Ternary rhombohedral Laves phases RE₂Rh₃Ga (RE = Y, La–Nd, Sm, Gd–Er)

2.1 Synthesis

Starting materials for the synthesis of the RE₂Rh₃Ga samples were pieces of the sublimed rare earth elements (Y, La, Pr, Nd, Sm, Gd–Er from Smart Elements; Ce from Sigma Aldrich, Sigma Aldrich Germany, Hamburg), rhodium powder (Agosi, Pforzheim, Germany) and gallium lumps (Emmerich am Rhein, Germany), all with stated purities better than 99.9%. The moisture-sensitive early rare earth elements La–Nd and Sm were kept in Schlenk tubes under purified argon prior to the reactions. The argon was purified with a titanium sponge (873 K), silica gel and molecular sieves.

The elements were weighed in the ideal 2:3:1 atomic ratio (the rhodium powder was previously cold-pressed into pellets with a diameter of 5 mm) and arc-melted in a water-cooled copper mold of a MAM-1 (Edmund Bühler GmbH, Hechingen, Germany) arc-furnace under an argon atmosphere of 800 mbar. Remelting the obtained buttons several times from each site ensured complete homogeneity. With the exception of the cerium-based sample the synthesized compounds showed some impurity phases, especially in the form of non-ordered Laves phases with the presumed composition RERh_2−x Ga_x [MgCu₂ type, confirmed by X-ray diffraction (XRD)].

To increase the phase purity all samples were sealed in evacuated quartz ampoules and treated with different annealing procedures. The Y₂Rh₃Ga sample was placed in the water cooled sample chamber of an induction furnace (Hüttinger Elektronik, Freiburg, Typ TIG 5/300) [41] and rapidly heated to a temperature of approximately 1100 K. This temperature was kept for 8 h until the sample was quenched by switching off the power supply of the high-frequency furnace. Also the Tb₂Rh₃Ga sample was inductively heated. A piece of the crushed arc-melted regulus was sealed in an evacuated quartz tube and heated shortly below its melting point for 10 min followed by reducing the power of the furnace within 20 min to a temperature of approximately 900 K which was kept for another 8 h followed by quenching.

The remaining samples were annealed in muffle furnaces. They were heated up to 1073 K within 2 h and then kept at this temperature for 10 (RE=La–Nd, Gd), respectively 28 days (Tb, Dy). The best results for the compounds containing holmium and erbium were obtained by annealing these samples at 773 K for 6 weeks. Except for Sm₂Rh₃Ga, these different annealing procedures led to X-ray pure samples suitable for physical property measurements. The crushed samples showed metallic luster and were stable in air over weeks.

2.2 X-ray image plate data and data collections

The RE₂Rh₃Ga bulk samples were characterized by X-ray powder diffraction using a Guinier camera equipped with an image plate system (Fujifilm, BAS-1800) using Cu Kα₁ radiation and α-quartz (a=491.30, c=540.46 pm) as an internal standard. The trigonal lattice parameters (Table 1) have been derived from least-squares refinements of the powder data. Comparing the experimental patterns to calculated ones [42] ensured correct indexing. As an example, we present the experimental and calculated powder pattern of Dy₂Rh₃Ga in Fig. 1.

Fig. 1:

Experimental (top) and calculated (bottom) Guinier powder pattern (CuK_α1 radiation) of Dy₂Rh₃Ga.

Mechanical fragmentation of the Y₂Rh₃Ga, Ce₂Rh₃Ga and Tb₂Rh₃Ga (annealed in the induction furnace) samples resulted in irregularly shaped single crystal fragments. These were glued to thin quartz fibers using beeswax. The crystal quality was subsequently tested by Laue photographs on a Burger camera (white molybdenum radiation, image plate technique, Fujifilm, BAS-1800). The intensitiy data sets were collected at room temperature using a Stoe StadiVari single crystal diffractometer equipped with a Mo micro focus source and a Pilatus detection system. The Gaussian-shaped profile of the X-ray source required scaling along with numerical absorption corrections. All relevant crystallographic data and details of the data collections and evaluations are listed in Table 2.

2.3 EDX data

The Y₂Rh₃Ga, Ce₂Rh₃Ga and Tb₂Rh₃Ga crystals measured on the diffractometer were analyzed semi-quantitatively using a Zeiss EVO MA10 scanning electron microscope with CeO₂, TbF₃, Rh and GaP as standards. No impurity elements heavier than sodium (detection limit of the instrument) were observed. The experimentally determined element ratios (34±2 at.% Y:50±2 at.% Rh:16±2 at.% Ga, 33±2 at.% Ce:52±2 at.% Rh:15±2 at.% Ga and 32±2 at.% Tb:53±2 at.% Rh:15±2 at.% Ga) were in close agreement with the ideal compositions (33.3:50:16.6). The variations of ±2 at.% result from the irregular shape of the crystal surfaces (conchoidal fracture).

2.4 Physical property measurements

Fragments of the buttons of the X-ray pure phases were attached to the sample holder rod of a vibrating sample magnetometer unit (VSM) using Kapton foil 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 flux densities up to 80 kOe (1 kOe=7.96×10⁴ A m⁻¹). For the Nd₂Rh₃Ga and Dy₂Rh₃Ga samples additionally heat capacity (HC) measurements were conducted. A piece of the sample was fixed to a pre-calibrated heat capacity puck using Apiezon N grease and measured in the temperature range of 2 to 20 K.

2.5 Solid state NMR spectroscopy

The ⁸⁹Y and ⁷¹Ga solid state NMR spectra of the diamagnetic representatives Y₂Rh₃Ga and YRh₂ were measured on Bruker DSX 500 (B₀=11.7 T), Bruker DSX 400 (B₀=9.4 T) and Bruker Avance III (B₀=7.05 T) NMR spectrometers at resonance frequencies of 24.496 MHz, 19.597 MHz (both ⁸⁹Y) and 91.486 MHz (⁷¹Ga). The spectra were referenced to aqueous solutions of Y(NO₃)₃ (8 mol L⁻¹ with 0.25 mol L⁻¹ Fe(NO₃)₃; δ_iso=−22.8 ppm) and Ga(NO₃)₃ (1 mol L⁻¹; δ_iso=0 ppm) at ambient temperature. The finely powdered sample was mixed with dry potassium chloride in an approximate volume ratio of 1:2 to reduce the electrical conductivity and density and was filled in conventional Si₃N₄ or ZrO₂ MAS rotors with 7 mm (Si₃N₄) and 4 mm (ZrO₂) diameter, respectively. The ⁸⁹Y spectra were recorded by using conventional rotor-synchronized π/2–τ–π–τ-spin-echo sequences with typical π/2-pulse lengths of 20–20.5 μs, relaxation delays of 0.5 s and MAS spinning frequencies of 4–7 kHz. Static ⁷¹Ga investigations were carried out by using the wideband uniform-rate smooth truncation (WURST) QCPMG sequence [43] with the WURST-80 pulse shape and 8-step cycling version. All spectra were recorded using the Bruker Topspin software [44] and analyzed with the Dmfit software [45]. The experimental data are summarized in Table 7.

2.6 Theoretical investigations

Quantum mechanical calculation of the electric field gradient (EFG) and the density of states (DOS) for YRh₂ and Y₂Rh₃Ga were performed on the basis of density functional theory. The experimental structures were optimized with the VASP package which uses the plane augmented waves (PAW) [46] method based on the local density approximation (LDA) [47]. The cubic YRh₂ was sampled with a 14×14×14 k-grid and the hexagonal Y₂Rh₃Ga with a 16×16×8 k-grid. Convergence was with respect to the k-meshes and was checked carefully, and calculations were performed with a cut-off energy of 500 eV.

The full potential linear augmented plane wave (FP-LAPW) method as implemented in the WIEN2k code [48] was used to calculate the electric field gradients main principal axis V_ZZ(Ga) and the asymmetry parameter η_Q(Ga). The QTL and TETRA programs included in the code were applied to calculate the s-DOS of Y in both compounds. To avoid core charge leakage and to ensure that the calculations run with appropriate efficiency the atomic-sphere radii (RMT) were chosen as large as possible (Y: 2.5–2.45 a.u., Rh: 2.5–2.41 a.u. and Ga: 2.29 a.u.). The default value for the separation energies of −6.0 Ry was chosen to separate core and valence states. The implemented GGA PBE exchange-correlation functional was chosen [49]. For the plane-wave cut-off, defined by RMT×K_max, we applied the default value of 7. The k-meshes for Wien2k calculations were 10×10×10 for YRh₂ and the rhombohedral representation of Y₂Rh₃Ga.

3.1 Structure refinements

Careful analyses of the three intensity data sets revealed R-centered lattices. The absence of further systematic extinctions led to the possible space groups R3̅m, R3m, R32, R3̅, and R3, of which the centrosymmetric group R3̅m was found to be correct during structure refinement. Isotypism of the RE₂Rh₃Ga compounds with the Mg₂Ni₃Si type structure [33] was already evident from the Guinier powder patterns and from a systematic check of the Pearson database [32]. Subsequently the atomic parameters of Mg₂Ni₃Si were used as starting values and the structures were refined on F² with anisotropic displacement parameters for all atoms using the Jana2006 [50], [51] routine. As a check for the correct composition and site assignment, the occupancy parameters were refined in a separate series of least-squares cycles. All sites were fully occupied within three standard deviations. No significant residual peaks were evident in the final difference Fourier syntheses. At the end, the positional parameters were transformed to the setting required for the group–subgroup scheme discussed below. The final positional parameters and interatomic distances are listed in Tables 3–5.

Further details of the structure refinements may be obtained from FIZ Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: +49-7247-808-666; e-mail: crysdata@fiz-karlsruhe.de) on quoting the deposition numbers CSD-432339 (Y₂Rh₃Ga), CSD-432341 (Ce₂Rh₃Ga) and CSD-432340 (Tb₂Rh₃Ga).

3.2 Crystal chemistry

The gallides RE₂Rh₃Ga (RE=Y, La–Nd, Sm, Gd–Er) are new representatives of the Mg₂Ni₃Si type structure [33], space group R3̅m, Pearson symbol hR18 and Wyckoff sequence dca. The cell volumes (Table 1 and Fig. 2) decrease from the lanthanum to the erbium compound as expected from the lanthanide contraction. Ce₂Rh₃Ga shows a drastic deviation from this smooth behavior. The significantly smaller cell volume (even smaller than Nd₂Rh₃Ga) is a clear hint for an intermediate cerium valence. This is discussed in more detail below along with the magnetic properties. A very similar trend of the cell volume is observed for the cubic Laves phases RERh₂ (Fig. 2) [32]. The cell volumes per formula unit (Z) of the gallides are slightly larger than those of the RERh₂ phases. This trend is also observed in the sequence GdRh₂ (MgCu₂ type, V/Z=0.0530 nm³ [52])→GdRhGa (TiNiSi type, V/Z=0.0573 nm³ [53])→GdGa₂ (AlB₂ type, V/Z=0.0639 nm³ [54]), indicating generally stronger RE–Rh vs. weaker RE–Ga bonding. Small anomalies in the c lattice parameter of the RE₂Rh₃Ga samples might be indicative of small homogeneity ranges.

Fig. 2:

Plot of the cell volumes of the RE₂Rh₃Ga and RERh₂ [32] Laves phases as a function of the rare earth element.

The crystal structure of Ce₂Rh₃Ga is exemplarily presented in Fig. 3 and discussed in the following. The network of condensed tetrahedra shows full rhodium-gallium ordering. All Rh₃Ga tetrahedra exclusively share corners, but in a well-defined motif. The Kagomé networks which extend in the ab plane are formed only by the rhodium atoms, and the gallium atoms connect adjacent networks. This ordering pattern leads to substantial differences in the geometry of the tetrahedra. Each rhodium atom has two gallium neighbors at 257 pm and four rhodium neighbors at the much longer distance of 281 pm.

Fig. 3:

The crystal structure of Ce₂Rh₃Ga. Cerium, rhodium, and gallium atoms are drawn as medium gray, black filled and open circles, respectively. The network of condensed Rh₃Ga tetrahedra and the diamond-related cerium substructure (magenta lines for the shorter and gray lines for the longer Ce–Ce distances) are emphasized. Interatomic distances are given in pm.

The Rh–Ga distance of 257 pm is indicative of substantial Rh–Ga bonding. It is only slightly longer than the sum of the covalent radii for Rh+Ga of 250 pm [55]. The [RhGa] (265–268 pm Rh–Ga) and [Rh₃Ga₉] (259–263 pm Rh–Ga) networks of CeRhGa [56] and Eu₂Rh₃Ga₉ [57] show even longer Rh–Ga distances.

The cerium atoms fill the large cavities formed by the network of tetrahedra. The topology reminds of the diamond structure. The substantial Rh–Ga interlayer bonding (between the Kagomé networks) leads to a strong decrease of the c/a ratio (√2√3=2.45 for CeRh₂ [52] in a related setting vs. 2.12 for Ce₂Rh₃Ga) and this directly influences the Ce–Ce distances: 4×327 pm in CeRh₂vs. 1×306 and 3×338 pm in Ce₂Rh₃Ga. All of these Ce–Ce distances are well below the Hill limit [58] for f electron localization (340 pm). This is in full agreement with the intermediate cerium valence (vide infra) and the absence of any magnetic ordering.

The structures of CeRh₂(≡Ce₂Rh₄) and Ce₂Rh₃Ga are strictly related by a group–subgroup scheme, which is presented in the Bärnighausen formalism [59], [60], [61] in Fig. 4. The translationengleiche symmetry reduction of index 4 (t4) from Fd3̅m to R3̅m leads to a splitting of the 16c rhodium site, enabling the 3:1 Rh/Ga ordering. Furthermore, we obtain a free c/a ratio and a free z parameter for the cerium atoms. These parameters allow the optimization of chemical bonding forced by the rhodium/gallium coloring. A 7:1 ordering on the tetrahedral network has recently been reported for orthorhombic Cd₄Cu₇As [28].

Fig. 4:

Group–subgroup scheme in the Bärnighausen formalism [59], [60], [61], [62] for the structures of CeRh₂ [52] and Ce₂Rh₃Ga. The index for the translationengleiche (t) symmetry reduction, the unit cell transformation, and the evolution of the atomic parameters are given.

Finally we focus on the valence electron count (VEC) of RERh₂ and RE₂Rh₃Ga (≡RERh_1.5Ga_0.5). The formation of a cubic or a hexagonal Laves phase depends on VEC. Johnston and Hoffmann [62] calculated the variation of the relative energy of the hexagonal and cubic tetrahedral network of Laves phases as a function of VEC. Cubic RERh₂ (VEC=21) and hexagonal RERh_1.5Ga_0.5 (VEC=18) perfectly match the predictions. Even the two cerium compounds with slightly higher VEC (a consequence of intermediate cerium valence; vide infra) fall in the same range.

3.3 Magnetic properties

Magnetic susceptibility data has been obtained only for the X-ray pure RE₂Rh₃Ga samples with RE=Y, La–Nd, and Gd–Er. The basic magnetic data that has been derived from these measurements are listed in Table 6. The results are discussed in the following paragraphs.

3.3.1 Y₂Rh₃Ga and La₂Rh₃Ga

The temperature dependences of the magnetic susceptibility of the yttrium and lanthanum compound are presented in Fig. 5. Both compounds are Pauli paramagnets with room temperature susceptibilities of χ=1.85(1)×10⁻⁴ emu mol⁻¹ and χ=1.30(1)×10⁻³ emu mol⁻¹, respectively. The weak upturns at lower temperature arise from tiny amounts of paramagnetic impurities. The present data clearly proves the absence of local moments on the rhodium atoms. Thus, the magnetic properties of the remaining phases arise from the rare earth elements only.

Fig. 5:

Temperature dependence of the magnetic susceptibility (χ data) of Y₂Rh₃Ga (red) and La₂Rh₃Ga (black) measured at 10 kOe.

3.3.2 Ce₂Rh₃Ga

The susceptibility and inverse susceptibility data of Ce₂Rh₃Ga are shown in Fig. 6 (top), indicating values in the order of 10⁻³ emu mol⁻¹ without any sign of magnetic ordering down to low temperatures. The χ⁻¹ data is curved, consequently no Curie–Weiss behavior is observed. The shape of the χ⁻¹ curves with the weak temperature dependence is typical for Ce-based intermetallics which exhibit valence fluctuations. The magnetic susceptibility of valence fluctuating compounds can be described with the so called interconfiguration fluctuation (ICF) model proposed by Hirst [63], which was later applied by Sales and Wohlleben in order to explain valence fluctuation behavior in intermetallic Yb compounds [64]. The ICF model can be used for systems were two distinct states of the rare earth atom, here Ce³⁺ and Ce⁴⁺, exist. The temperature dependence of the magnetic susceptibility is described as:

Fig. 6:

Magnetic properties of Ce₂Rh₃Ga. Top: temperature dependence of the magnetic susceptibility (χ and χ⁻¹ data) measured at 10 kOe; the fit according to Sales and Wohlleben is depicted in red. Bottom: Magnetization isotherms at 3, 10, and 50 K along with the calculated temperature dependence of the cerium valence, depicted in red.

(1)χ(T)=(NA3kB)[μn2ν(T)+μn−12{1−ν(T)}T+Tsf]+nCT+χ0

with N_A being the Avogardo’s number, k_B the Boltzmann constant, μ the magnetic moment of the respective Ce ion and the spin fluctuation temperature T_sf. χ₀ is a temperature independent term, C the Curie constant (for free Ce³⁺, C=0.807 emu mol⁻¹ K⁻¹), and n the fraction of stable Ce³⁺. The overall susceptibility is described by three terms: (i) a valence fluctuation part, (ii) the contribution of the stable Ce³⁺ ions and (iii) a temperature independent part. The valence fluctuations are described by the pseudo-Boltzmann statistic shown in equation (2) which contains the spin fluctuation temperature T_sf and E_ex describing the energy difference between the two cerium ground states according to E_ex=E(Ce³⁺)–E(Ce⁴⁺).

(2)ν(T)=(2Jn+1){(2Jn+1)+(2Jn−1+1)exp[−EexkB(T+Tsf)]}

For the Ce cations the fluctuations take place between the 4f⁰ and 4f¹ configurations. With J₁=μ_eff,1=0, J₂=5/2 and μ_eff,2=2.54 μ_B the magnetic data can be fitted and T_sf=1599(15) K, E_ex=3072(27) K, n=0.0268 and χ₀=1.6×10⁻³ emu mol⁻¹ were extracted. In order to prevent over-determination, the temperature independent part χ₀ and n were fitted first and fixed for the rest of the procedure, hence no standard deviations are given for these two parameters. The extracted values for T_sf and E_ex are larger compared to, e.g. valence fluctuating CeMo₂Si₂C [65], CeRhSi₂ [66] or Ce₂Rh₃Si₅ [66], but comparable to the ones found for the solid solutions CeRu_1−x Ni_x Al [67] or CeRu_1−x Pd_x Al [68]. In addition to parameters extracted from the fitted data, the average cerium valence can be obtained using eq. 2 to calculate ν(T). The change of the cerium valence vs. temperature is plotted in Fig. 6 (bottom, red), showing a temperature-dependent shift of the cerium valence. The magnetization isotherms exhibit highly reduced magnetic moments with saturation magnetizations of μ_sat=0.05(1) μ_B per formula unit compared to the expected magnetization of μ_sat,theo=2.14 according to g_J×J.

Finally it is interesting to note that binary CeRh₂ also shows intermediate cerium valence. This was substantiated for polycrystalline material as well as for Czochralski grown single crystals via resistivity measurements, evaluation of the de Haas–van Alphen effect and L_III absorption studies [69], [70].

3.3.3 Pr₂Rh₃Ga–Er₂Rh₃Ga

For the remaining RE₂Rh₃Ga series with RE=Pr, Nd, and Gd–Er conventional magnetism with cooperative ordering phenomena is observed. The magnetic measurements are depicted in Figs. 7–13. The top panels show the magnetic susceptibility (χ and χ⁻¹ data), measured at 10 kOe. The paramagnetic region is fitted using the Curie-Weiss law to extract the effective magnetic moment μ_eff and the Weiss constant θ_P (listed in Table 6). For all compounds the effective magnetic moments are in good agreement with the calculated theoretical moments μ_calc. The middle panels depict the zero-field cooling (ZFC) and field-cooling (FC) measurements at an external field of 100 Oe. The bottom panels display the magnetization isotherms recorded at different temperatures. The isotherms way above the ordering temperatures show linear temperature dependencies, as expected for paramagnetic materials. The saturation magnetization (μ_sat) was determined from the 3 K isotherm at 80 kOe. In the following paragraphs the measurements of the individual compounds are briefly discussed and interesting features are outlined.

Fig. 7:

Magnetic properties of Pr₂Rh₃Ga. Top: temperature dependence of the magnetic susceptibility (χ and χ⁻¹ data) measured at 10 kOe. Middle: temperature dependence of the magnetic susceptibility in zero-field cooling and field cooling mode measured at 100 Oe; the inset shows the derivative dχ/dT vs. T used to determine the Curie-temperature. Bottom: Magnetization isotherms at 3, 10, 25, 75, and 100 K.

Fig. 8:

Magnetic properties of Nd₂Rh₃Ga. Top: temperature dependence of the magnetic susceptibility (χ and χ⁻¹ data) measured at 10 kOe. Middle: temperature dependence of the magnetic susceptibility in zero-field cooling and field cooling mode measured at 100 Oe; the heat capacity measurement is depicted in red. Bottom: magnetization isotherms at 3, 10, 50, and 100 K.

Fig. 9:

Magnetic properties of Gd₂Rh₃Ga. Top: temperature dependence of the magnetic susceptibility (χ and χ⁻¹ data) measured at 10 kOe. Middle: temperature dependence of the magnetic susceptibility in zero-field cooling and field cooling mode measured at 100 Oe. Bottom: magnetization isotherms at 3, 10, 30, 50, and 80 K.

Fig. 10:

Magnetic properties of Tb₂Rh₃Ga. Top: temperature dependence of the magnetic susceptibility (χ and χ⁻¹ data) measured at 10 kOe. Middle: temperature dependence of the magnetic susceptibility in zero-field cooling and field cooling mode measured at 100 Oe. Bottom: magnetization isotherms at 3, 10, 50, and 100 K.

Fig. 11:

Magnetic properties of Dy₂Rh₃Ga. Top: temperature dependence of the magnetic susceptibility (χ and χ⁻¹ data) measured at 10 kOe. Middle: temperature dependence of the magnetic susceptibility in zero-field cooling and field cooling mode measured at 100 Oe. Bottom: magnetization isotherms at 3, 10, 50, and 100 K.

Fig. 12:

Magnetic properties of Ho₂Rh₃Ga. Top: temperature dependence of the magnetic susceptibility (χ and χ⁻¹ data) measured at 10 kOe. Middle: temperature dependence of the magnetic susceptibility in zero-field cooling and field cooling mode measured at 100 Oe. Bottom: magnetization isotherms at 3, 10, 50, and 100 K.

Fig. 13:

Magnetic properties of Er₂Rh₃Ga. Top: temperature dependence of the magnetic susceptibility (χ and χ⁻¹ data) measured at 10 kOe. Middle: temperature dependence of the magnetic susceptibility in zero-field cooling and field cooling mode measured at 100 Oe. Bottom: magnetization isotherms at 3, 10, 50, and 100 K.

The ZFC/FC measurements of Pr₂Rh₃Ga (Fig. 7) show an anomaly characteristic for ferromagnetic ordering at T_C=6.3(1) K. The transition temperature was determined from the derivative dχ/dT vs. T curve (Fig. 7, middle, inset). The magnetization isotherm recorded at 3 K confirms the ferromagnetic ground state of Pr₂Rh₃Ga.

Two anomalies occur in the ZFC/FC measurements of Nd₂Rh₃Ga (Fig. 8). This is unusual since the crystal structure contains only one rare earth site, therefore additional heat capacity measurements were conducted (Fig. 8, middle, red). One observes a sharp λ-shaped anomaly at T=4.8(1) K along with a small shoulder. The shoulder can be attributed to the impurity of the sample (although pure on the level of X-ray powder diffraction) while the main anomaly corresponds to the intrinsic magnetic transition. The ferromagnetic character of the transition is again evident from the magnetization isotherm recorded at 3 K.

The susceptibility measurements of Gd₂Rh₃Ga (Fig. 9) at 10 kOe reveal a positive Weiss constant θ_P=51.7(1) K, suggesting ferromagnetic interactions in the paramagnetic temperature region. The ZFC/FC measurement in contrast shows an anomaly characteristic for antiferromagnetic ordering at a Neél temperature of T_N=43.0(1) K. The antiferromagnetic character of the transition is also evident from the magnetization isotherms recorded at 3, 10 and 25 K, all showing a so called meta-magnetic step (spin-reorientation from an antiparallel to a parallel alignment). The corresponding critical field is below 10 kOe, therefore the high-field measurement suggests ferromagnetic ordering.

Similar behavior is observed for Tb₂Rh₃Ga (Fig. 10) with θ_P=37.5(1) K. The ZFC/FC measurement shows two anomalies, one characteristic for antiferromagnetic, the other characteristic for ferromagnetic ordering. Since the order of magnitude for the susceptibility of ferromagnetic materials is much larger compared to antiferromagnetic materials, the weak FM transition most likely originates from a tiny amount of an unknown impurity (although the sample is pure on the level of X-ray powder diffraction). For the AFM transition a Neél temperature of T_N=33.4(1) K was determined. The antiferromagnetic character of the transition is also evident from the magnetization isotherms recorded at 3 and 10 K, which show a meta-magnetic step, at a critical field below 10 kOe.

The ZFC/FC measurement of Dy₂Rh₃Ga (Fig. 11) shows two anomalies with characteristics of ferromagnetic ordering at T_C,1=10.9(1) K and T_C,2=13.3(1) K. To investigate which one is intrinsic, a heat capacity measurement was conducted (Fig. 11, middle, inset). Two lambda anomalies were observed at T=10.4(1) K and T=13.0(1) K. Since the area under the signal corresponds to the amount of the respective phase present, the anomaly at T=10.4(1) K has to be the intrinsic one. The magnetization isotherms recorded at 3 and 10 K, below the ordering temperature, confirm the ferromagnetic ground state of the compound and show weak hystereses.

Ho₂Rh₃Ga (Fig. 12) and Er₂Rh₃Ga (Fig. 13) order ferromagnetically at T_C=10.9(1) and T_C=13.1(1) K, respectively. The ferromagnetic ground state of both gallides is also evident from the magnetization isotherms recorded at 3 and 10 K.

3.4 Solid state NMR spectroscopy

The ⁸⁹Y and ⁷¹Ga solid state NMR spectra of the compound Y₂Rh₃Ga and, for comparison, the binary Laves phase YRh₂ are shown in Figs. 14 and 15. In agreement with their crystal structures, each spectrum exhibits only one single signal characterized by a very high resonance shift, which exceeds the chemical shift range of typical diamagnetic yttrium compounds (100–400 ppm) significantly [71]. Based on the theoretical calculations discussed below we attribute the high resonance frequency to a strong Knight shift contribution originating from the interaction of the magnetic moments of the ⁸⁹Y and ⁷¹Ga nuclei with the spin density of the conduction electrons near the Fermi edge.

Fig. 14:

Experimental and simulated (red lines) ⁸⁹Y MAS NMR spectra of YRh₂ (top; B₀=11.7 T; ν_rot=4 kHz) and Y₂Rh₃Ga (middle and bottom; B₀=11.7 T and 9.4 T; ν_rot=7 kHz). The signal of the ternary phase exhibits anisotropically broadened spinning sideband manifolds due to a strong Knight shift anisotropy.

Fig. 15:

Experimental ⁷¹Ga NMR spectrum of Y₂Rh₃Ga with simulation (red line) recorded at an external magnetic flux density of B₀=7.05 T under static conditions.

The ternary Laves phase Y₂Rh₃Ga shows a significantly higher resonance frequency, suggesting a larger Knight shift contribution than observed for the binary compound YRh₂. In addition, a sizeable resonance shift anisotropy is observed, manifesting itself in a spinning sideband manifold. The difference of s-electron density at the Fermi-edge, also determined by total-DOS calculations (vide infra), suggests a partial compensation of the electron withdrawing effect of the highly electronegative Rh (EN=2.28 [55]) atoms by the additional electron density of the Ga atoms (EN=1.81 [55]). The observed shift anisotropy (Δσ=−560 ppm, η_σ =0 (Table 7), observed in the field-dependent NMR spectra) is consistent with the axially symmetric local environment of the Y atoms (crystallographic 6c site, symmetry 3m).

The lineshape of the static ⁷¹Ga NMR spectrum is dominated by strong second-order quadrupolar perturbations originating from the interaction of the I=3/2 nucleus with a strong electric field gradient produced by the non-cubic coordination sphere of the Ga atoms. The experimental quadrupole coupling parameters (C_{Q, exp}=23.24 MHz, η_{Q, exp}=0) are found in excellent agreement with the calculated values (C_{Q, calc}=23.53 MHz, η_{Q, calc}=0), revealing an axially symmetric electric field gradient as expected from the symmetry (3̅m) of the Wyckoff site 3a. Overall, the extremely well-defined ⁷¹Ga NMR spectrum characterized by a singular value of C_Q implies an essentially perfectly ordered structure and the absence of disordering and/or mixed site occupancy. The ⁷¹Ga resonance shift is comparable to values found for other intermetallic gallides [72], [73], [74].

3.5 Electronic structure and NMR parameters

To understand the experimentally observed differences of the ⁸⁹Y NMR signal shifts, electronic structure calculations of YRh₂ and Y₂Rh₃Ga were performed. The total DOS of both compounds is presented in Fig. 16. In a first approximation, the NMR signal shift of metallic materials is frequently dominated by the s-electrons at the Fermi level (s-DOS_EF), since they have a nonzero probability at the nuclear site [75], [76]. This correlation was verified for the di- and tetragallides of the alkaline earth metals and NaGa₄ [73], [77]. Recently, the validity of this approximation has been confirmed by a careful analysis of the shift contributions in these materials [78]. Consistent with this simple correlation, Y₂Rh₃Ga possesses a significantly higher calculated s-DOS_EF than YRh₂ as indicated in Fig. 17.

Fig. 16:

Total density of states (DOS) for Y₂Rh₃Ga (red line) and YRh₂ (black line).

Fig. 17:

s-Contributions of the angular momentum decomposed electronic density of states (s-DOS) for Y in YRh₂ (black) and Y₂Rh₃Ga (red).

Beside this, the calculations of the EFGs main principal axis V_ZZ and the asymmetry parameter η_Q of the Ga atoms are in excellent agreement with the NMR experiments (see Section 3.4 and Table 7). The highly symmetric Y₂Rh₃Ga possesses a relatively large and negative value of V_ZZ=−9.092 10²¹ Vm⁻². This indicates a very anisotropic prolate charge distribution of the Ga atoms compared to other Ga compounds [72], [73], [74]. The asymmetry parameter η_Q=0 is in agreement with the experimental value and the site symmetry (3̅m). Considering this site symmetry, V_ZZ has to be aligned parallel to the c axis of the unit cell. The charge distributions point towards the Rh triangles above and below the Ga atoms with short Rh–Ga distances. This may indicate bonding interactions of these two types of atoms.