	Eu3	355.2		1	Eu3	320.5		1	Sb5	366.3
	2	Eu3	391.3		2	Eu2	369.4		1	Eu1	364.7		2	Eu3	375.6
	2	Eu2	392.9		1	Sb3	392.4		1	Eu3	399.2		1	Sb1	392.4
													1	Sb4	395.5
Sb4	1	Sb5	286.9	Sb5	1	Al2	246.0
	1	Eu1	313.0		1	Sb4	286.9
	1	Eu1	330.4		2	Eu2	360.1
	1	Sb1	351.7		2	Eu3	363.5
	2	Eu3	369.8		1	Sb3	366.3
	2	Eu2	382.3		2	Eu3	376.1
	1	Sb3	395.5

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Physical property measurements

The powdered samples of Eu₅Al₂Sb₆ and Sr₅Al₂Sb₆ were packed in polyethylene (PE) capsules and attached to the sample holder rod of a Vibrating Sample Magnetometer unit (VSM) for measuring the magnetization M(T,H) in a Quantum Design physical property measurement system (PPMS). The samples were investigated in the temperature range of 2.5–300 K with magnetic fields up to 80 kOe.

For the heat capacity measurement of Eu₅Al₂Sb₆, one piece of the sample was fixed to a pre-calibrated heat capacity puck using Apiezon N grease and investigated in the temperature range of 2.0 to 100 K.

A cold pressed tablet (∅ 4.2 mm) of Eu₅Al₂Sb₆ was annealed at 773 K for 4 weeks. The sintered material (Archimedes density 90(1)%) was used for the resistivity experiments. The measurements were carried out in the AC transport mode³¹ of a Quantum-Design physical property measurement system (PPMS). The ACT puck was modified by a van-der-Pauw press contact assembly purchased from Wimbush Science & Technology. The probes are spring contacts, gold plated over nickel; the distance between the pins was set to 2 mm. The resistivity was measured between 2–300 K with a data point every 0.1 K up to 20 K and one data point every 1 K up to 300 K. The AC frequency was set to 17 Hz with a measurement time of 1 s. The recorded data of channel 1 & 2 was converted according to the van-der-Pauw equation given in the Quantum Design Application Note 1076-304.

Mössbauer spectrosopy

The 21.53 keV transition of ¹⁵¹Eu with an activity of 130 MBq (2% of the total activity of a ¹⁵¹Sm:EuF₃ source) and a Ba^121mSnO₃ source were used for the ¹⁵¹Eu and ¹²¹Sb Mössbauer spectroscopic experiments, which were conducted in the usual transmission geometry. The measurements were performed with a commercial helium-bath cryostat and a liquid nitrogen bath cryostat. The temperature of the absorber was set to 5 and 78 K, while the source was kept at room temperature. The temperature was controlled by a resistance thermometer (∼0.5 K accuracy). The sample was enclosed in a small PVC container, and the required sample mass was calculated based on the work by Long et al.³² Fitting of the spectrum was performed with the NORMOS-90 program system.³³

Theoretical methodology

Electronic structure calculations on Eu₅Al₂Sb₆ and Sr₅Al₂Sb₆ were performed using the projector augmented wave method (PAW) of Blöchl^34,35 coded in the Vienna ab initio simulation package (VASP).^36,37 All VASP calculations employed the generalized gradient approximation (GGA) with exchange and correlation treated by Perdew–Burke–Enzerhoff (PBE).³⁸ To describe the electron correlation associated with Eu 4f states, an on-site Hubbard repulsion U parameter³⁹ was applied with an effective U_eff = 6 eV on the Eu atom. The cutoff energy for the plane wave calculations was set to 500 eV and the Brillouin zone integration was carried out using 6 × 7 × 5 Γ-centered k-point meshes. The Bader charge analysis was based on VASP calculations with subsequent calculations with the Bader program developed by the Henkelman group.^40–42

Results and discussion

Crystal chemistry

Eu₅Al₂Sb₆ crystallizes in the orthorhombic crystal system with the space group Pnma (no. 62) and lattice parameters of a = 1027.55(7), b = 1200.28(6), c = 1324.22(7) pm, isostructural to Sr₅Al₂Sb₆, which forms the respective prototype.¹¹ The structure can be considered as the Zintl phase according to (Eu²⁺)₅(Al³⁺)₂(Sb³⁻)₄(Sb₂⁴⁻) with Sb₂⁴⁻ being covalently bound dumbbells. An extended view of the crystal structure of Eu₅Al₂Sb₆ is shown in Fig. 1. The Al and Sb atoms form a polyanionic [Al₂Sb₆]¹⁰⁻ framework, while the Eu cations are found in cavities. The polyanion can be described as a branched strand of distorted edge- and corner-sharing aluminium centred tetrahedra running along the a axis (Fig. 2, top). Two Sb2 atoms form the shared edge while the Sb3 atoms are corner-shared. The Sb1 and (Sb4–Sb5) dumbbells finally complete the coordination environments (Fig. 2, top). The shortest interatomic distances can be found between Al and Sb (264–274 pm), which are in the range of the sum of the covalent radii (125 + 141 = 266 pm⁴³). In addition Sb–Sb (289 pm) contacts can be found which are in line with the sum of the covalent radii (2 × 141 = 282 pm⁴³) of the element and with an antimony-antimony single bond observed in other Zintl phases e.g., BaSb₂ (CaSb₂ type: 291 pm;⁴⁴ BaSb₂ type: 291–296 pm⁴⁵) or EuSb₂ (CaSb₂ type: 293 pm⁴⁶). The coordination environment of the Sb₂⁴⁻ anion is depicted in Fig. 2 (bottom). In between the polyanion three crystallographically independent Eu atoms are found with coordination numbers of seven and eight and interatomic distances from 320 to 397 pm (Fig. 3).

Fig. 1 Extended view of the crystal structure of Eu₅Al₂Sb₆ along [010]. The bonding within the polyanion is highlighted along with the tetrahedral coordination environments surrounding the Al atoms. Eu atoms are depicted in blue, Al atoms as open white circles and Sb atoms in orange.

Fig. 2 (top) Branched strand-like [Al₂Sb₆]¹⁰⁻ polyanion of the Zintl phase Eu₅Al₂Sb₆ running along [100]; (bottom) coordination environment and interatomic distances, given in pm, of the Sb₂⁴⁻ anion; the Sb–Sb bond is highlighted.

Fig. 3 Coordination environments surrounding the three crystallographically independent Eu atoms in Eu₅Al₂Sb₆. Interatomic distances are given in pm. Eu atoms are depicted in blue, Al atoms as open white circles and Sb atoms in orange.

Magnetic measurements

A high-field susceptibility measurement of Eu₅Al₂Sb₆ conducted in ZFC mode at 10 kOe (Fig. 4, top panel) indicates magnetic ordering at low temperatures and paramagnetic behaviour above the Curie-temperature. A Curie–Weiss fit of the reciprocal magnetic susceptibility in the paramagnetic region (50–300 K) was used to determine the effective magnetic moment (μ_eff = 8.32(1) μ_B per Eu atom) and the Weiss constant (θ_p = −1.8(1) K). The magnetic moment is slightly higher than the calculated moment of a Eu²⁺ ion (μ_calc = 7.94 μ_B) but still indicates that the europium atoms are divalent. To obtain more information about the magnetic ground state ZFC/FC (zero-field-cooled/field-cooled) measurements at 100 Oe were conducted. Fig. 4 (middle panel) depicts the measurement indicating at least two anomalies: an antiferromagnetic transition at T_N = 3.5(1) K and a second transition at T = 12.5(1) K. Heat capacity measurements (depicted in red in Fig. 4, middle panel) reveal the presence of three intrinsic magnetic ordering phenomena at T₁ = 12.3(1), T₂ = 10.6(1) and T₃ = 3.0(1) K. While T₁ and T₃ are in line with the ZFC/FC experiment, T₂ must correspond to the change of slope between 8–12 K, visible in the 100 Oe susceptibility measurements. The intensity of the features in the C_P curve characterizes them all as transitions corresponding to the material itself. While the transition at T_N = 3.5(1) K is undoubtedly of antiferromagnetic nature, T₁ and T₂ are not as clear to interpret. Since the susceptibility rises below T = 12.5(1) K a second antiferromagnetic transition (AFM) can be ruled out. A ferromagnetic transition (FM) on the other hand would be more dominant in nature. Mössbauer spectroscopic studies (vide infra) revealed that the AFM transition at T_N = 3.5(1) K has to be associated with the Eu1 site (4c). Getting back to the magnitude of the transition – since both plain AFM and FM transitions can be ruled out with respect of the magnitude of the magnetic transitions, a canted antiferromagnetic state is the only explanation remaining. The net moment of the Eu2 and Eu3 sites is small causing only a small rise in the low field susceptibility measurements. Finally magnetization isotherms were recorded at 3, 10, 25 and 50 K (Fig. 4, bottom panel). The isotherm at 50 K shows a linear field dependency in line with paramagnetic behaviour. The isotherms at 10 and 25 K show a curved trace without any tendency for saturation. The 3 K isotherm finally exhibits an “s-shaped” character caused by a spin-reorientation also called metamagnetic step, underlining the antiferromagnetic ground state. The critical field was determined to be H_crit = 20.2(1) kOe from the derivative of the 3 K isotherm. The saturation magnetization is μ_sat = 5.4(1) μ_B per Eu atom at 3 K and 80 kOe. This is lower than the expected saturation magnetization of 7 μ_B according to g_J × J.

Fig. 4 Magnetic properties of Eu₅Al₂Sb₆: (top) temperature dependence of the magnetic susceptibility (χ and χ⁻¹ data) measured at 10 kOe; (middle) magnetic susceptibility in zero-field-cooled/field-cooled (ZFC/FC) mode, measured at 100 Oe in the low-temperature range, and in red the heat capacity measurements in zero-field between 2–50 K are shown; (bottom) magnetization isotherms recorded at 3, 10, 25 and 50 K.

Sr₅Al₂Sb₆ in contrast exhibits diamagnetic behaviour (Fig. S2, ESI†), as expected for a semiconducting material with only small amounts of charge carriers available up to room temperature. The susceptibility at 300 K is χ = −480(5) × 10⁻⁶ emu mol⁻¹, which is in good agreement with the sum of the diamagnetic increments of χ(Sr₅Al₂Sb₆) = −599 × 10⁻⁶ emu mol⁻¹ using the tabulated values for the respective ions (χ(Sr²⁺) = −19 × 10⁻⁶ emu mol⁻¹; χ(Al³⁺) = −2 × 10⁻⁶ emu mol⁻¹).⁴⁷ The values for Sb³⁻ and Sb₂⁴⁻ are not available and have been estimated with respect to the neighbouring anions Te²⁻ and I⁻ (χ(Sb³⁻) = −90 × 10⁻⁶ emu mol⁻¹; χ(Sb₂⁴⁻) = −140 × 10⁻⁶ emu mol⁻¹).

Electrical resistivity

The temperature dependence of the electrical resistivity of Eu₅Al₂Sb₆ is depicted in Fig. 5. The measured data exhibits the behaviour of the semiconductor. In region (I), at low temperatures, only a limited amount of charge carriers can overcome the band gap. With increasing temperature (II), ‘saturation’ or ‘exhaustion’ occurs, since the doped (extrinsic) charge carriers get promoted, causing a temperature independent plateau. Finally, the intrinsic charge carriers start to take over (III), however, the distinct behaviour of the materials itself is seen only at even higher temperatures (vide infra).^48,49 Analysis of the data between 150–300 K using the relation ρ ∝ e^E_g/2kT for intrinsic semiconductors yielded a band gap of 0.10(2) eV. From the electronic structure, a band gap of 0.52 eV was determined. The band gaps of Eu₅Al₂Sb₆ are smaller compared to Sr₅Al₂Sb₆ (experimental: 0.5 eV; calculated 0.8 eV),¹² which were determined at temperatures >500 K. These differences between isotypic compounds are not unusual as seen from the M₂CdAs₂ (M = Ca, Eu) systems, where the Ca-compound exhibits a band gap of ∼1 eV, while Eu₂CdAs₂ has a band gap of ∼0.3 eV.⁵⁰ This feature can be attributed to the mixing of Eu 4f–5d states, as seen in many optical materials.^51–53 A closer look at the resistivity data reveals that the region between 150–300 K, used to determine the band gap, might not be fully ‘intrinsic’. Assuming a linear trend, extrapolation of the data to high temperatures would cause the resistivity to cut the temperature axis at ∼450 K. Therefore a kink of the resistivity at higher temperatures is very likely, similar to what has been observed for Sr₅Al₂Sb₆.¹² When the resistivity of Eu₅Al₂Sb₆ is compared to isotypic Sr₅Al₂Sb₆, it is evident that both compounds exhibit similar resistivities at 300 K (Sr₅Al₂Sb₆: ρ(300 K) ∼ 1.8 Ω cm; Eu₅Al₂Sb₆: ρ(300 K) = 1.4(1) Ω cm).¹² The observed resistivity is also in line with other non-isotypic Zintl compounds, e.g. Ca₅Ga₂Sb₆ (ρ(300 K) ∼ 0.1 Ω cm),²³ Sr₅In₂Sb₆ (ρ(300 K) = 10 Ω cm)²⁵ or Eu₅In₂Sb₆ (ρ(300 K) ∼ 0.085 Ω cm).²⁷

Fig. 5 Temperature dependence of the electrical resistivity of Eu₅Al₂Sb₆. The different regions are highlighted by colours; for explanation see text. The inset depicts the determination of the band gap.

¹²¹Sb and ¹⁵¹Eu Mössbauer spectroscopy

To further prove the presence of Eu²⁺ in Eu₅Al₂Sb₆, ¹⁵¹Eu Mössbauer spectra were recorded at 78 K and 5 K (Fig. 6, top and bottom). The obtained fitting parameters are listed in Table 4. The 78 K spectrum could be fitted with two signals, and the 5 K spectrum with four signals. The two signals in the 78 K spectrum could be attributed to Eu²⁺ and Eu³⁺; the latter one contributed ∼1%, hence it can be considered to be an Eu³⁺ impurity (most likely surface oxidation). The main signal shows an isomer shift of δ = −11.35(1) mm s⁻¹, and the impurity signal is found at δ = +1.2(1) mm s⁻¹. The four signals at 5 K can be attributed to the three crystallographic Eu positions in Eu₅Al₂Sb₆ and again to the small Eu³⁺ impurity. The main signals show isomer shifts of δ = −11.23(6), −11.41(4) and −11.47(4) mm s⁻¹, being in line with Eu²⁺ and the magnetic data discussed above, and the impurity signal is found at δ = −0.2(2) mm s⁻¹. As a consequence of the non-cubic site symmetry of the europium atom, the signals of the 5 K spectra show quadrupole splittings of ΔE_Q = −1.0(2) mm s⁻¹, −4.4(7) mm s⁻¹ and −1.9(3) mm s⁻¹, respectively. The experimental line widths of Γ = 3.2(1), 3.1(1) and 2.8(1) mm s⁻¹ are within the usual range.^54–58 Of the three signals at 5 K, two signals exhibit significant magnetic hyperfine field splitting (B_hf = 23.1(1) and 20.0(1) T) along with the third signal showing only a small hyperfine field splitting of B_hf = 3.2(1) T. The observed hyperfine fields are in line with other intermetallic europium compounds.^54–58 The areas of the three signals were fixed with a 1 : 2 : 2 ratio, corresponding to the respective site multiplicities of the crystal structure (4c and 2 × 8d). The signal with the small hyperfine field can be therefore attributed to the Eu1 site (4c), which at 5 K is not magnetically ordered (but shows at least some short-range order), whereas the Eu2 and Eu3 sites (both 8d) show a full hyperfine field splitting, in line with their magnetic ordering phenomena at temperatures >5 K. This fits well to the magnetic data, where the antiferromagnetic ordering occurs at T_N = 3.5(1) K, below the 5 K used to record the Mössbauer spectra. The small difference between T_N and the measurement temperature is causing a minor hyperfine field for the Eu1 site. The ¹²¹Sb Mössbauer spectra of Sr₅Al₂Sb₆ measured at 78 K and Eu₅Al₂Sb₆, (78 and 5 K) are depicted in Fig. 7 along with the respective fits. The crystal structure contains three crystallographic sites for the Sb³⁻ anions (2 × 4c and 8d) and two sites forming the Sb₄²⁻ anion (2 × 4c), therefore the spectrum was fitted using two signals, one for the sum of the Sb³⁻ and one for the sum of the ‘Sb²⁻’ anions. The area ratio of the two signals was fixed in a 2 : 1 ratio (Sb³⁻ : ‘Sb²⁻’). While for the ‘Sb²⁻’ signal shifts of δ ∼ −10 mm s⁻¹ were found, the Sb³⁻ signal exhibits shifts of δ ∼ −8 mm s⁻¹ (Table 4). For the latter one, the observed isomer shift is in line with other antimonides containing formally Sb³⁻ anions, e.g. the binary alkali metal antimonides Li₃Sb,⁵⁹ and A₃Sb (A = Na, K, Rb),⁶⁰ the III–V semiconductors AlSb, GaSb and InSb,⁶¹ the MT₂Sb₂ (M = Eu, Yb; T = Mn, Zn) series,⁶² the antimonide oxides RETSbO (RE = La–Sm, Gd; T = Mn, Zn)⁶³ or the half-Heusler phases YbTSb (T = Ni, Pd, Pt, Cu, Ag, Au)⁶⁴ and ScTSb (T = Ni, Pd, Pt)⁶⁵ all with isomer shifts around δ ∼ −8 mm s⁻¹. Antimonide dumbbells in contrast are rather rare with respect to ¹²¹Sb Mössbauer spectroscopic investigations. One example that can be found in the literature is α-Zn₁₃Sb₁₀, which can be formulated as (Zn²⁺)₁₃(Sb³⁻)₆(Sb₂⁴⁻)₂. The Mössbauer spectroscopic data was also fitted using two signals in the respective fixed ratio of 3 : 2. Isomer shifts of −8.17(2) and −9.73(2) mm s⁻¹ were derived,⁶⁶ which are in line with the data presented herein. In contrast to the zinc phase (ΔE_Q = 0 mm s⁻¹), the dumbbells in Sr₅Al₂Sb₆ and Eu₅Al₂Sb₆ exhibit asymmetric coordination environments (Fig. 2, bottom), therefore a rather large quadrupole splitting is observed (ΔE_Q = +2.9 and −8.9 as well as +3.6 and −9.9 mm s⁻¹) for the Sb₂⁴⁻ signals in both compounds. The low temperature measurements of Eu₅Al₂Sb₆, conducted at 5 K, at first glimpse show an increase of the line width, in line with a transferred hyperfine field from the Eu atoms. The data can be fitted with this increase of the line width or alternatively with fixed isomer shifts and line widths taken from the 78 K measurements and freely refined quadrupole splitting and hyperfine field parameters. The respective parameters are listed in Table 4, the fit depicted in Fig. 7 corresponds to the variant with increased line widths and no refined magnetic hyperfine field.

Fig. 6 Experimental (data points) and simulated (continuous lines) ¹⁵¹Eu Mössbauer spectra of Eu₅Al₂Sb₆ at 78 and 5 K. The red line corresponds to the sum of the different signals used for fitting; they are labeled according to Table 4, and the green signals (#1) are the Eu³⁺ impurities.

Table 4 Fitting parameters for ¹²¹Sb and ¹⁵¹Eu Mössbauer spectroscopic measurements of Eu₅Al₂Sb₆. δ: isomer shift; Γ: experimental line width; ΔE_Q: quadrupole splitting; B_hf: magnetic hyperfine field; A: signal area ratio

	T (K)	#	Ion	δ (mm s^−1)	Γ (mm s^−1)	ΔEQ (mm s^−1)	B hf (T)	A (%)
a Value fixed in the last cycle. b Ratio of signals #1 : #2 fixed to 2 : 1. c Ratio of signals #2 : #3 : #4 fixed to 1 : 2 : 2, ratio of #1 to Σ(#2 + #3 + #4) refined.
Eu5Al2^121Sb6	78	1	Sb^3−	−8.3(1)	3.1(2)	+2.9(1)	—	66.67^b
		2	Sb2^4−	−9.7(2)	3.0(2)	−8.9(1)	—	33.33^b
No Bhf	5	1	Sb^3−	−8.3(1)	3.5(1)	+4.4(3)	—	66.67^b
		2	Sb2^4−	−9.8(1)	3.1(1)	−9.9(4)	—	33.33^b
With Bhf	5	1	Sb^3−	−8.3^a	3.1^a	+2.9(2)	3.1(1)	66.67^b
		2	Sb2^4−	−9.7^a	3.0^a	−10.7(3)	1.3(1)	33.33^b
Sr5Al2^121Sb6	78	1	Sb^3−	−8.2(1)	3.8(2)	+3.6(3)	—	66.67^b
		2	Sb2^4−	−9.9(2)	3.6(2)	−9.9(2)	—	33.33^b
^151Eu5Al2Sb6	78	1	Eu^3+	+1.2(1)	3.0^a	—	—	1.1
		2	Eu^2+	−11.35(1)	2.7(1)	−4.4(1)	—	98.9
	5	1	Eu^3+	−0.2(2)	3.0^a	—	—	1.9^c
		2	Eu^2+	−11.23(6)	3.2(1)	−4.4(7)	3.6(3)	19.6^c
		3	Eu^2+	−11.41(4)	3.1(1)	−1.9(3)	23.1(1)	39.25^c
		4	Eu^2+	−11.47(4)	2.8(1)	−1.0(2)	20.0(1)	39.25^c

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Fig. 7 Experimental (data points) and simulated (continuous lines) ¹²¹Sb Mössbauer spectra of Sr₅Al₂Sb₆ at 78 K and Eu₅Al₂Sb₆ at 78 and 5 K. The red line corresponds to the sum of the different signals used for fitting; they are labeled according to Table 4.

Theoretical calculations

To gain more insights into the possible magnetic exchange interactions and magnetic orderings in Eu₅Al₂Sb₆, the electronic structure and total energies of eleven magnetically ordered models (see Fig. 8) were examined: they included one ferromagnetic (FM) model, two antiferromagnetic (AFM1, AFM2) models and eight ferrimagnetic (Fi1–Fi8) models. Due to the overall structural complexity, the repeating unit of each model was limited to one crystallographic unit cell, that is, a total of 4 × Eu1, 8 × Eu2 and 8 × Eu3 atoms. The results of this analysis are summarized in Fig. 8 and Table 5. The spin-polarized density of states (DOS) curve for the FM state is plotted in Fig. 9. There is a small band gap (ca. 0.52 eV from the most stable AFM1 model) at the Fermi level, consistent with the semiconducting behaviour found experimentally. The Eu majority spin states are all occupied while its minority spin states are all unoccupied, indicating a high spin f⁷ (Eu²⁺) configuration. Ten spin exchange parameters within Eu₅Al₂Sb₆ were evaluated by performing a mapping analysis^67–69 based on the eleven magnetic models (FM, Fi1–Fi8, AFM1 and AFM2) shown in Fig. 8. The ten spin exchange paths include the Eu1–Eu2 interactions (J₁), the Eu1–Eu3 interactions (J₂), two types of Eu2–Eu3 interactions (J₃ and J₃′), Eu2–Eu2 interactions (J₄), three types of Eu3–Eu3 interactions (J₅, J₆, J₆′) and two types of Eu1–Eu1 interactions (J₇ and J₈). The relative energies, per unit cell (u.c.), of the eleven magnetic models determined from our VASP calculations are summarized in Fig. 8. The energies of these models can also be approximated in terms of the spin Hamiltonian,
in which, J_ij is the spin exchange parameter for the interaction between the spin sites i and j. By applying this energy expression for spin dimers with N unpaired spins per spin site, the total spin exchange energy expression for each of the eleven models are summarized in Table 5. By mapping the relative energies of the eleven models determined by VASP calculations onto the corresponding relative energies determined from the above exchange energies, we obtained the values of J_ij listed in Table 5. These parameters are really small compared with other rare-earth compounds with high ordering temperatures,^70,71 but they are consistent with the experimentally found small Weiss constant (weak interactions) and low ordering temperatures. Most of the interactions (seven) are antiferromagnetic except for J₁, J₃ and J₆. Based on the calculated spin exchange parameters, one antiferromagnetic state (AFM1) has the lowest energy, but this energy is only slightly lower than those of AFM2 and Fi1 (see Fig. 8), whereas all other ferrimagnetic models are at least 36 meV u.c.⁻¹ higher in energy. The only difference between AFM1, AFM2 and Fi1 is the spin arrangement on the four Eu1 atoms in the unit cell (see Fig. 8, top three models), as all other atoms have the same spin arrangements, that is intra-chain antiferromagnetic interactions in Eu2 and Eu3 chains and ferromagnetic Eu2 and Eu3 layers. In addition, the energy differences between these models are very small (less than 1.5 meV u.c.⁻¹). Therefore, the Eu1 spin arrangements within the unit cell may fluctuate between these three cases. Below T_N = 3.5(1) K, antiferromagnetic states (AMF1 or AFM2) prevail and the magnetic phase transition related to the ordering of Eu1 atoms is observed. The magnetic ordering at 12.5 K is more complicated but both ferromagnetic and antiferromagnetic interactions exist based on the calculated spin exchange parameters. So, the magnetic ordering at 12.5 K should be either ferrimagnetic or canted antiferromagnetic.

Fig. 8 Eleven magnetic structure models of Eu₅Al₂Sb₆ constructed using the crystallographic unit cell with their relative energies (in meV u.c.⁻¹) in parentheses. Only Eu atoms are shown in each model. Red and blue colors indicate oppositely oriented magnetic moments of Eu. The ten spin exchange paths in Eu₅Al₂Sb₆ (J₁–J₈, J₃′ and J₆′) are shown in the FM model. The green circles highlight the Eu1 atoms.

Table 5 Total energies and spin exchange energy expressions for the eleven magnetic structure models of Eu₅Al₂Sb₆. N_Eu = 7

Models	Energy^a (meV u.c.^−1)	Spin exchange energy expression (meV)
a Total energy relative to model FM from VASP calculation.
AFM1	−90.86
AFM2	−90.82
Fi1	−89.53
Fi2	−53.06
Fi3	−45.06
Fi4	−38.30
Fi5	−38.23
Fi6	−37.67
Fi7	−31.92
Fi8	−12.42
FM	0.00
J (meV)		J 1 = +0.0031, J2 = −0.035, J3 = +0.021, J3′ = −0.044, J4 = −0.065, J5 = −0.015, J6 = +0.040, J6′ = −0.080, J7 = −0.013, J8 = −0.00041

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Fig. 9 Total and partial spin polarized density of states (DOS) of Eu₅Al₂Sb₆ (ferromagnetic model). The Fermi level is denoted by the dashed line.

The calculated Bader effective charges for Eu₅Al₂Sb₆ and Sr₅Al₂Sb₆ are listed in Table 6. In both Eu₅Al₂Sb₆ and Sr₅Al₂Sb₆, the Eu, Sr and Al atoms have positive effective charges while Sb atoms have negative effective charges. The effective charges found on the Eu atoms are all between +1 and +2, which indicates that Eu³⁺ can be ruled out, in accordance with the ¹⁵¹Eu Mössbauer result that found Eu²⁺. However, the fact that the effective charges on Eu atoms are less than +2 indicates the presence of some partial covalent bonding interactions between Eu and Sb (or Al).

Table 6 Bader charges in Eu₅Al₂Sb₆ and Sr₅Al₂Sb₆

Eu5Al2Sb6	Atom	Eu1	Eu2	Eu3	Sb1	Sb2	Sb3	Sb4	Sb5	Al1	Al2
	Charge	+1.18	+1.18	+1.24	−1.59	−1.68	−1.63	−1.08	−1.30	+1.51	+1.44
Sr5Al2Sb6	Atom	Sr1	Sr2	Sr3	Sb1	Sb2	Sb3	Sb4	Sb5	Al1	Al2
	Charge	+1.32	+1.31	+1.36	−1.71	−1.78	−1.71	−1.21	−1.39	+1.49	+1.43

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Conclusions

The Zintl phase Eu₅Al₂Sb₆, which crystallizes isostructural to Sr₅Al₂Sb₆ (Pnma, no. 62, a = 1027.55(7), b = 1200.28(6), c = 1324.22(7) pm), was synthesized from the elements in niobium ampoules and characterized by powder and single crystal X-ray diffraction. In the orthorhombic crystal structure, the Al and Sb atoms form branched strands, consisting of Al³⁺, Sb³⁻ and Sb₂⁴⁻ dumbbells. The three Eu sites are located in cavities. Three magnetic ordering phenomena at T₁ = 12.3(1), T₂ = 10.6(1) and T₃ = 3.0(1) K were observed in the susceptibility measurements and confirmed by heat capacity measurements. ¹⁵¹Eu Mössbauer spectroscopic studies confirmed the divalent oxidation state of all three Eu atoms. Measurements at 5 K, therefore below T₁ and T₂, showed a hyperfine field splitting for two of the three Eu sites due to magnetic ordering. The calculated densities of states using an antiferromagnetic model indicate the presence of a band gap in accordance with the semiconducting behavior found by electrical conductivity. Based on the spin exchange parameters calculated using mapping analysis, the spin exchange interactions in Eu₅Al₂Sb₆ are really small compared with other magnetically ordered rare-earth compounds. In addition, the magnetic phase transition at T_N = 3.5(1) is related to the ordering of the Eu1 atoms. Bader charge analysis confirms the divalent oxidation state of Eu, but also indicates significant covalent interactions involving the Eu atoms.

Acknowledgements

We thank Dipl.-Ing. U. Ch. Rodewald for the single crystal intensity data collection. Boniface P. T. Fokwa and Yuemei Zhang thank San Diego Supercomputer Center for providing computing resources.

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Footnote

† Electronic supplementary information (ESI) available: Powder X-ray diffraction data of Eu₅Al₂Sb₆ and susceptibility data of Sr₅Al₂Sb₆. See DOI: 10.1039/c7qm00057j

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