A comparison of the structure and localized magnetism in Ce 2 PdGa 12 with the heavy fermion CePdGa 6

Single crystals of Ce 2 PdGa 12 have been synthesized in Ga ﬂux and characterized by X-ray diffraction. This compound crystallizes in the tetragonal P 4 = nbm space group, Z ¼ 2 with lattice parameters of a ¼ 6 : 1040 ð 2 Þ ˚A and c ¼ 15 : 5490 ð 6 Þ ˚A. It shows strongly anisotropic magnetism and orders antiferromagnetically at T N (cid:4) 11K. A ﬁeld-induced metamagnetic transition to the ferromagnetic state is observed below T N . Structure–property relationships with the related heavy-fermion antiferromagnet CePdGa 6 are discussed. r 2005 Elsevier Inc. All rights reserved.


Introduction
Ce-based intermetallic compounds have attracted interest because of their variety of electronic properties. Extensive studies have been performed to understand so called ''heavy fermion'' states at low temperatures where large values of magnetic susceptibility and electronic specific heat are observed as a result of f-electrons coupling with conduction electrons [1]. The search for new layered materials is important in exploring new heavy fermion superconductors and in deepening our understanding of the role of structural dimensionality. This is indeed the case for the highest T c to date, of a Ce-based heavy fermion superconductor, which is found in the layered CeCoIn 5 (T c ¼ 2:3 K) [2].
We have previously reported the synthesis and structure of a new Ce-based layered intermetallic compound, CePdGa 6 , and its La-analog [3]. CePdGa 6 exhibits heavy fermion behavior with a specific heat coefficient g$230-400 mJ/mol-Ce K 2 . It shows highly anisotropic magnetism and orders antiferromagnetically at T N $5.5 K. The layered nature of the crystal structure, consisting of face-sharing CeGa 8/4 and edge-sharing PdGa 8/2 rectangular prisms alternating in a 1:1 ratio along the c-axis, is consistent with anisotropy observed in the magnetism. In the CeGa 8/4 layers, Ce is coordinated to 8 Ga atoms at the corners of rectangular prisms, forming face-sharing rectangular prisms. Meanwhile, the PdGa 8/2 layers consist of edge-sharing rectangular prisms with Pd at the center and Ga atoms at the corners.
In our search for new layered materials in ternary Ce-Pd-Ga system, we have discovered a new phase, Ce 2 PdGa 12 . The tetragonal structure is composed of Ce-Ga and PdGa 8/2 layers, similar to CePdGa 6 . Magnetic and specific heat measurements suggest an antiferromagnetic (AF) ground state of Ce 2 PdGa 12 , whose spin configuration transforms from a collinear AF to a canted one on lowering temperature. Moreover, we have found a field-induced metamagnetic transition in the AF state. We will discuss the structure-property relationships with the related heavy-fermion antiferromagnet CePdGa 6 .

Synthesis
Single-phase crystals of La 2 PdGa 12 and Ce 2 PdGa 12 were obtained by using flux growth methods. La or Ce ingot (3N, Ames Laboratory), Pd (5N, Alfa Aesar), and Ga (5N, Alfa Aesar) were placed into an alumina crucible in a 1:1:20 ratio. The contents were sealed into an evacuated fused silica tube, and the ampoule was heated to 1423 K for 2 h and allowed to cool to 723 K at a rate of 8 K/h, at which point the ampoules were immediately inverted and spun with a centrifuge. Plate-like single crystals were mechanically extracted. Typical crystal size ranged between 0.125 and 1 cm 3 . No noticeable degradation of the crystals in air was observed.
Single-phase crystals of LaPdGa 6 and CePdGa 6 were obtained by similar methods. La or Ce ingot (3N, Ames Laboratory), Pd (5N, Alfa Aesar), and Ga (5N, Alfa Aesar) were placed into an alumina crucible in a 1:1.5:15 ratio. After sealing the contents into a fused silica tube, the ampoule was heated at 1423 K for 2 h and allowed to cool quickly to 773 K at a rate of 150 K/h. The samples were then slow cooled at a rate of 8 K/h to 673 K, at which point the ampoules were immediately inverted and spun with a centrifuge. Single crystals were mechanically extracted. Flux growth methods using a 1:1:20 ratio of Ce:Pd:Ga and a heat treatment up to 1423 K followed by cooling at a rate of 8 K/h and centrifugation at 623 K yielded a mixture of CePdGa 6 and Ce 2 PdGa 12 .

X-ray diffraction
A suitable 0.03 Â 0.03 Â 0.08 mm 3 silver-colored fragment of Ce 2 PdGa 12 was mounted onto the goniometer of a Nonius KappaCCD diffractometer equipped with MoK a radiation (l ¼ 0:71073Å). Data were collected up to y ¼ 30:01 at 293 K. A similar treatment was applied to a 0.05 Â 0.08 Â 0.08 mm 3 silver-colored fragment of La 2 Pd-Ga 12 . Further crystallographic parameters for Ce 2 PdGa 12 and its La analog are provided in Table 1. The space group and atomic positions from Sm 2 NiGa 12 were used as an initial structural model for the structure determination of both La 2 PdGa 12 and Ce 2 PdGa 12 compounds. The structural model was refined using SHELXL97 [4]. Data were corrected for extinction and refined with anisotropic displacement parameters. Data were also corrected for absorption by a multi-scan method using HKL Scalepack. Atomic positions and displacement parameters for both compounds are provided in Table 2, and selected interatomic distances are provided in Table 3. To ensure homogeneity and sample quality, single-crystal X-ray diffraction was performed on several single crystals from multiple batches of samples. Single-crystal X-ray diffraction experimental results are consistent with the temperature schemes to obtain single-phase CePdGa 6 and Ce 2 PdGa 12 .

Physical property measurements
Magnetization data were obtained using a Quantum Design Magnetic Property Measurement System SQUID magnetometer. The temperature-dependent magnetization data were obtained first under zero-field cooled (ZFC)  conditions from 2 to 330 K under a field of 0.1 T. Magnetization was then measured upon heating to obtain field-cooled (FC) data after cooling to 2 K under field. Field (H)-dependent measurements were collected at 2 K with H swept between 0 and 5.5 T. These procedures were followed for crystallographic ab-plane of the crystal aligned parallel and perpendicular to the magnetic field. The specific heat was measured by a thermal relaxation method from 20 to 0.35 K at zero magnetic field and ambient pressure using a Quantum Design Physical Property Measurement system. The entropy was obtained by integrating the specific heat divided by the temperature with respect to the temperature.
The structure can be viewed as Ce atoms residing in Ga cavities of a three-dimensional network of [PdGa]. The [PdGa] subunit can then be further divided into PdGa 6 segments and Ga-only segments. Within the PdGa 6 segment, there are slightly distorted PdGa 8/2 rectangular prisms, where the Pd atom is coordinated to eight Ga atoms: four Ga3 atoms with interatomic distances of 2.5512(10) Å and four other Ga3 atoms by 2.5558(10) Å . These distances are typical of Pd-Ga bonds in Pd 5 Ga 3 [6], PdGa 5 , Pd 2 Ga [7], and in CePdGa 6 [3] where the bonding distances range between 2.388 and 2.701 Å . In addition, the sum of the two covalent radii of Ga (1.25 Å ) and Pd (1.28 Å ) is 2.53 Å [8], which is close to our experimental Pd-Ga distances in Ce 2 PdGa 12 . The Ga3-Ga3 interatomic distance along the ab-plane is 3.0501(9) Å , too long to be considered a bond according to the 1.25 Å covalent La layer Ce layer

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3.2824 (13) Ce-Ga3 ( Â 2) 3.2808(11) (10) Ga-only segment Ga-only segment To illustrate the striking resemblance between the two structures, the structure of CePdGa 6 and the structure of Ce 2 PdGa 12 , are presented in Fig. 2. The unit cell of CePdGa 6 , which is shown as solid lines in Fig. 2a, can be viewed as a primitive unit cell with Ce at the origin. Pd atoms bisect each of the edges along the c-axis, and two Ga layers-each consisting of either Ga1 or Ga3-separate the Ce and Pd atoms. Fig. 2b shows that there is a similar packing arrangement found in Ce 2 PdGa 12 . In fact, Ce 2 PdGa 12 can be viewed as CePdGa 6 units (shown as solid lines) alternating with a Ga-only segment along the c-axis.

Magnetism
In order to compare the magnetic data of CePdGa 6 and Ce 2 PdGa 12 , we have re-measured the magnetization on single crystals of single-phase CePdGa 6  The field dependence of the magnetization M for Ce 2 PdGa 12 , as shown in Fig. 5, was measured under fields along the c-axis and ab-plane. Interestingly, the c-axis magnetization shows a jump at 2.5 T, after showing a linear increase with the field. This indicates a metamagnetic transition, most likely due to a spin-flip transition from an antiferromagnetic to a ferromagnetic state. Along the crystallographic ab-plane, on the other hand, M increases rapidly up to B ¼ 1 T and reaches the value $0.2 m B at 5 T. A small hysteresis is observed below 0.1 T at 2 K, indicating the system has a ferromagnetic component in the ab-plane. The field dependence is similar to CePdGa 6 [3] where the magnetization shows a jump at 2 T, lower than the metamagnetic transition of Ce 2 PdGa 12 .

Specific heat
As discussed in the synthesis section, we have established synthetic routes to obtain single-phase crystals for both CePdGa 6 and Ce 2 PdGa 12 . Their temperature dependences of the specific heat were measured and are shown in Fig. 6. There are small deviations in the data from our previous report on CePdGa 6 [3]. Because CePdGa 6 and Ce 2 PdGa 12 can coexist under a certain growth condition (see Section 2.1), the previous report on the specific heat and magnetism of CePdGa 6 has minor effects from the inclusion of Ce 2 PdGa 12 [3]. The magnetic part of the specific heat, C m /T, for Ce 2 PdGa 12 (Fig. 6a) and CePdGa 6 ( Fig. 6b) is estimated by subtracting the specific heat C P /T of the La-analogue from the specific heat C P /T of the Ce-compound. For clarity, we show C P /T for both Ce and La-analogues in each inset of Fig. 4. A sudden jump at 11 K, coincident with its antiferromagnetic transition, is observed in the C m /T of Ce 2 PdGa 12 . Similarly a peak is observed in the heat capacity is observed at the antiferromagnetic transition temperature of 5.5 K for CePdGa 6 . C m /T shows electronic specific heat coefficient g of$72 mJ/mol K 2 at T close to 0 K and almost constant with $140 mJ/mol K 2 at T4T N for Ce 2 PdGa 12 , smaller than g ($230-400 mJ/ mol K 2 ) for CePdGa 6 .

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The corresponding entropies for the f-electron contribution can be estimated by integrating C m /T for Ce 2 PdGa 12 and CePdGa 6 . The entropy (S) released below T N is about 6000 (mJ/mole-K) for Ce 2 PdGa 12 , while it is around 5000 (mJ/mole-K) for CePdGa 6 . These values are roughly close to Rln2 ($5800 mJ/mole-K), which represents a doubly degenerate ground state in the paramagnetic regime. In addition, the suppressed entropy at T N in CePdGa 6 is attributable to Kondo effect.

Structure-property relationships
Two distinct Ce-Ce distances represent the structure of both compounds: Ce-Ce distances along the ab-plane, (Ce-Ce) ab, and c-axis, (Ce-Ce) c . In CePdGa 6 , the Ce-Ce interatomic distances are 4.350(3) Å in the ab-plane and 7.922(6) Å along the c-axis [3]. As for Ce 2 PdGa 12 , since Ce atoms separate PdGa 8/2 and Ga-only segments that stack along the c-axis, there are two distinct (Ce-Ce) c distances along the c-axis. Thus, the (Ce-Ce) ab interatomic spacing in Ce 2 PdGa 12 is 4.318(6) Å and (Ce-Ce) c distances measure 7.664(5) Å and 7.882(6) Å . For both compounds, one would expect the magnetic correlations in the ab-plane to be stronger than those along the c-axis.
Coupled with the comparable crystal structures and the similar Ce-Ce distances found in both compounds, CePdGa 6 and Ce 2 PdGa 12 are expected to share similar overall physical properties, that is, an antiferromagnetic ground state and metamagnetic transition under a field applied along the c-axis. On the other hand, there are still some differences between the two. The higher Ne´el temperature with ferromagnetic component and the smaller g for Ce 2 PdGa 12 may result from the difference of the number of Pd in the unit cell.
Ce-Ce distances are longer than the Hill limit, suggesting that Ce f moments interact through RKKY (Ruderman-Kittel-Kasuya-Yosida) interactions by hybridizing with conduction electrons of surrounding Ga atoms. Hybridization also induces the Kondo effect that should suppress the Ne´el order by competing with RKKY interactions. Reduced entropy (S$5000 mJ/mole-K) at T N in CePdGa 6, suggests that the Kondo effect is more pronounced in CePdGa 6 , suppressing T N further in comparison with Ce 2 PdGa 12 . However, the difference in the Ce-Ga hybridization should not be the main reason for the differences between the two compounds because the Ce-Ga interatomic distances are nearly the same for both compounds. Hence, it is likely that the Pd atoms affect the magnetic properties by providing carriers to the systems. Ce 2 PdGa 12 has one less Pd atom than ''Ce 2 Pd 2 Ga 12 '' (obtained by doubling the chemical formula of CePdGa 6 ). Generally, the decrease in the carrier number should result in two effects: (1) more localized nature of 4f electrons because of lack of screening by conducting carriers, and (2) proximity to the ferromagnetic state through RKKY interactions.  6. The magnetic portion of the specific heat, C m /T, of (a) Ce 2 PdGa 12 and (b) CePdGa 6 as a function of temperature are shown. The line serves as a guide for the eye. C m /T is obtained by subtracting the heat capacity of the La-analog (shown as white circles in inset) from the total heat capacity of each respective compound (shown as black circles in inset).

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The observed weaker Kondo effects along with ferromagnetic components in Ce 2 PdGa 12 are indeed consistent with the smaller number of carriers due to less Pd in comparison with CePdGa 6 .

Conclusion
We have synthesized Ce 2 PdGa 12 , which has a structure closely related to CePdGa 6 . Our magnetic and thermal measurements have revealed double magnetic transitions. An antiferromagnetic transition occurs at 11 K, while a ferromagnetic component in the ab-plane appears by means of a second transition at $5 K. This metamagnetic transition is most likely due to a spin flop interaction. Comparing the structures and magnetic behavior with those for CePdGa 6 , we argue that the f-electron state of Ce 2 PdGa 12 is more localized and close to a ferromagnetic state because the carrier density is decreased by the lack of Pd atoms. It would be interesting to further study the effects of layering and Pd carriers by synthesizing a compound such as ''Ce 3 PdGa 18 ''. This insertion of Ga layers between each 'CePdGa 6 layer' may allow us to tune the transition temperature further.
Crystallographic Information Available: Crystallographic information files are available for La 2 PdGa 12 and Ce 2 Pd Ga 12 .