Magnetic properties of the germanides RE₃Pt₄Ge₆ (RE=Y, Pr, Nd, Sm, Gd–Dy)

2.1 Synthesis

Starting materials for the syntheses of the RE₃Pt₄Ge₆ samples were sublimed pieces of the RE elements (smart elements), platinum pieces (Agosi), and germanium lumps (Wacker), all with stated metal-based purities better than 99.9%. Small pieces of the moisture sensitive RE elements (Pr, Nd and Sm) were first cut under dried n-hexane and kept under argon in a Schlenk tube prior to the reactions. The other RE elements were handled in air. In a first step, the RE pieces and the germanium lumps were arc-melted [6] separately to small buttons under an argon atmosphere of 750 mbar. The argon was purified over titanium sponge (873 K), silica gel, and molecular sieves. The respective appropriate amounts of platinum were added to the RE metal and germanium buttons. The starting materials were placed in a copper crucible and arc-melted six times to ensure homogeneity. The resulting samples exhibit metallic luster and are stable in air over months. The polycrystalline powders are grey. Subsequently, the arc-melted buttons were sealed in evacuated silica tubes and annealed in a special water-cooled device [7] in an induction furnace (Hüttinger Elektronik, Freiburg, type TIG 5/300). The buttons were rapidly heated to temperatures slightly below the melting point, kept at this temperature for 2 h and finally cooled to room temperature within several hours (power decrease of 10 V per 10 min).

2.2 X-ray diffraction

The polycrystalline RE₃Pt₄Ge₆ samples were characterized by Guinier patterns (imaging plate detector, Fujifilm BAS-1800) with CuKα₁ radiation and α-quartz (a=491.30 and c=540.46 pm) as an internal standard. The lattice parameters (Table 1) were deduced from least-squares fits of the Guinier data [8] using the structural model of Ce₃Pt₄Ge₆.

Small single crystals of the Y₃Pt₄Ge₆ sample were selected from the carefully crushed button of the annealed sample. The crystals were glued to thin quartz fibers and investigated by Laue photographs in a Buerger camera (white molybdenum radiation; imaging plate technique, Fujifilm, BAS-1800) to check their quality. Intensity data of a suitable crystal was collected at room temperature using a Stoe IPDS-II diffractometer. A numerical absorption correction was applied to the data set. Details about the data collection and the crystallographic parameters are summarized in Tables 2–4 .

Further details of the crystal structure investigation 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 number CSD-433387.

2.3 Physical property investigations

Polycrystalline pieces of the annealed ingots were packed in kapton foil and attached to the sample holder rod of a vibrating sample magnetometer (VSM) unit 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 external magnetic fields up to 80 kOe (1 kOe=7.96×10⁴ A m⁻¹).

For the heat capacity measurement of Tb₃Pt₄Ge₆, 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 1.9–75 K.

3.1 Structure refinement

The intensity data set obtained for Y₃Pt₄Ge₆ shows additional reflections, as it has been observed for Ce₃Pt₄Ge₆ previously [1]. Therefore the interpretation is equivalent and will be handled rather concise as the focus of this work are the magnetic properties. For additional details regarding the structure solution and refinement were refer to the literature [1]. The additional reflections can be interpreted as satellites with 1/2 along a*. The corresponding superspace group that can be derived is Cmcm(α,0,0)0s0 (SSG 63.1.13.2) with lattice parameters of a=434.73(6), b=2598.5(3) and c=430.67(6) pm. The notation of Stokes, Campbell and van Smaalen for the superspace groups was used [10], [11]. After refinement of the basic structure the satellites were added to the refinement and positional or occupational modulations for the atoms were applied. The chosen superspace group allows for additional degrees of freedom, however, some modulation components are very small (Table 3). While Y1, Pt1, Pt2, Ge1 and Ge2 show positional modulations along x1/x4 and x2/x4, Y2 and Ge3 exhibit occupational modulations along x1/x4. The occupational modulations were fitted using a crenel function; for the positional modulations simple harmonic functions were used (Fig. 1). It was possible to refine modulated anisotropic atomic displacement parameters (ADP) for all atoms showing positional modulations. As a check for the correct composition, the occupancy parameters were refined in a separate series of least-squares cycles. All sites were fully occupied within three standard deviations. There was no indication of mixing on any site. The final difference electron-density synthesis revealed a negative peak, which is, however, not uncommon in modulated structure refinements using crenel functions. It is caused by the inability to refine modulated anisotropic displacement parameters for these atoms. Details of the structure refinement are listed in Tables 2 and 3, interatomic distances of the approximant are given in Table 4.

Fig. 1:

Sections of the Fourier maps (based on F_obs) of the orthorhombic (3+1)D refinement with superspace group Cmcm(α,0,0)0s0 (α=1/2a*) of the commensurately modulated structure of Y₃Pt₄Ge₆. Summation over 100 pm of the projected directions was conducted. Contour lines for all atoms correspond to a difference of 20 e Å⁻³ for Y, 50 e Å⁻³ for Pt, and 10 e Å⁻³ for Ge.

3.2 Crystal chemistry

The lattice parameters of all prepared compounds refined from Guinier powder X-ray data are listed in Table 1 and exhibit the expected trend of the lanthanide contraction from Ce₃Pt₄Ge₆ to Dy₃Pt₄Ge₆. This is in contrast to the literature data, where substantial anomalies for the a axis of Pr₃Pt₄Ge₆ and the c axis of Dy₃Pt₄Ge₆ are reported. Careful indexing and comparison of the respective intensities with the help of calculated ones is essential for the precise refinement of the lattice parameters. Y₃Pt₄Ge₆ shows lattice parameters similar to the Tb compound, in line with the similar ionic radii according to the tabulated Shannon data [12].

As Y₃Pt₄Ge₆ has been investigated by single-crystal X-ray diffraction, the crystal chemistry of this compound will be described in the following paragraph. The crystal structure can be described as an intergrowth of CaBe₂Ge₂- and YIrGe₂-type slabs that are stacked along [001] (Fig. 2). While the CaBe₂Ge₂ slabs exhibit hexagonal prisms, the YIrGe₂ slabs form pentagonal prisms. The hexagonal prisms are occupied by the Y1 atoms, the pentagonal prisms by the Y3 atoms (Fig. 3). The interatomic Y–Ge distances range between 298 and 338 pm and the Y–Pt distances between 317 and 333 pm. These distances are in line with that of other yttrium-platinum-germanides e.g. YPtGe₂ (YIrGe₂ type) [13] or YPt₂Ge₂ (LaPt₂Ge₂ type) [14]. Within the CaBe₂Ge₂ arrangements tetrahedral [PtGe_4/4] layers are found and exhibit only heteroatomic bonds with interatomic Pt–Ge distances of 239–263 pm, again in line with e.g. YPt₂Ge₂ (LaPt₂Ge₂ type) or TiNiSi-type YPtGe [15]. In the YIrGe₂ fragment additionally Ge–Ge bonds with distances of 264 pm are found (265 pm in YIrGe₂ [13]). The occupational modulation of the Y2 and Ge3 atoms removes the statistic disorder of the half-occupied sites. The pentagonal prisms are now facing either to the right or to the left along the a axis in an ordered manner. In contrast to previous structural models, no half occupied sites are needed in this description [2]. The positional modulation of the remaining atoms can be easily understood as the orientation of the pentagonal prisms influences the surrounding Pt/Ge framework. The atoms close to these prisms therefore exhibit the strongest positional modulations. In Figs. 3 and 4 the 3D approximant of Y₃Pt₄Ge₆ is used to depict the structure. The group-subgroup relationship between the (3+1)D structure and the 3D approximant has been discussed in detail before, and further crystal chemical details are also given in [1].

Fig. 2:

Extended unit cell of the commensurate supercell structure of the RE₃Pt₄Ge₆ series. The YIrGe₂- and CaBe₂Ge₂-type slabs are labelled and highlighted by color. RE atoms are depicted as blue, Pt atoms as black and Ge atoms as open circles.

Fig. 3:

Coordination environments surrounding the RE1 (top left) RE2 (top right) and RE3 (bottom) atoms in the crystal structure of RE₃Pt₄Ge₆ series. RE atoms are depicted as blue, Pt atoms as black and Ge atoms as open circles.

Fig. 4:

Temperature dependence of the magnetic susceptibility χ of Y₃Pt₄Ge₆, measured at 10 kOe.

3.3 Physical properties

The magnetic properties of the RE₃Pt₄Ge₆ series (RE=Y, Pr, Nd, Sm, Gd, Tb) were determined via susceptibility and magnetization experiments. Dy₃Pt₄Ge₆ could not be obtained in an X-ray pure form, hence lattice parameter refinement was possible but no magnetic data was recorded. The temperature dependence of the magnetic and inverse magnetic susceptibility (χ and χ⁻¹ data) was measured at 10 kOe. Y₃Pt₄Ge₆ exhibits diamagnetic behavior above 100 K, but below this temperature an increase is visible (Fig. 4). This upturn is caused by paramagnetic impurities and known as a Curie tail. The intrinsic diamagnetism overcompensates the Pauli paramagnetism induced by the conduction electrons.

For the paramagnetic compounds a fit of the χ⁻¹ data in the range above 75 K using the Curie-Weiss law revealed the effective magnetic moments μ_eff and the Weiss constant θ_P. The effective magnetic moment along with the respective theoretical values are given in Table 5 and indicate that the RE cations are in a stable trivalent oxidation state. The negative value of the Weiss constant for all compounds points towards antiferromagnetic interactions in the paramagnetic regime. Pr₃Pt₄Ge₆ and Nd₃Pt₄Ge₆ exhibit the typical behavior of paramagnetic materials. No magnetic ordering is visible in the zero field cooled/field cooled (ZFC/FC) measurements, conducted at 100 Oe, down to 2.5 K (middle panels in Figs. 5 and 6). The magnetization isotherms (bottom panels in Figs. 5 and 6) recorded at 50 K show a linear increase, typical for a paramagnetic material. The 10 K isotherms show a slight curvature, the 3 K isotherms a pronounced bent. This points towards saturation effects at low temperatures.

Fig. 5:

Magnetic properties of Pr₃Pt₄Ge₆: (top) Temperature dependence of the magnetic susceptibility χ and its reciprocal χ⁻¹ measured with a magnetic field strength of 10 kOe; (middle) magnetic susceptibility in zero-field- (ZFC) and field-cooled (FC) mode at 100 Oe; (bottom) magnetization isotherms at 3, 10, and 50 K.

Fig. 6:

Magnetic properties of Nd₃Pt₄Ge₆: (top) Temperature dependence of the magnetic susceptibility χ and its reciprocal χ⁻¹ measured with a magnetic field strength of 10 kOe; (middle) magnetic susceptibility in zero-field- (ZFC) and field-cooled (FC) mode at 100 Oe; (bottom) magnetization isotherms at 3, 10, and 50 K.

Sm₃Pt₄Ge₆ exhibits the expected van Vleck paramagnetism, caused by the close proximity of the excited J=7/2 multiplet with respect the ground state J=5/2 multiplet of the Sm³⁺ ions. The energy difference between these states is only about 1550 K, while the respective other angular momentum levels are correspondingly higher. A very small paramagnetic moment of 0.845 μ_B caused by an antiparallel coupling of the L=5, S=5/2 Russel-Saunders states is subsequently observed for free Sm³⁺ cations. In order to describe the magnetic behavior of intermetallic samarium compounds, Stewart developed a theory taking polarization effects, interionic Heisenberg exchange couplings and the population of the J=7/2 and the J=5/2 ground states into account. The unexpected simple form χ(T)=χ₀+D/(T–θ) was derived [16]. Hamaker and coworkers were able to prove that χ(T) for polycrystalline SmRh₄B₄ can be described by the equation

χM(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 an energy scale, which is defined as δ=7ΔE/20 and describes the differences of the ground and excited states. The first term in the formula given above represents the Curie-Weiss susceptibility of the J=5/2 ground state, while the second part represents the van Vleck susceptibility caused by the J=7/2 multiplet, which is only slightly higher in energy [17]. 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 [18]. It should be mentioned that both equations neglect crystal-field splittings of each J level and the mixture of one with another.

The fit obtained using the Hamaker equation given above for the data of Sm₃Pt₄Ge₆ is shown in red in Fig. 7. The temperature region between 25 and 275 K can be described very well, resulting in fit parameters of μ_eff=1.51(1) μ_B, θ_P=−36.7(1) K and δ=159(2) K (Fig. 5). The effective magnetic moment is larger than the 0.845 μ_B of the free ion for the J=5/2 Hund’s rule ground state of Sm³⁺, δ=159(2) K corresponds to ΔE=454 K. While the moment is significantly higher compared to the theoretical value, the energy difference is smaller compared to the 1550 K predicted by Stewart. A look at the literature reveals that several compounds exhibit lower values. 850 K are found for SmOs₄Sb₁₂ [19], 1080 K for SmRh₄B₄ [17], 412, 265, and 1488 K for SmCo₂Zn₂₀, SmRu₂Zn₂₀, and SmPd₂Cd₂₀ [20], respectively. Some of these compounds also exhibit enhanced magnetic moments, e.g 1.7 μ_B are found for SmFe₂Zn₂₀ and 0.99 μ_B for SmCo₂Zn₂₀ [20]. For SmCo₂Ge₂ and the silicide SmCu₂Si₂ also enhanced effective magnetic moments of μ_eff=1.12 μ_B are reported [21], [22].

Fig. 7:

Magnetic properties of Sm₃Pt₄Ge₆: (top) Temperature dependence of the magnetic susceptibility χ and its reciprocal χ⁻¹ measured with a magnetic field strength of 10 kOe, the fit of the data is plotted in red; (bottom) magnetization isotherms at 3, 10, 50 and 100 K.

Finally, the magnetic data of Gd₃Pt₄Ge₆ and Tb₃Pt₄Ge₆ are discussed. Both compounds exhibit antiferromagnetic ordering, visible already in the 10 kOe measurements (Figs. 8 and 9, top panel). From the low-field measurements depicted in the middle panel, Néel temperatures of T_N=8.1(1) K for Gd₃Pt₄Ge₆ and T_N=11.0(1) K for Tb₃Pt₄Ge₆ could be deduced, in line with the negative paramagnetic Curie temperatures. No bifurcation is visible in both cases. For Tb₃Pt₄Ge₆ an additional anomaly is visible at T=~6 K, which is weak and unclear in nature at first. Heat capacity measurements (Fig. 9, middle panel) have proven that the feature is intrinsic as it produces a well λ-shaped signal. Thus this anomaly can be interpreted as spin reorientation at T_R=5.7(1) K due to the smaller heat tone as determined from heat capacity.

Fig. 8:

Magnetic properties of Gd₃Pt₄Ge₆: (top) Temperature dependence of the magnetic susceptibility χ and its reciprocal χ⁻¹ measured with a magnetic field strength of 10 kOe; (middle) magnetic susceptibility in zero-field- (ZFC) and field-cooled (FC) mode at 100 Oe; (bottom) magnetization isotherms at 3, 10, and 50 K.

Fig. 9:

Magnetic properties of Tb₃Pt₄Ge₆: (top) Temperature dependence of the magnetic susceptibility χ and its reciprocal χ⁻¹ measured with a magnetic field strength of 10 kOe; (middle) magnetic susceptibility in zero-field- (ZFC) and field-cooled (FC) mode at 100 Oe and heat capacity measurements (in red); (bottom) magnetization isotherms at 3, 20, 50 and 100 K.

The magnetization isotherms (Figs. 8 and 9, bottom panel) above the magnetic phase transitions are linear, in line with the expected paramagnetic behavior. The 20 K isotherm in Tb₃Pt₄Ge₆ shows a slight curvature towards high fields. The 3 K isotherms are in both cases measured below the ordering temperatures of the respective compounds. The isotherm of Gd₃Pt₄Ge₆ exhibits a nearly linear behavior with an upturn towards high fields. This could be the onset of a so called meta-magnetic step (antiparallel to parallel spin realignment). As no steep increase is visible, the antiferromagnetic ground state must be very stable, in line with the low saturation magnetization of μ_sat=3.10(1) μ_B per Gd³⁺ atom, which is significantly lower as compared to the expected 7 μ_B per Gd³⁺ according to g_J×J. Tb₃Pt₄Ge₆ in contrast exhibits two meta-magnetic steps at critical fields of H_cr,1=22.0(5) and H_cr,2=32.6(5) kOe. The saturation magnetization is μ_sat=5.05(1) μ_B per Tb³⁺ atom, which is again lower than the expected 9 μ_B per Tb³⁺according to g_J×J. The two meta-magnetic steps underline the antiferromagnetic ground state with reorientations at two different fields.