Single crystal growth and heat capacity measurements of triangular lattice R2Pt6Ga15 (R =rare earth)

We have succeeded in synthesizing the single crystal of R2Pt6Ga15 (R=La-Nd, Sm- Lu) with hexagonal Sc0.67Fe2Si5-type structure using Ga self flux method. The crystal structure was confirmed by the powder X-ray method. The unit-cell volume V of R2Pt6Ga15 follows the lanthanide concentration except R = Ce, Eu and Yb, indicating that the valences of R = La, Pr, Nd, Sm, Gd-Tm, and Lu ion are trivalent, whereas those of R = Ce, Eu and Yb ion are deviate from trivalent. We have measured the specific heat C(T) of R2Pt6Ga15. It is found that the magnetic order takes place in R2Pt6Ga15 (R=Pr, Nd, Sm-Tm). Moreover, the multiple phase transitions were observed in R2Pt6Ga15 (R = Nd, Eu, Gd and Ho).


Introduction
In highly correlated f electron system, many anomalous physical properties have been discovered around the quantum critical point. Among the Yb member compounds, YbRh 2 Si 2 [1], β-YbAlB 4 [2] and quasi-crystal Au 51 Al 34 Yb 15 [3] exhibit anomalous quantum critical behaviors which cannot be explained by the conventional Hertz-Millis-Moriya (HMM) theory [4,5,6]. In YbRh 2 Si 2 , the magnitude of magnetic frustration effect can be important role to take place these critical behaviors . In rare earth compound, the magnetic ground state is explained by the competition between the Kondo effect and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, so-called Doniach phase diagram [7]. The magnetic frustration effect can also suppress to the magnetic order such like the Kondo effect. The quantum critical behavior due to the magnetic frustration effect in Ce 2 Pt 2 Pb [8] with Shastry -Sutherland lattice and YbAgGe [9] with distorted kagome lattice have been observed. To search for the compound with the magnetic frustration is possible to discover the novel quantum phenomena.
The R 2 Pt 6 X 15 (R = rare earth, X = Al, Ga) system with hexagonal Sc 0.67 Fe 2 Si 5 -type structure (space group P6 3 /mmc) would be one of the suitable candidate to research the magnetic frustrate system. The R ions coordinate the triangular lattice layer and the nearest R-R distance is about 4.3Å [10]. While, the distance between triangular-lattice layers is about 8.7Å along c-axis, which is more than twice as long as the in-plane R ion distance, namely the magnetic R-ions in R 2 Pt 6 Ga 15 form a two-dimensional triangular-lattice. In R 2 Pt 6 X 15 , R 2 Pt 6 Al 15 (R=Ce, Gd-Lu) [10,11,12,13,14,15] and R 2 Pt 6 Ga 15 (R=La, Ce, Pr) [16,17,18] have ever been reported. The lattice parameters of a and c of Ce 2 Pt 6 Ga 15 are 4.326 and 16.522 Å , respectively, whereas those of Yb 2 Pt 6 Al 15 are 4.266 and 16.361Å , respectively. It is possible to synthesize R 2 Pt 6 X 15 (R = heavy rare earth). Therefore, we have searched for new R 2 Pt 6 Ga 15 compound and measured the specific heat of R 2 Pt 6 Ga 15 .

Experimental
The single crystals of R 2 Pt 6 Ga 15 (R=La-Nd, Sm-Lu) were grown in Ga-flux method. Rare earth, Pt and Ga materials were placed in an alumina crucible and sealed in an evacuated quartz tube. The sealed tubes were heated to 1100 • C, soaked for 5 hours, then cooled down to 300 • C in 160 hours. The excess Ga was spun off in a centrifuge, and then washed out in distilled water. Figure 1 shows the photograph of obtained single crystal R 2 Pt 6 Ga 15 . Typical sample size is from 2 to 5 mm. The single phase of the hexagonal R 2 Pt 6 Ga 15 (R=La-Nd, Sm-Lu) structure was confirmed by the powder X-ray diffraction method. We obtained the lattice parameters of R 2 Pt 6 Ga 15 by Rietveld analysis. Figure 2 displays the lattice constants a, c, and unit-cell volume V of R 2 Pt 6 Ga 15 . V monotonously shrinks from R= La to Lu except R = Ce, Eu and Yb, indicating that the R 2 Pt 6 Ga 15 system follows the well-known lanthanide concentration except R = Ce, Eu and Yb. The results indicate that the valences of R = La, Pr, Nd, Sm, Gd-Tm and Lu ion are likely to be trivalent, while those of R = Eu and Yb ion are close to divalent.
The specific heat C(T ) measurement from 300 to 2 K was carried out by the relaxation method using a commercial physical property measurement system (PPMS; Quantum Design).  The temperature dependence of heat capacity C(T ) of R 2 Pt 6 Ga 15 .
The data of La 2 Pt 6 Ga 15 and Ce 2 Pt 6 Ga 15 were taken from Yamashita et al [18].

Results and discussion
We have measured the C(T ) of R 2 Pt 6 Ga 15 . Figure 3 shows the temperature dependence of C(T ) of R 2 Pt 6 Ga 15 (R=La-Nd, Sm-Lu) below 25 K. The C(T ) of La 2 Pt 6 Ga 15 and Ce 2 Pt 6 Ga 15 were taken from Yamashita et al [18]. There is no phase transition below 2 K for R 2 Pt 6 Ga 15 (R = La, Ce, Yb and Lu). The C(T ) of R 2 Pt 6 Ga 15 (R = La, Yb and Lu) follow C(T ) = γT + βT 3 expression in low temperature. The γ of Yb 2 Pt 6 Ga 15 and Lu 2 Pt 6 Ga 15 are 25 and 19 mJ/mol K 2 , It is found that there are anomalies of C(T ) due to the magnetic order in R 2 Pt 6 Ga 15 (R=Pr, Nd, Sm-Tm). Moreover, the multiple phase transitions were observed in R 2 Pt 6 Ga 15 (R = Nd, Eu, Gd and Ho). There is an anomaly in the magnetic susceptibility around the phase transition [19], indicating that the phase transitions are magnetic order. The magnetic order temperature T M corresponding to the middle point between the peak and the onset roughly follows the de Gennes scaling and T M in R 2 Pt 6 Ga 15 with R = light rare earth deviate from the de Gennes scaling, as shown in Fig. 4, where g J is the Lande g-factor and J is the total angular momentum and we assumed that the valence of Eu ion is divalent. This result and the order of T M are similar to that of RCu 2 Si 2 and RRhIn 5 with no geometrical frustration [20,21]. The suppression of T M due to the magnetic frustration effect in R 2 Pt 6 Ga 15 (R=Pr, Nd, Sm-Tm) would be negligible small. However, whether the magnetic frustration effect is strong or not is dependent to the magnetic structure of R 2 Pt 6 Ga 15 . If the magnetic structure of R 2 Pt 6 Ga 15 is XY-type, the magnetic frustration effect would be observed and the complex magnetic structure is possible. We are measuring the magnetic properties and intend to measure neutron diffraction of R 2 Pt 6 Ga 15 .