Gallium-containing Heusler phases ScRh₂Ga, ScPd₂Ga, TmRh₂Ga and LuRh₂Ga – magnetic and solid state NMR-spectroscopic characterization

1 Introduction

The Heusler phase structure, originally determined for MnCu₂Al [1], [2] is one of the basic ternary structure types in the large family of intermetallic compounds. More than 1500 entries are listed in the Pearson data base [3]. The variability in composition is remarkable. Most Heusler phases form as a combination of two different transition metals (or a transition (T) metal with a rare earth (RE) metal) with a p element of the 3^rd, 4^th, or 5^th main group. For various application prospects, Heusler phases were thoroughly studied with respect to high magnetic ordering temperatures and permanent magnetic materials, superconductivity, topological insulators, thermoelectrics, spintronics and the magnetocaloric effect [4], [5], [6], [7, and references cited therein]. Detailed computational studies [8], [9], [10], [11], [12] allowed a systematization of the magnetic behavior of Heusler phases and new ones could be predicted on the basis of combinatorial scans. A main structural feature of Heusler phases concerns extended homogeneity ranges and structural disorder.

Although the family of Heusler phases contains a huge number of representatives, there is still a large potential for new materials with promising properties. Phase analytical work recently revealed an extension towards magnesium and cadmium containing Heusler phases REPd₂Mg, REPd₂Cd, REAg₂Mg, REAu₂Mg and REAu₂Cd [13] and pronounced solid solutions Y(T_0.5T′_0.5)₂X (T/T′=Pd, Ag, Au; X=Mg, In) [14] which were studied by magnetic susceptibility measurements, and by ²⁵Mg, ⁸⁹Y ¹¹³Cd and ¹¹⁵In solid state MAS NMR spectroscopy. A noteworthy result is the high Curie temperature of T_C=98.3 K for GdAg₂Mg [13]. Extension of the Heusler crystal chemistry to divalent magnesium and cadmium allows for a reduction of the valence electron count and an effective influence on the physical properties. To give an example, complete substitution of Mg in GdAg₂Mg by In leads to an antiferromagnetic ground state for GdAg₂In and a severe drop of the magnetic ordering temperature to T_N=10 K [15], [16].

When screening the Pearson data base [3] it becomes evident that gallium-containing Heusler phases so far have mostly been observed with a combination of two different transition metals. To this point, with the rare earth elements only the scandium-containing phases ScT₂Ga (T=Co, Ni, Cu, Pd) [17], [18], [19], [20], [21] have been reported. During recent phase analytical studies of the rhodium-rich parts of the RE-Rh-Ga systems [22], [23], [24], [25] we obtained the new Heusler phases RERh₂Ga with the small rare earth elements Sc, Tm, and Lu. Their structural details, magnetic properties and solid state NMR spectroscopic data are reported herein and compared to those of ScPd₂Ga [19].

2 Experimental

2.3 Structure refinements

Both data sets showed cubic F-centered lattices and isotypism with the well-known MnCu₂Al [1], [2] structure. Space group Fm3̅m was already evident from the powder patterns (Fig. 1). The positional parameters of MnCu₂Al were used as starting values and the structures were refined on F² with Jana2006 [28] with isotropic displacement parameters for all atoms. Since Heusler phases often show homogeneity ranges and disorder, we refined the occupancy parameters in separate series of least-squares cycles. The rhodium sites of both crystals were fully occupied within two standard deviations. The Lu-containing crystal showed a statistical distribution of Lu and Ga atoms on the Wyckoff sites 4a and 4b which led to the final composition Lu_0.97Rh₂Ga_1.03. In contrast, only the 4a site of the Sc-containing single crystal showed a mixed occupation of Sc and Ga atoms, resulting in the composition Sc_0.88Rh₂Ga_1.12. The final difference Fourier syntheses showed no significant residual peaks. The final positional parameters, isotropic displacement parameters as well as the interatomic distances are given in Tables 2–4 .

Fig. 1:

Experimental Guinier powder pattern (CuKα₁ radiation) of LuRh₂Ga (annealed at 730 K for 14 d) compared to the calculated ones of LuRh₂Ga, Lu_0.97Rh₂Ga_1.03 (both MnCu₂Al type) and (Lu_0.5Ga_0.5)Rh (CsCl type).

Table 3:

Atomic coordinates and equivalent isotropic displacement parameters (pm²) for Lu_0.97Rh₂Ga_1.03 and Sc_0.88Rh₂Ga_1.12 with x=y=z and U_eq=1/3 (U₁₁+U₂₂+U₃₃).

Atom	Wyck. site	x	Ueq	s.o.f.
Lu0.97Rh2Ga1.03
Lu/Ga	4a	0	96(6)	79(2)/21(2)
Rh	8c	1/4	135(10)	1
Ga/Lu	4b	1/2	136(12)	81(1)/19(1)
Sc0.88Rh2Ga1.12
Sc/Ga	4a	0	83(5)	88(2)/12(2)
Rh	8c	1/4	59(3)	1
Ga	4b	1/2	69(3)	1

1. U_eq=U₁₁=U₂₂=U₃₃. U₁₂=U₁₃=U₂₃=0.

Table 4:

Interatomic distances (pm) in the structures of LuRh₂Ga and ScRh₂Ga.

LuRh2Ga				ScRh2Ga
Lu:	8	Rh	274.1	Sc:	8	Rh	268.0
	6	Ga	316.5		6	Ga	309.5
Rh:	4	Lu	274.1	Rh:	4	Sc	268.0
	4	Ga	274.1		4	Ga	268.0
	6	Rh	316.5		6	Rh	309.5
Ga:	8	Rh	274.1	Ga:	8	Rh	268.0
	6	Lu	316.5		6	Sc	309.5

1. All distances of the first coordination spheres are listed. Standard deviations are equal or smaller than 0.1 pm. Note the mixed occupancies listed in Table 3.

Further details of the crystal structure investigations 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-433136 (Lu_0.97Rh₂Ga_1.03) and CSD-433122 (Sc_0.88Rh₂Ga_1.12).

3 Crystal chemistry

The new gallides RERh₂Ga with the small rare earth elements thulium, lutetium and scandium crystallize with the Heusler phase structure. In agreement with the lanthanide contraction we observe a slightly smaller cell volume for LuRh₂Ga as compared to TmRh₂Ga (Table 1) and a severe drop on going to ScRh₂Ga with the smallest rare earth element.

In the following we exemplarily discuss the structural features of Lu_0.97Rh₂Ga_1.03. The unit cell is presented in Fig. 2. The lutetium and gallium atoms build up a rocksalt-type substructure in which all tetrahedral voids are filled by the rhodium atoms. Table 3 and Fig. 2 immediately emphasize the disorder problem in the Lu_0.97Rh₂Ga_1.03 structure. Although the refined composition is close to the ideal one, both four-fold sites show Lu/Ga mixing. This disorder is pronounced if the two elements have similar size and valence, and it also depends on the thermal treatment of the respective sample. The Lu/Ga mixing drastically influences the X-ray powder pattern. In Fig. 1 we present the experimental pattern of the LuRh₂Ga sample along with three calculated ones: (i) the MnCu₂Al model with complete Lu/Ga ordering, (ii) the MnCu₂Al model with the Lu/Ga mixing as obtained from the structure refinement, and (iii) a CsCl type subcell with random Lu/Ga distribution. The experimental pattern shows no superstructure reflections, indicating a distribution of different domains with differing degrees of Lu/Ga mixing. These domains, however, still show short-range ordering. The selected single crystal which anyway contains ca. 10¹⁴ unit cells shows superstructure reflections which force a doubling of the CsCl subcell in all three directions. Cutouts of the hk4 and hk5 layers are presented as examples in Fig. 3.

Fig. 2:

Crystal structure of Lu_0.97Rh₂Ga_1.03. The Rh atoms are drawn as blue circles. The mixed occupancy of the 4a and 4b Wyckoff sites by Lu (gray) and Ga (red) atoms are emphasized. The site occupancy factors for these sites are given as well.

Fig. 3:

Cutout of the reciprocal layers hk4 (left) and hk5 (right) resulting from the single-crystal measurement of Lu_0.97Rh₂Ga_1.03. The F-centered lattice as well as some of the observed reflections are emphasized. Yellow points indicate intensity maxima.

Since the Heusler phase structure is a superstructure of the bcc packing [31], [32] we observe coordination number 14 (8+6 or 4+4+6) for all atoms in LuRh₂Ga. The strongest bonding interactions occur for the Lu–Rh contacts. The Lu–Rh distances of 274 pm are even slightly shorter than the sum of the covalent radii [33] for Lu+Rh of 281 pm. This LuRh slab in LuRh₂Ga nicely matches with the binary LuRh having a distance of 289 pm [34]. In contrast we observe weaker Rh–Ga bonding. The Rh–Ga distances within the RhGa₄ tetrahedra of 274 pm are much longer than the sum of the covalent radii [33] for Rh+Ga of 250 pm, as well as the Rh–Ga distance of 260 pm in CsCl type RhGa [35].

4 Magnetic properties

The samples were investigated in zero field cooled (ZFC) mode applying a magnetic field of 10 kOe after cooling down to 3 K. The temperature dependence of the magnetic susceptibility χ of the scandium and lutetium compounds is presented in Fig. 4. ScPd₂Ga (χ(300 K)=1.2(2)×10⁻⁵ emu mol⁻¹), ScRh₂Ga (χ(300 K)=2.5(1)×10⁻⁴ emu mol⁻¹) and LuRh₂Ga (χ(300 K)=2.6(2)×10⁻⁵ emu mol⁻¹) show weak, slightly positive susceptibilities, classifying these Heusler phases as Pauli paramagnetic. The upturns at low temperature (especially for the LuRh₂Ga sample) can be ascribed to small amounts of paramagnetic impurities. An additional examination of the samples down to 2.1 K with an external field of 20 Oe revealed no indication for superconductivity.

Fig. 4:

Magnetic susceptibility of LuRh₂Ga (black), ScRh₂Ga (red) and ScPd₂Ga (blue) measured in ZFC mode with an external field of 10 kOe as a function of temperature.

The temperature dependence of the reciprocal susceptibility χ of the TmRh₂Ga sample (Fig. 5) measured in ZFC mode could be fitted with the Curie-Weiss law. The resulting experimental magnetic moment μ_exp=7.57(1) μ_B Tm atom⁻¹ is close to the theoretical value of the free Tm³⁺ ion (μ_eff=7.56 μ_B [36]) indicating stable trivalent thulium. The paramagnetic Curie temperature θ_P=–5.9(5) K indicates weak antiferromagnetic interactions in the paramagnetic regime. An additional measurement of TmRh₂Ga in zero field cooled/field cooled mode with a field strength of 100 Oe (not displayed) revealed no indication for magnetic ordering. Magnetization isotherms of TmRh₂Ga taken at 3, 10, 50 and 150 K are presented in the bottom panel of Fig. 5. At 50 and 150 K a linear field dependence is observed as expected from a paramagnet. The isotherms measured at 3 and 10 K exhibit saturation effects. The maximal observed magnetization of TmRh₂Ga at 80 kOe and 3 K of μ_sat=4.2(1) μ_B per thulium atom is lower than the theoretical saturation magnetization of 7 μ_B per thulium atom [36].

Fig. 5:

Magnetic properties of TmRh₂Ga: (top) Temperature dependence of the magnetic susceptibility χ and its reciprocal χ⁻¹ measured at 10 kOe; (bottom) Magnetization isotherms of TmRh₂Ga measured at 3, 10, 50 and 150 K.

5 ⁴⁵Sc and ⁷¹Ga solid state NMR spectroscopy

Figure 6 summarizes the ⁴⁵Sc and ⁷¹Ga solid-state MAS NMR spectra of the Heusler compounds ScRh₂Ga and ScPd₂Ga. In agreement with their crystal structures both compounds give rise to one dominant signal according to one crystallographic site occupied by Sc and Ga atoms, respectively. The ⁴⁵Sc NMR spectrum of ScPd₂Ga shows an additional signal with an approximate area fraction of 5% indicating the presence of a Sc containing impurity phase. Both the ⁴⁵Sc and ⁷¹Ga NMR spectra exhibit strong Knight shifts, indicating a high concentration of spin-polarized conduction electrons near the Fermi edge at the nuclear origin. If Sc/Ga mixing occurs on the 4a and 4b Wyckoff sites, the spectra are further expected to be influenced by Knight shift distributions and nuclear electric quadrupolar interactions, which may arise from locally distorted environments caused by this mixing. This effect has been previously noted for various other 1:2:1 and 1:1:1 Heusler and half-Heusler compositions [13], [14], [37], [38], [39], [40]. While both the ⁴⁵Sc and ⁷¹Ga nuclei can be considered sensitive probes for such distortion effects, the ⁴⁵Sc isotope may be considered more sensitive, owing to its larger quadrupole moment.

Fig. 6:

Experimental and simulated (colored lines) ⁴⁵Sc (top) and ⁷¹Ga (bottom) MAS NMR spectra of the Heusler phases ScPd₂Ga (left) and ScRh₂Ga (right) recorded at an external magnetic field of B₀=11.7 T and spinning frequencies of ν_rot=25–28.0 kHz. The inset highlights the typical central transition line shape due to second-order quadrupolar effects in the presence of a distribution of quadrupolar coupling constants, as observed in the ⁴⁵Sc spectrum of ScRh₂Ga. Signals caused by impurities are denoted with +.

Figure 6 illustrates that the manifestations of nuclear electric quadrupolar coupling in these two ternary scandium gallides are distinctly different. In ScPd₂Ga, the ⁴⁵Sc quadrupolar coupling is rather weak. It manifests itself by a sideband pattern from the outer |±1/2〉↔|±3/2〉, |±3/2〉↔|±5/2〉 and |±5/2〉↔|±7/2〉 Zeeman transitions which are broadened by the anisotropy of first-order quadrupolar perturbations, covering a frequency range of only 400 kHz. No second-order quadrupolar effects are detectable in this case. The ⁷¹Ga NMR spectrum shows no evidence for any quadrupolar coupling. Only a broad Gaussian line shape is observed suggesting that there is a wide distribution of isotropic Knight shifts.

The situation is distinctly different in ScRh₂Ga. The ⁴⁵Sc MAS NMR spectrum shows a pronounced signal asymmetry, characterized by a characteristic low-frequency tail typically observed when second-order quadrupole perturbations with a wide distribution of nuclear electric quadrupole coupling constants occur. In such cases, it is hard to observe the spinning side band pattern arising from the first-order quadrupolar perturbation, as their intensity will be spread out over an extended frequency range of several MHz. The stronger quadrupolar coupling (compared to ScPd₂Ga) also manifests itself in the ⁷¹Ga MAS-NMR spectrum, which shows a first-order quadrupolar spinning side band pattern covering about 500 kHz. Based on these data we conclude that the effect of mixed Sc/Ga occupancy is significantly stronger in ScRh₂Ga than in ScPd₂Ga. On the other hand, the Knight shift distribution in the Rh compound appears to be narrower than in ScPd₂Ga, suggesting that the structural origins producing distribution effects in quadrupolar coupling (local environments) and magnetic shielding (local and non-local contributions) are different. Overall, the present results indicate that solid state NMR may be a useful method for providing semi-quantitative information on the extent of site disordering in intermetallic compounds.