Magnetic hyperfine field splitting in the Zintl phase Eu₂Mg₄Si₃

2.1 Synthesis

Single-crystalline samples of Eu₂Mg₄Si₃ were synthesized by the Mg self-flux technique. Europium ingots (99.9%, Rare Metallic Co.), magnesium shots (99.99%, Rare Metallic Co.), and a silicon wafer (99.999%, Rare Metallic Co.) were used as starting materials. The mixture of Eu, Mg, and Si in the molar ratio of 2:30:3 was placed in a molybdenum crucible and sealed by arc-welding under a pure argon atmosphere in order to prevent evaporation of Eu and Mg. The crucible was encapsulated in an evacuated quartz ampoule. At first, the ampoule was slowly heated up to T=1470 K and subsequently cooled to 970 K with a rate of 5 K h⁻¹ in an electric furnace. Finally, the excess Mg flux was removed by spinning the ampoule in a centrifuge. Needle-shaped single crystals of Eu₂Mg₄Si₃ were obtained.

2.2 Mössbauer spectroscopy

For the ¹⁵¹Eu Mößbauer spectroscopic measurement of Eu₂Mg₄Si₃ the 21.53 keV transition of ¹⁵¹Eu of a ¹⁵¹Sm:EuF₃ source with an activity of 50 MBq was used (0.91% of the total activity; I=7/2 to I=5/2 transition). The sample was prepared in a thin-walled PMMA container (2 cm diameter) with an optimized thickness according to Long et al. [15]. The measurement was conducted in a continuous flow cryostat system (Janis Research Co LLC) at 5.7, 9 and 78 K while the source was kept at room temperature. The program WinNormos for Igor was used to fit the spectrum [16].

3.1 Crystal chemistry

For the interpretation of the Mössbauer spectroscopic data we need a short crystal chemical description of Eu₂Mg₄Si₃. This silicide is isotypic with the metal-rich phosphide Hf₂Co₄P₃, space group P6̅2m [13]. The Pearson data base [3] lists 26 entries for this structure type. Besides several other metal-rich phosphides, also the non-magnetic (compounds without a permanent magnetic moment) silicides Sr₂Mg₄Si₃ and Ba₂Mg₄Si₃ are isotypic with Eu₂Mg₄Si₃. Keeping the electronegativity differences in mind it is interesting to note that also the aurides Sr₂In₄Au₃ and Eu₂In₄Au₃ [17] and the arsenide Yb₂Cu₄As₃ [18] adopt the same structure type.

The Eu₂Mg₄Si₃ structure contains three crystallographically independent europium sites. Their Mg/Si coordination is presented in Fig. 1 along with the site symmetry. The Eu1 atoms have coordination number 14 (site symmetry m2m) which consists of a hexagonal prismatic coordination by two Mg₃Si₃ hexagons and two additional Mg1 atoms in-between. The highest coordination number (CN 15) occurs for the Eu2 atoms with the same hexagonal prismatic coordination by two Mg₃Si₃ hexagons and three additional Mg2 atoms. This results in 6̅.. site symmetry. The Eu3 atoms have the most irregular coordination by two Mg₃Si₂ pentagons with two Mg2 and one Si1 atom in-between. We will address these coordination modes again in the ¹⁵¹Eu Mössbauer spectroscopic section.

Fig. 1:

Coordination of the europium atoms in the Eu₂Mg₄Si₃ structure. Europium, magnesium and silicon atoms are drawn as medium grey, blue and magenta circles, respectively. Atom designations and site symmetries are indicated.

Another structural feature concerns the europium substructure. The structural arrangement of the europium atoms determines the magnetic coupling. It is readily evident from Fig. 2 that several triangular arrangements appear in this peculiar europium substructure. The Eu1 atoms form triangles with 451 pm edge length. These triangles are shifted with respect to the Eu2–Eu3 substructure (437 pm Eu2–Eu3) by half the lattice parameter c. Such triangular arrangements typically lead to frustration in the magnetically ordered regimes, similar to the many Fe₂P/ZrNiAl-type phases [19] or the recently reported rare earth (RE)-rich phases RE₁₀TX₃ (X=Al, Mg, Cd) [20], [21].

Fig. 2:

Projection of the europium layers of the Eu₂Mg₄Si₃ structure onto the ab plane. The three crystallographically independent europium sites at z=0 and z=1/2 are indicated. The in-plane distances are Eu1–Eu1 of 451 pm and Eu2–Eu3 of 437 pm. The shortest Eu–Eu distance in the c direction corresponds to the lattice parameter (443 pm).

3.2 ¹⁵¹Eu Mössbauer spectroscopy

Figure 3 shows the ¹⁵¹Eu Mössbauer spectra of the Eu₂Mg₄Si₃ sample at 78, 9 and 5.7 K along with transmission integral fits. The corresponding fitting parameters are summarized in Table 1.

Fig. 3:

Experimental and simulated ¹⁵¹Eu Mössbauer spectra of Eu₂Mg₄Si₃ at T=78 (top), 9 (middle) and 5.7 (bottom) K.

The 78 K spectrum looks like a singlet at first sight; however, the experimental line width parameter was too large to account for a single europium site. A reasonable fit of the spectrum was obtained with a superposition of two signals. This fit relies on the analyses of the individual europium coordination polyhedra (Fig. 1). The larger signal (62.5% intensity) with an isomer shift of −11.29 mm s⁻¹ covers the Eu1 and Eu2 sites. The latter have six silicon neighbors and both polyhedra are very similar. In contrast we observe only five silicon neighbors for the Eu3 atoms, and their signal appears at δ=−9.16 mm s⁻¹. The lower number of silicon neighbors removes less electron density from the Eu3 atoms. We can thus conclude that Eu1 and Eu2 show a slightly higher iconicity as compared to Eu3. In the paramagnetic range Eu1 and Eu2 are very similar, and their individual signals cannot be resolved in the ¹⁵¹Eu Mössbauer spectrum. The quadrupole splitting parameters (which account for the lower site symmetry) and the experimental line width parameters could be refined without constraints.

Now we directly turn to the spectrum at T=5.7 K, collected in the magnetically ordered regime. We observe a broad signal with some structure, readily indicating a complex superposition of three sub-signals with individual hyperfine fields. The spectrum was well reproduced with the following model: Eu1 and Eu3 with higher hyperfine fields of 20.4 and 22.4 T, respectively, and a much smaller hyperfine field of 5.4 T for Eu2, responsible for the large hump of the spectrum. The higher fields for Eu1 and Eu3 indicate almost full hyperfine field splitting. Similar fields have been observed in a variety of magnetically ordered europium intermetallics [22]. Due to the comparatively low resolution of the spectrum (caused by the superpositions) and correlations between the fitting parameters, we fixed the line width parameter of all three sub-signals to 2.7 mm s⁻¹. These results are similar to those of isotypic Eu₂In₄Au₃ [17]. The magnetically different behavior of the distinct europium sites is certainly due to magnetic frustration within the triangular arrangement of the europium atoms (Fig. 2).

Finally we discuss the spectrum at T=9 K, which was taken in between the two Néel temperatures of T_N1=9.6 and T_N2=8.4 K [14]. The signal is almost symmetric but significantly broadened with respect to the 78 K spectrum. Attempts to fit the spectrum with a superposition of two or three signals with different small hyperfine fields failed; a consequence of the vicinity to the magnetic ordering temperature. Usually in such temperature ranges one observes large correlation of the parameters. The 9 K signal thus corresponds to the (not resolved) envelope of the three sub-spectra and the enhanced line width and quadrupole parameter account for the distribution of small hyperfine fields on the europium sites. Again, this is similar to the 10 K spectrum of Eu₂In₄Au₃ [17].