Single crystal growth and magnetic properties of pseudo-kagome lattice RRhPb (R = Nd, Sm and Gd)

We have synthesized single crystals of RRhPb (R = Nd, Sm and Gd) with hexagonal ZrNiAl-type structure from Pb-flux. The crystal structures were confirmed by powder X-ray diffraction and the compositions were determined by electron-probe micro-analyzer (EPMA). We have measured their magnetic properties of RRhPb. It is found that the RRhPb (R = Nd, Sm and Gd) are antiferromagnets with two successive phase transitions with magnetic ordering occuring at TN1 = 3.6 K and TN2 = 3.4 K in NdRhPb, TN1 = 11.5 K and TN2 = 8.3 K in SmRhPb and TN1 = 17.6 K and TN2 = 15.3 K in GdRhPb.


Introduction
Rare earth and actinide intermetallic compounds with the hexagonal ZrNiAl-type structure (RTX : R=rare earth, actinide, T =transition metal, X=Al, Ga, In, Sn and Pb) are one of the extensively studied systems [1,2]. The R-T (1) layer and T (2)-X layer are stacked along c-axis as shown in Fig. 1. The R ion of the R-T (1) layer coordinates a psudo-kagome lattice possessing geometrical frustration. The typical 120 • array of magnetic moments observed in TbNiIn, DyNiIn, YbAuIn, DyAuIn and ErAuIn arises from this frustration [3,4].
In heavy fermion systems, interesting magnetic order has been found. CePdAl is a heavy fermion antiferromagnet with antiferromagnetic temperature T N = 2.7 K and specific heat coefficient γ = 250 mJ/mol K 2 [5]. The magnetic structure of CePdAl consists of three inequivalent Ce sites. The magnetic ordering vector q = (1/2, 0, τ ) where τ 0.35 weakly depends on temperature. Two-thirds of the Ce ions order while one-third does not order below T N . The magnetic structure is considered to originate from the geometrical frustration [6].
The search for new compounds with ZrNiAl-type structure is motivated by the possible discovery of new physical phenomena due to the geometrical frustration. Until now, there are few studies on RT Pb systems [7,8,9,10] and physical properties have been only reported for CeT Pb (T = Pd, Rh and Pt). This prompted the study of single crystal growth and physical properties of RRhPb (R = Nd, Sm and Gd) reported here.

Experimental
The single crystals of RRhPb (R = Nd, Sm and Gd) were grown from Pb-flux. 3N (99.9 ) R = Nd, Sm and Gd, 4N Rh, and 5N Pb were reacted in with starting composition of 1:1:10. These materials were placed in an alumina crucible and sealed in an evacuated quartz tube. The sealed tubes were heated to 1150 • C, soaked for 12 hours, then cooled down to 700 • C in 90 hours. The excess Pb was spun off in a centrifuge.
The single phase of the hexagonal ZrNiAl-type structure was confirmed by powder X-ray diffraction. The powder was obtained from crashed single crystals. Figure 2 shows the powder X-ray diffraction patterns of the RRhPb. We mixed in Si powder as a standard. The X-ray diffraction patterns gave a = 7.706Å, c = 3.951Å for NdRhPb, a = 7.695Å c = 3.876Å for SmRhPb, and a = 7.697Å, c = 3.826Å for GdRhPb. The crystal compositions and homogeneity were determined by using an electron-probe microanalyzer with wavelength dispersive spectrometers (EPMA-WDS; JEOL-8530). We used NdB 6 , SmB 6 , Gd 3 Ga 5 O 12 , Rh and PbF 2 as standard reference materials for EPMA. The chemical compositions were determined to be Nd:Rh:Pb = 1.00:1.02:1.04, Sm:Rh:Pb = 1.00:0.93:0.96 and Gd:Rh:Pb = 1.00:1.05:1.06, which were in good agreement with the ideal 1:1:1 stoichiometry.
The magnetic properties were measured by using a commercial superconducting quantum interference device magnetometer (Quantum Design). Figure 3 shows the reciprocal magnetic susceptibility 1/χ(T ) of NdRhPb as a function of temperature at 0.1 T. Above 70 K, 1/χ(T ) can be fit by a Curie-Weiss law. We estimated that the effective moment µ eff and Weiss temperature θ p are 3.78 µ B and -1 K for H || c, and 3.83 µ B and -55 K for H || a respectively, indicating that the effective moment is close to the value expected for Nd +3 configuration (µ eff = 3.62 µ B ). χ(T ) has a broad kink around T M1 = 3.6 K and a maximum at T M2 = 3.4 K for H || a. On the other hand, χ(T ) has a maximum T M1 = 3.6 K but anomaly not observed at T M2 = 3.4 K for H || c. The decreasing of χ(T ) below T M1 for H || c is about 5 times larger than that for H || a, indicating that the NdRhPb is an antiferromagnet with two successive transition and an Ising-like magnetic structure.  Figure 4 shows the reciprocal magnetic susceptibility of SmRhPb as a function of temperature at 1 T. χ(T ) can not be fit with the susceptibility using a modified Curie-Weiss law χ = χ 0 + C/(T − θ p ) because the parameters were not fixed. We need to estimate the energy level splitting and the valence of Sm-ion in SmRhPb. The χ(T ) has a maximum at T M1 = 11.5 K and a kink at T M2 = 8.3 K for H || c. For H || a, χ(T ) has two anomaly at T M1 and T M2 and χ(T ) is almost independent to the temperature below T M2 , indicating that the magnetic hard axis would be around c-axis. Figure 5 shows 1/χ(T ) of GdRhPb measured in 0.1 T. Above 50 K, 1/χ(T ) can be fit with a Curie-Weiss law. We estimated that the µ eff and θ p are 8.04 µ B and 9 K for H || c, and 8.06 µ B and 10 K for H || a, respectively, indicating that the magnetic anisotropy is weak. The effective moment is close to the value expected for Gd +3 (µ eff = 7.94 µ B ). A peak at T M1 = 17.6 K and a weak drop at T M2 = 15.3 K for H || c and a are observed.

Results and discussion
We have measured the magnetic properties of RRhPb (R=Nd, Sm and Gd). We summarized the results in table 1. It is found that the RRhPb (R = Nd, Sm and Gd) are antiferromagnets with two successive phase transitions. The successive transitions with ZrNiAl-type structure have been observed in PrNiAl, NdPdAl, NdNiAl, YbAgGe, and so on [11,12,13,14]. These double transitions appear to be a common phenomena in ZrNiAl-type structure.
This structure has the geometrical frustration. Therefore the suppression of T M is expected, especially strong for SmRhPb because of its magnetic structure. The   Lande g-factor and J is the total angular momentum), namely the suppression of T M in SmRhPb is not strong. The |θ p |/T M is less than 1, except for NdRhPb for H || a (probably due to the uniaxial magnetic anisotropy). The effect of geometrical frustration in RRhPb (R = Nd, Sm and Gd) appears to be negligible.

Conclusion
We have succeeded in growing the single crystals of RRhPb (R=Nd, Sm and Gd) using Pb-flux. We have confirmed the crystal structures of RRhPb (R=Nd, Sm and Gd) using powder X-ray diffraction. The RRhPb (R = Nd, Sm and Gd) are antiferromagnets with two successive phase transitions. The magnetic transitions occur at T N1 = 3.6 K and T N2 = 3.4 K in NdRhPb and appear Ising-like. The magnetic transitions take place at T N1 = 11.5 K and T N2 = 8.3 K in SmRhPb with magnetic hard axis c. GdRhPb exhibits magnetic transitions at T N1 = 17.6 K and T N2 = 15.3 K. The effect of geometrical frustration in RRhPb (R = Nd, Sm and Gd) appears to be negligible.