Extending the knowledge on the quaternary rare earth nickel aluminum germanides of the RENiAl₄Ge₂ series (RE=Y, Sm, Gd–Tm, Lu) – structural, magnetic and NMR-spectroscopic investigations

2.1 Synthesis

The RENiAl₄Ge₂ (RE=Y, Sm, Gd–Tm, Lu) members were synthesized from the elements using arc-melting techniques. Starting materials were rare earth ingots (Sigma-Aldrich, Smart Elements, 99.9%), nickel wire (Alfa Aesar, 99.9%), aluminum turnings (Koch Chemicals, 99.99%) and germanium chunks (Chempur, 99.999%). The starting materials were weighed in the ideal stoichiometry of 1:1:4:2 (RE:Ni:Al:Ge) and arc-melted under an argon atmosphere of about 800 mbar [42]. The obtained buttons were re-melted several times to increase the homogeneity. The samples were subsequently enclosed in evacuated quartz tubes and annealed in a second step (973 K, 14 d) to increase their overall phase purity and homogeneity. The annealing led to X-ray pure samples, suitable for physical property measurements. All samples obtained by these processes show metallic luster and are stable under ambient conditions over weeks. In order to obtain single crystals, the method published by Sieve et al. [41] was employed. The elements were weighed in a ratio of 1:1:10:5 (RE:Ni:Al:Ge) into aluminum oxide crucibles. These were sealed in evacuated quartz tubes and heated to T=1073 K for 4 days. Afterwards, the samples were cooled to T=773 K with 2 K h⁻¹. The excess aluminum flux was dissolved in 5 m NaOH, leaving behind well shaped single crystals along with unreacted germanium. These flux-grown crystals were used for the structure determination experiments.

2.2 X-ray diffraction

The annealed polycrystalline samples were analyzed by powder X-ray diffraction experiments: Guinier technique, imaging plate system (Fuji film, BAS 1800), CuKα₁ radiation and α-quartz (a=491.30 and c=540.46 pm) as internal standard. The trigonal lattice parameters were obtained by least-squares refinements on the basis of the YNiAl₄Ge₂ data set from the literature (Table 1). Crystals of YNiAl₄Ge₂, GdNiAl₄Ge₂ and LuNiAl₄Ge₂, grown from Al flux, were glued to thin quartz fibers using beeswax. The crystallite quality was checked by Laue photographs on a Buerger precession camera (white molybdenum radiation; imaging plate system, Fuji film, BAS 1800). Intensity data sets of suitable single crystals were collected at room temperature on an IPDS-II (graphite-monochromatized MoKα radiation; λ=71.073 pm; oscillation mode). Numerical absorption corrections were applied to all data sets. Details of the data collection and structure refinements can be found in Tables 2–4.

CSD 1953918–1953920 contain the supplementary crystallographic data for this paper. The data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/structures.

2.3 Physical property measurements

Annealed pieces of the X-ray pure RENiAl₄Ge₂ (RE=Y, Sm, Gd–Tm, Lu) samples were attached to the sample holder rod of a vibrating sample magnetometer (VSM) using Kapton foil for measuring the magnetization M(H,T) in a Quantum Design Physical Property Measurement System (PPMS). All samples were investigated in the temperature range of 2.5–300 K with applied external magnetic fields of up to 80 kOe (1 kOe=7.96×10⁴ A m⁻¹).

2.4 Solid-state NMR spectroscopy

²⁷Al solid-state NMR spectra of YNiAl₄Ge₂ and LuNiAl₄Ge₂ were recorded with a Bruker Avance Neo (B₀=14.1 T) and an Agilent DD2 (B₀=5.7 T) NMR spectrometer using magic-angle spinning rates between 37 and 40 kHz. To reduce the electrical conductivity and density, the finely powdered samples were mixed in approximate volume ratios of 1:2 with dry potassium bromide and filled into a conventional ZrO₂ MAS rotor with 1.3 or 1.6 mm diameter. The spectra were recorded using conventional single-pulse experiments with typical pulse lengths of 0.1–0.5 μs (corresponding to flip angles below 30°) and relaxation delays of 0.1 s. Triple-quantum (TQ-) MAS-NMR spectra were recorded at 14.1 T, at a spinning speed of 35.0 kHz using the standard three-pulse zero-filtering sequence. The high-power (90 W) excitation and reconversion pulses were 1.8 and 0.6 μs long, and were followed by a weak (0.6 W) detection pulse of 7 μs length. A relaxation delay of 100 ms was used. Solid AlF₃ was used as secondary standard (−16 ppm) [44], referring to a 1 molar aqueous solution of Al(NO₃)₃. Data was processed and simulated with the DMfit program [45].

2.5 Quantum-chemical calculations

Electronic structure calculations, using the experimentally obtained structure of YNiAl₄Ge₂ from the literature [41] and the single-crystal data of LuNiAl₄Ge₂ presented here, were performed using the projector augmented wave method (PAW) of Blöchl [46], [47] coded in the Vienna ab initio simulation package (VASP) [48], [49]. All VASP calculations employed the generalized gradient approximation (GGA) using the exchange-correlation functional by Perdew-Burke-Ernzerhof (PBE) [50]. The cut-off energy for the plane wave calculations was set to 500 eV and the Brillouin zone integration was carried out using a 15×15×3 Γ-centered k-point mesh generated with the Monkhorst pack algorithm [51]. The subsequent Bader charge calculations, as developed by the Henkelman group, were based on the VASP results [52], [53], [54].

3.1 Structure refinements

The obtained single crystal data sets showed rhombohedral lattices, and space group R3̅m was found to be correct during the structure refinements. Isotypism to the SmNiAl₄Ge₂-type structure was evident from both single crystal and powder X-ray diffraction experiments. Starting values for the structure refinements were obtained using the SuperFlip [55] program package, implemented in Jana2006 [56], [57]. All atomic positions and anisotropic displacement parameters were subsequently refined, again using the Jana2006 program package. Occupancy parameters of all crystallographic sites were individually refined in separate series of least-squares refinements in order to check for the correct composition. The final difference Fourier syntheses were featureless. The refined atomic parameters, displacement parameters and interatomic distances can be found in Tables 3 and 4.

3.2 Crystal chemistry

The quaternary rare earth nickel aluminum germanides of the RENiAl₄Ge₂ series (RE=Y, Sm, Gd–Tm, Lu) crystallize in the rhombohedral SmNiAl₄Ge₂-type structure with space group R3̅m and Z=3. As expected and shown in Fig. 1, the lattice parameters and unit cell volumes decrease nearly linearly when going from the gadolinium to the lutetium compound due to the lanthanide contraction. The isostructural yttrium compound YNiAl₄Ge₂ exhibits lattice parameters similar to the ones of TbNiAl₄Ge₂, in line with the comparable ionic radii of the trivalent cations (Y³⁺: 104 pm; Tb³⁺: 102 pm; CN=8 [58], [59]).

Fig. 1:

Trigonal lattice parameters and unit cell volumes of the RENiAl₄Ge₂ (RE=Y, Sm, Gd–Tm, Lu) series (SmNiAl₄Ge₂ type).

The following discussion of the crystal structure and the interatomic distances will be based on the refined single crystal data obtained for GdNiAl₄Ge₂. This crystal structure can be described in two ways. First by slabs of [GdGe₂]^δ− (CdI₂ type) and [NiAl₄]^δ+ (CsCl type) as is shown in Fig. 2, left. This description is in line with the Bader charges (vide supra). Alternatively, one can utilize a bonding centered approach. By the interpretation of the interatomic distances, the Ni, Al and Ge atoms form polyanionic slabs with composition [NiAl₄Ge₂]^δ−. These slabs are separated by the rare earth atoms and get stacked along [001] with an ABC sequence (Fig. 2, middle). The rare earth atoms exhibit coordination number CN=12 and are surrounded by six Al and six Ge atoms (Fig. 3, top) in the shape of a distorted hexagonal prism with corrugated six-membered rings. The structure can be also described as an alternating intergrowth of CsCl- and Ce₂SO₂-type fragments, as depicted in Fig. 2 (middle). The interatomic distances are Gd–Al=363 and Gd–Ge=295 pm, suggesting no significant Gd–Al interactions and only weak Gd–Ge bonding (vide infra). No Gd–Ni contacts below 400 pm are observed. The Gd atoms form planar hexagonal densely packed layers (Fig. 2, right) with Gd–Gd distances of 410 pm, suggesting potential magnetic frustration (vide infra). Within the [NiAl₄Ge₂] layers, the Ni atoms exhibit an eight-fold coordination solely by Al atoms. Six Al1 atoms form a cyclohexane like ring (Ni–Al1=247 pm), while the Al2 atoms cap its bottom and top (Ni–Al2=241 pm; Fig. 3, middle left). These distances are in the range of typical bonding interactions (Σ(r_cov)=Ni+Al=115+125=240 pm) and comparable with those of NiAl (250 pm, CsCl type) or Ni₂Al₃ (244–254 pm, own type). Alternatively, this coordination environment can be described as a distorted cube. The Al1–Al1 distances are 274 pm, while the Al1–Al2 distances are 292 pm. These entities form layers that get capped by the Ge atoms. The Ge atoms themselves are coordinated on one side by four Al atoms (3×256+1×270 pm) in a highly asymmetric mode (Fig. 3, middle right), while the other side of the Ge atoms is exposed to the Gd atoms (Gd–Ge=295 pm) forming the outer layer of the [NiAl₄Ge₂] slabs. Both, the Ge–Al and the Gd–Ge distances are slightly longer compared to the sum of the covalent radii (Σ(r_cov)=Ge+Al=122+125=247 pm; Σ(r_cov)=Gd+Ge=161+122=283 pm) and suggest weak interactions. Similar distances can be found in Gd₂Al₃Ge₄ (Gd–Ge=302–318 pm, Ba₂Cd₃Bi₄ type) or Gd₅Ge₃ (299–307 pm, Mn₅Si₃ type). The coordination environments of Al1 and Al2 are depicted in Fig. 3, bottom.

Fig. 2:

Extended unit cell of GdNiAl₄Ge₂, depicted along the b axis. (left) Description as slabs of CsCl- and CdI₂-type. An ABC stacking sequence of both slabs is observed, the one for the CsCl layers is given. The distorted Gd@Ge₆ octahedra are shown in blue, the Ni@Al₈ cubes are drawn in grey. Gadolinium, nickel, aluminum, and germanium atoms are depicted as blue, black, open white and green circles, respectively. (middle) The layer-like arrangement of the [NiAl₄Ge₂]^δ− slabs is highlighted. Bonding in between the slabs has been omitted for clarity. (right) Views along the c axis on the [NiAl₄Ge₂]^δ− slabs (top) and the hexagonally closest packed gadolinium layers (bottom).

Fig. 3:

Coordination environments surrounding the Gd (top), Ni (middle left), Ge (middle right), and Al atoms (bottom) in the crystal structure of GdNiAl₄Ge₂. Gadolinium, nickel, aluminum and germanium atoms are depicted as blue, black, open white, and green circles, respectively. Interatomic distances (in pm), Wyckoff sites and site symmetries are given.

3.3 Magnetic properties

The magnetic properties of the RENiAl₄Ge₂ series (RE=Y, Sm, Gd–Tm, Lu) have been determined by susceptibility and magnetization experiments, the extracted data is listed in Table 5. Low-field measurements (20 Oe) of YNiAl₄Ge₂ and LuNiAl₄Ge₂ were conducted between T=2.1–6 K. No superconductivity was observed, however. Both compounds exhibit nearly temperature-independent behavior (Fig. 4), indicating that all constituent elements exhibit closed shells. The upturn of the susceptibility at low temperatures originates from paramagnetic impurities (Curie tail). The susceptibilities at T=300 K are χ_{300 K} (YNiAl₄Ge₂)=−9.29(5)×10⁻⁵ emu mol⁻¹ and χ_{300 K}(LuNiAl₄Ge₂) =−1.23(5)×10⁻⁴ emu mol⁻¹. These negative values indicate that the intrinsic diamagnetism overcompensates the Pauli paramagnetism caused by the conduction electrons of the metallic materials.

Fig. 4:

Temperature dependence of the magnetic susceptibility of YNiAl₄Ge₂ (black) and LuNiAl₄Ge₂ (red).

The other compounds exhibit paramagnetism, solely arising from the open-shell 4fⁿ electron configuration of the rare earth atoms. As stated by Sieve and coworkers [41], the interatomic distances of the rare earth atoms suggest that the interactions within the layers (e.g. Er–Er=407 pm [31]) are significantly stronger compared to the interlayer interactions (1077 pm [31]). However, due to the triangular arrangements of the rare earth atoms, geometrical spin frustration can arise [60], [61], leading to interesting magnetic phenomena, e.g. spin-glass behavior. All compounds were investigated by zero-field-cooled (ZFC) experiments with an applied external magnetic field of 10 kOe. The inverse susceptibility χ⁻¹ was fitted using the modified Curie-Weiss law, and the effective magnetic moment μ_eff and the paramagnetic Curie temperature θ_P were extracted. In the case of SmNiAl₄Ge₂, the van Vleck theory was used. All compounds exhibit values for μ_eff that are close to those calculated (μ_calcd) for the free trivalent ions (see Table 5). The ordering temperatures (where observed) were further determined by low field (100 Oe) zero-field-cooled/field-cooled (ZFC/FC) measurements. The Néel temperatures of the paramagnetic→antiferromagnetic transitions were obtained from the observed peaks in the respective zero-field-cooled curves. Finally, magnetization isotherms above and below the magnetic ordering temperatures (where applicable) were recorded. The saturation magnetizations μ_sat were obtained from the 3 K isotherms at 80 kOe. Due to the polycrystalline character of all investigated samples, these values are for some compounds significantly lower compared to the theoretical values calculated according to g_J×J. The small Weiss constants θ_P indicate weak (three-dimensional) magnetic interactions, in line with the large distances between the slabs. The positive signs could arise from a weak ferromagnetic coupling between these layers, suggesting so called A-type antiferromagnetism [62].

In the following paragraphs, the magnetic properties of the investigated compounds are discussed. For SmNiAl₄Ge₂ these observations are, however, in contrast to the observations in the literature [41]. Sieve and coworkers observed a bifurcation between the ZFC and FC curves already near T=300 K along with a pronounced hysteresis loop in the magnetization isotherms. We have observed that SmNiAl₄Ge₂ exhibits the expected van Vleck paramagnetism, along with antiferromagnetic ordering at low temperatures. The ZFC/FC measurements show only a minor splitting, possibly caused by trace impurities. The van Vleck behavior is caused by the close proximity of two states (ground state J=5/2; excited state J=7/2). The calculated energy difference between these states is only about 1550 K, all others of the respective angular momentum levels are considerably higher in energy. The small effective magnetic moment of the Sm³⁺ cations (μ_eff,calcd=0.845 μ_B) arises from the antiparallel coupling of the L=5, S=5/2 Russel-Saunders states. Stewart developed a theory to describe the magnetism of intermetallic samarium compounds, taking polarization effects, interionic Heisenberg exchange couplings and the population of the J=7/2 and J=5/2 ground states into account. Unexpectedly, a simple formula χ(T)=χ₀+D/(T–θ) was derived [63]. Hamaker and coworkers were able to prove that χ(T) for polycrystalline SmRh₄B₄ can be described by the equation

χ(T)=NAkB(μeff23(T−θP)+μB2δ)

where μ_eff is the effective magnetic moment, θ_p is the Weiss constant, μ_B is the Bohr magneton, N_A is the Avogadro number and k_B is the Boltzmann constant. δ is defined as δ=7ΔE/20 in units of K and describes the energy differences of the ground and excited states. The first term represents the Curie-Weiss susceptibility of the J=5/2 ground state, while the second part is the van Vleck susceptibility caused by the J=7/2 multiplet, which is only slightly higher in energy [64]. Using the coefficients for the free ion values mentioned in the literature, this equation can be obtained from a more general one, that was published by Stewart [65]. It should be mentioned that both equations neglect crystal-field splitting of each J level and the mixture of one with another.

SmNiAl₄Ge₂ exhibits antiferromagnetic ordering below T_N=15.9(1) K. The susceptibility was fitted using the Hamaker equation in the temperature region between 25 and 110 K (Fig. 5), resulting in fit parameters of μ_eff=0.77(1) μ_B, θ_p=−30.5(1) K and δ=247(2) K (red curve, Fig. 4). The effective magnetic moment is slightly smaller than the value of 0.845 μ_B of the free ion, δ=247(2) K corresponds to ΔE=706 K. The energy difference is smaller compared to the value of 1550 K predicted by Stewart, however, a look into the literature reveals that several compounds were shown to exhibit lower values. ΔE=454 K are found for Sm₃Pt₄Ge₆ [66], 850 K for SmOs₄Sb₁₂ [67], 1080 K for SmRh₄B₄ [64], 412, 265, and 1488 K for SmCo₂Zn₂₀, SmRu₂Zn₂₀, and SmPd₂Cd₂₀ [68], 1346 K for SmPdGa₃ [69], 1366 K for HP-SmPdSn [70], but also even higher values such as ΔE=2691 K for SmPt₆Al₃ are known [71].

Fig. 5:

Temperature dependence of the magnetic susceptibility (χ and χ⁻¹ data) of SmNiAl₄Ge₂, the fit using the van Vleck law is depicted as red curve [64].

Fig. 6 depicts the magnetic data of GdNiAl₄Ge₂. The top panel shows the χ and χ⁻¹ data. The Curie-Weiss fits yielded an effective magnetic moment of μ_eff=8.09(1) μ_B, slightly above the theoretical value of μ_calc=7.94 μ_B, pointing towards 4f-5d hybridization effects. The paramagnetic Curie temperature is θ_P=+1.2(1) K. The low field measurements (Fig. 6, middle) have confirmed the antiferromagnetic ordering (AFM), already observed in the high-field measurements. The Néel temperature is T_N=16.4(1) K, and no bifurcation between the ZFC and FC curves is visible. The magnetization isotherms at 50 and 100 K (Fig. 6, bottom) finally exhibit a linear trend, as expected for paramagnetic materials. The 3 and 10 K isotherms, both below the AFM transition, exhibit a slightly curved behavior, indicating a rather stable antiferromagnetic ground state. The ordered spin state gets gradually destroyed with increasing field, leading to a saturation magnetization of μ_sat=6.73(1) μ_B (3 K, 80 kOe), the expected saturation being 7 μ_B according to g_J×J.

Fig. 6:

Magnetic properties of GdNiAl₄Ge₂: (top) temperature dependence of the magnetic susceptibility (χ and χ⁻¹ data) measured at 10 kOe; (middle) magnetic susceptibility in ZFC/FC mode at 100 Oe; (bottom) magnetization isotherms at T=3, 10, 50 and 100 K.

Figure 7 finally depicts the magnetic data of TbNiAl₄Ge₂. The Curie-Weiss fit yielded an effective magnetic moment of μ_eff=9.76(1) μ_B that is in good agreement with the theoretical value of μ_calc=9.72 μ_B, and the paramagnetic Curie temperature is θ_P=+2.7(1) K. The Néel temperature is T_N=9.7(1) K, and a small bifurcation between the ZFC and FC curve is visible, pointing to traces of ferromagnetic impurities. The magnetization isotherms above the ordered state (50 and 100 K, Fig. 7, bottom) exhibit a linear trend indicating paramagnetic behavior. The 10 K isotherm is curved due to the proximity of the Néel temperature, while for the 3 K isotherm an S-shaped behavior can be observed. This feature is called a meta-magnetic step or spin reorientation, where the antiferromagnetic ground state is turned into a ferromagnetic state upon increasing the field. The ordered antiferromagnetic state gets gradually destroyed, therefore a broad maximum can be observed in the first derivative of the 3 K isotherm leading to a critical field of H_crit=10(1) kOe. The saturation magnetization is μ_sat=6.61(1) μ_B (3 K, 80 kOe), the expected saturation is 9 μ_B according to g_J×J.

Fig. 7:

Magnetic properties of TbNiAl₄Ge₂: (top) temperature dependence of the magnetic susceptibility (χ and χ⁻¹ data) measured at 10 kOe; (middle) magnetic susceptibility in ZFC/FC mode at 100 Oe; (bottom) magnetization isotherms at T=3, 10, 50 and 100 K.

3.4 ²⁷Al solid-state NMR spectroscopy

Figure 8 shows the solid-state ²⁷Al MAS-NMR spectra of the central transition region for YNiAl₄Ge₂ and LuNiAl₄Ge₂ measured at B₀=14.1 T. For both compounds, two distinct resonances are observed in an approximate 1:1 ratio, confirming the presence of two crystallographically distinct aluminum sites in the crystal structures. To extract the relevant interaction parameters for these species, one would normally simulate the corresponding line-shapes on the basis of second-order quadrupolar perturbations, using e.g. the program DMfit [45]. In the present case, such tentative simulations are shown in Fig. 8, but produce unsatisfactory results. They apparently suggest non-axially symmetric electric field gradients characterized by an asymmetry parameter η of close to 0.3, despite the fact that both Al species reside on sites with three-fold rotational symmetry (point group 3m). Furthermore, for the low-frequency signal the difficulty arises, that the line-shape features are not sufficiently distinct to allow an unambiguous simulation in terms of an axially symmetric field gradient. Rather, it appears that the MAS-NMR line shapes of these aluminum species are additionally influenced by distributions of isotropic magnetic (de-)shielding (and possibly electric field gradients), which might arise from structural (stacking faults) or site occupancy disordering effects. To obtain further insights, triple-quantum (TQ)-MAS-NMR data was measured (Fig. 9). For both compounds, the line-shapes associated with the high-frequency signal can be observed with much better precision than in regular MAS-NMR spectra by analyzing the TQMAS sub-spectra (“slices”) obtained at the fixed frequency corresponding to the center of gravity in the F1 dimension. Using this approach (method 1), the nearly axially symmetric electric field gradient for the high-frequency signals near +482 and +467 ppm is clearly revealed in both compounds, whereas this method still turns out to be unsatisfactory for the low-frequency signals. Alternatively the 2D spectra can be analyzed in terms of isotropic magnetic (de-)shielding δ_iso^ms and the second-order quadrupolar effects (SOQE=C_Q(1+η²/3)^1/2) by comparing the centers of gravity in the F1 and F2 dimensions [72] (method 2). Table 6 summarizes the line shape parameters obtained for the high-frequency signal by both methods, where the observed discrepancies (~±10 ppm for magnetic (de-)shielding and ~±1 MHz for C_Q) give an impression of the potential systematic errors associated with these different analysis methods. For the low-frequency signal only method 2 produced satisfactory results; thus no independent information regarding the asymmetry parameter is available here.

Fig. 8:

²⁷Al MAS-NMR spectra of YNiAl₄Ge₂ (top, recorded at a rotor frequency of 40.0 kHz) and LuNiAl₄Ge₂ (bottom, recorded at a rotor frequency of 37.0 kHz). Spinning sidebands arising from the non-central transitions of Al1 and Al2 are marked with the symbols * and #, respectively. Tentative line shape simulations based on non-axially symmetric electric field gradients are shown in red.

Fig. 9:

(left) ²⁷Al TQMAS-NMR spectra of YNiAl₄Ge₂ and LuNiAl₄Ge₂. (right) Sub-spectra obtained for the Al1 site obtained at the fixed frequency corresponding to the center of gravity in the F1 dimension, and comparison with the simulated spectrum (dashed curves).

The assignments of the two signals observed for the two distinct crystallographic sites Al1 and Al2 are based on the comparison of the experimental C_Q or SOQE data with predicted values based on electric field gradient calculations, as listed in Table 7. Furthermore, the significant difference in the isotropic magnetic (de-)shielding contributions, δ_iso^ms, between Al1 and Al2 signifies a large difference between the s-density of states (s-DOS) at the Fermi level for these two aluminum species. While the values measured for Al1 are comparable to those obtained in numerous other intermetallic compounds [18], [20], [22], [75], resulting in a substantial Knight shift contribution, the δ_iso^ms value for the Al2 site indicates a much smaller Knight shift. This result is consistent with the band structure calculations revealing also a significant difference between the s-DOS of Al1 and Al2 (vide infra). Finally, we note that mere reliance on the single-pulse MAS spectra at B₀=14.1 T would have resulted in the wrong scientific conclusion of non-axially symmetric sites for both Al1 and Al2. Most likely the deviation of the ²⁷Al MAS-NMR line shape from that theoretically expected for axial symmetry is due to the effect of disordering phenomena causing a distribution of isotropic magnetic shielding contributions, which results in a loss of the distinct MAS-NMR line shape features. This distribution effect is also evident in the 2D TQ-MAS-NMR spectrum, which shows a distinct sloping effect in the direction of the diagonal, as a consequence of a distribution of isotropic magnetic (de-)shielding effects. The axial symmetry of the local environments of Al1 and Al2 is further confirmed by additional spectra measured at a lower magnetic field strength (B₀=5.7 T, data not shown), where the effect of quadrupolar interactions on the MAS-NMR line shapes is significantly stronger, while the influence of isotropic magnetic (de-)shielding distributions is reduced at the lower field strengths. Thus, the results of the present study highlight the importance of MAS and TQ-MAS work for the extraction of reliable NMR parameters if distribution effects of different interaction parameters (such as isotropic magnetic (de-)shielding and quadrupolar coupling) are present.

3.5 Quantum-chemical calculations

The electronic structures of YNiAl₄Ge₂ and LuNiAl₄Ge₂ have been calculated and their densities of states (DOS) are presented in Fig. 10. Both compounds are metallic as indicated by the non-zero DOS at the Fermi level (E_F). The f states of Lu at −5.5 eV, which are absent for Y, are the only significant difference between the DOS of YNiAl₄Ge₂ and LuNiAl₄Ge₂.

Fig. 10:

DOS of LuNiAl₄Ge₂ (a) and YNiAl₄Ge₂ (c) with the partial DOS indicated by colored lines. The Fermi level E_F (dashed line) is set to 0 eV. The pDOS corresponding to the two Al sites are shown in b and d, respectively.

At low energies around −10 eV the DOS consists mainly of Ge states, while the 3d orbitals of Ni dominate between −4 and −1 eV. Around E_F, between −1 and +1 eV, a deep pseudo-gap is observed indicating electronic stability. Above +1 eV, unoccupied states of Y or Lu in the respective compounds are contributing most to the total DOS. At E_F all the elements contribute almost equally to the total DOS. However, the partial DOS with s character for an Al1 atom in YNiAl₄Ge₂ is 0.0147 states per eV for the individual atom at E_F and thus almost twice as large as for an Al2 atom, for which the partial DOS with s character is only 0.0083 states per eV at E_F. Likewise for LuNiAl₄Ge₂ the s-DOS is 0.0156 states per eV for an Al1 atom at E_F and therefore higher as for an Al2 atom, for which the partial DOS with s character is only 0.0123 states per eV at E_F. These differences in the s-DOS at E_F reflects the difference of the isotropic magnetic de-shielding contributions, δ_iso^ms, observed in the solid-state ²⁷Al MAS-NMR measurements.

The calculated NMR parameters for YNiAl₄Ge₂ and LuNiAl₄Ge₂ are provided in Table 7. Comparing the corresponding results of the calculations with the experimental quadrupolar coupling constants C_Q, the NMR signal at +482 ppm can be assigned to Al1. The signal at +69 ppm with the much weaker quadrupole interaction on the other hand most likely corresponds to Al2. Similarly, the two ²⁷Al solid-state NMR signals in the spectra of LuNiAl₄Ge₂ can be assigned to Al1 (+467 ppm) and Al2 (+85 ppm).

Finally, the Bader charge analysis reveals almost equal charges on Al1, Al2 and Y of ca. +1.5 for all of them (Table 8). These charges are significantly smaller than +3 for both Al and Y, which indicates that these elements are involved in significant covalent bonding interactions. According to these calculations, the Ge atoms are the respective anions with a charge of −2.15, while the Ni atoms exhibit a calculated charge of −3.15. While the relative charge distributions among cations and anions are in accord with the electronegativities of the elements, the large difference in absolute values between the anions is somewhat surprising as Ni has only a slightly smaller electronegativity than Ge [76]. The Bader charges of LuNiAl₄Ge₂ are comparable to those of YNiAl₄Ge₂.