Crystal Growth, Structure, Magnetic, and Transport Properties of TbRhIn5

Single crystals of TbRhIn 5 were synthesized using the flux growth method. TbRhIn 5 adopts the HoCoGa 5 structure type and crystallizes in the space group P4/mmm, Z ) 1. Lattice parameters are a ) 4.6000(6) Å, c ) 7.4370(11) Å, and V ) 157.29(6) Å 3 . Transport measurements show that TbRhIn 5 is metallic (d F /dT > 0). A sharp antiferromagnetic transition is observed at T N ) 48 K in the susceptibility data for TbRhIn 5 , which is highly anisotropic when the field is oriented along the c axis and a - b plane of the crystal and has an average effective moment of 9.72 (cid:237) B /Tb 3 + .


Introduction
][3][4][5][6][7][8][9][10] Heavy fermions show normal metallic behavior at room temperature, while at lower temperatures, the conduction electrons begin to screen the magnetic moment, resulting in effective masses approximately 2 orders of magnitude higher than that of a free electron.Since the effective mass of an electron is proportional to the electronic specific heat (γ), a large Sommerfeld coefficient (>100 mJ/mol K 2 ) may be observed. 2cently, these compounds have been reviewed and summarized. 11][14] The rare earth ions in intermetallic compounds are well separated, so that any direct exchange between two neighboring f shells is negligible. 15,16Because of their metallic nature, however, the magnetic interaction between two such ions can take place via the polarization of the conduction band electrons, as in the case of the elemental rare-earth metals.This Ruderman-Kittel-Kasuya-Yoshida (RKKY) indirect exchange interaction is responsible for cooperative magnetic ordering. 15The competition between Ruderman-Kittel-Kasuya-Yoshida (RKKY) interactions and the Kondo effect (the progressive screening of the magnetic moments by the conduction electrons at low temperatures) is important because the heavy fermion state is formed when the Kondo effect overcomes the RKKY interaction. 17eMIn 5 (M ) Co, Rh, Ir) is a special class of heavy fermion materials which show magnetic ordering and unconventional superconductivity at low temperatures. 18,19he coexistence of magnetism and superconductivity is quite unusual and, in fact, is magnetically mediated.Heavy fermion intermetallic compounds which show both magnetic ordering and superconductivity are of interest because they present the opportunity to study the competition or coexistence between the two mechanisms.
The crystal structure of CeMIn 5 (M ) Co, Rh, Ir), 20,21 which adopts the HoCoGa 5 -structure type, 22 consists of alternating layers of CeIn 3 and MIn 2 layers stacked along the c axis.Bulk CeIn 3 is a heavy fermion antiferromagnet which exhibits pressure-induced superconductivity. 23Ce-CoIn 5 (γ ≈ 290 mJ/mol of Ce K 2 ,) 24 under ambient conditions, has the highest superconducting transition temperature (T c ) 2.3 K) reported for any heavy fermion compound. 18The magnetization of CeCoIn 5 is highly anisotropic, exhibiting a weak metamagnetic transition around 4.2 T along the c axis, while it gradually increases along the a-b plane. 25CeRhIn 5 orders antiferromagnetically at T N ) 3.8 K and becomes superconducting at 2 K upon the application of >16 kbar of pressure with a γ ≈ 420 mJ/mol of Ce K 2 . 18CeIrIn 5 , under ambient conditions, has the largest Sommerfeld coefficient for the series with γ ≈ 750 mJ/mol of Ce K 2 . 26The superconducting temperature of CeIrIn 5 is 0.4 K, however there is a resistivity drop at 1.2 K, of which there is debate about the mechanism responsible for the decrease in resistivity. 18Upon the application of pressure, the transition temperature at 0.4 K increases to a maximum value of ∼1 K at approximately 15 kbar.The highest ordering temperatures reported for this class of compounds are those observed in GdRhIn 5 and GdIrIn 5 which order antiferromagnetically at Ne ´el temperatures of 40 and 42 K, respectively. 27,28Reduced spatial dimensionality and magnetic anisotropy, as a function of the rare-earth element, have been observed in LnRhIn 5 (Ln ) Ce, Nd, Sm, Gd).In an effort to further study the effects of magnetic anisotropy in Kondo systems, we were prompted to study TbRhIn 5 .In this manuscript we compare the structure, transport, and physical properties of single crystals of TbRhIn 5 with other magnetic analogues, CeRhIn 5 , SmRhIn 5 , NdRhIn 5 , and GdRhIn 5 .

Experimental Section
Synthesis.Tb pieces, Rh powder, and In shot (Alfa Aesar), all with stated purities of g99.9%, were combined in an atomic ratio of 1:1:20.The starting materials were then placed into an alumina crucible and sealed in an evacuated fused silica tube.The sealed sample was then gradually heated from room temperature to 1373 K at a rate of 473 K/h for 2 h, then slowly cooled at 281 K/h to 923 K, at which point the excess flux was removed via centrifugation.Synthesis yielded aggregates of layered crystals exhibiting a metallic luster as shown in Figure 1.
Single-Crystal X-ray Diffraction.A 0.025 × 0.025 × 0.075 mm 3 single-crystal fragment was placed on a glass fiber and mounted on the goniometer of a Nonius Kappa CCD diffractometer equipped with Mo KR radiation (λ ) 0.71073 Å).Data were collected at 293(2) K.Additional data collection and crystallographic parameters are presented in Table 1.
The structures were solved with the SHELXL software package 29 using CeRhIn 5 as a structural model.The atomic displacement parameters were treated anisotropically, and an extinction coefficient was applied to the data after a final least-squares cycle.The atomic coordinates and displacement parameters are provided in Table 2, and selected interatomic distances are listed in Table 3.
0.0833 params 12 ∆F max(e Å -3 ), ∆Fmin(e Å -3 ) 3.24, -4.52 extinction coeff 0.0066( 7) Physical Property Measurements.Magnetic properties were measured on single crystals using a Quantum Design (SQUID) magnetometer.The temperature-dependent susceptibility was measured in an applied field of 1000 G up to room temperature after being cooled to 2 K under zero magnetic field.Field-dependent magnetization data were also collected from zero field to 10 T at 2 K.The resistivity (down to 2 K) data were measured using a standard four-probe method with a Quantum Design physical property measurement system (PPMS) at ambient pressure.Specific heat data was determined using the thermal transport option on the PPMS.The heat capacity of the TbRhIn 5 was measured at zero field in the temperature range of 300-0.36K. Single crystals of the nonmagnetic analogue, LaRhIn 5 which were used for heat capacity measurements, were also grown using the flux method at Los Alamos National Lab (LANL).

Results and Discussion
TbRhIn 5 is isostructural to the CeMIn 5 (M ) Co, Rh, Ir) compounds which adopt the HoCoGa 5 -type structure (P4/ mmm). 22The structure consists of four atoms in the asymmetrical unit: Tb, Rh, In1, and In2 atoms occupying the 1a, 1b, 1c, and 4i Wycoff positions, respectively.Figure 2 shows the crystal structure of TbRhIn 5 which consists of alternating layers of TbIn 3 cuboctahedra and RhIn 2 rectangular prisms that contain two independent indium sites, In1 and In2.The coordination of Tb in the cuboctahedra is 8-fold to In1 and 4-fold to In2 with distances of 3.2140(12) and 3.2527(4) Å, respectively.These distances are in good agreement with the Tb-In interatomic distances in the binary compounds, Tb 2 -In and TbIn 3 , in which the Tb-In distances range from 3.025 to 3.359 Å. 30 In CeCoIn 5 , the cuboctahedra are elongated along the c axis, while a shortening of the c axis is observed in the Ir analogue.The ratio of Ce-In2/Ce-In1 in CeRhIn 5 is close to unity, indicating that the cuboctahedra are not distorted. 31he ratio of Tb-In2/Tb-In1 is 1.014, suggesting that the cuboctahedra in TbRhIn 5 are quite symmetrical.
The Rh atom is coordinated to eight In2 atoms and forms the edge of the neighboring rectangular prism.The Rh-In2 distance in TbRhIn 5 is 2.7316(9) Å and is comparable to the Rh-In2 distances of 2.7572(3) Å observed in LaRhIn 5 , as well as the summation of the atomic radii for rhodium and indium. 31The In1-In2 and In1-In1 interatomic distances in TbRhIn 5 are 3.2140 (12) and 3.2527(4) Å, respectively, which are in good agreement with the values observed in RhIn 32 and RhIn 3 , 33,34 ranging from 3.200 to 3.580 Å.
Physical Properties.The temperature dependence of the magnetic susceptibility of TbRhIn 5 is shown in Figure 3 for the field (1000 G) both along the c axis and in the a-b plane.A large anisotropy in the susceptibility data is observed.A sharp antiferromagnetic transition appears at 48 K. Above T N , the inverse susceptibility obeys the Curie-Weiss law and is well fit by [1/χ(T) ) (Tθ)/C] in the temperature range of 80-300 K.We find an average effective moment of ∼9.72 µ B /Tb 3+ ion along the c axis and the a-b plane with Weiss temperatures of θ ) -75 and -5 K, respectively.The effective moment is in agreement with the full Hund's moment for Tb 3+ which is 9.72 µ B. The negative θ values indicate antiferromagnetic correlations, which are quite strong along the c axis.
Figure 4 shows the field-dependent magnetization of TbRhIn 5 at 2 K along the c axis and the a-b plane up to 7 T.The magnetization increases with field up to 7 T with induced moments at the maximum field equal to 1. 18   a Ueq is defined as one-third of the trace of the orthogonalized Uij tensor.

Properties of TbRhIn 5
Inorganic Chemistry, Vol.45, No. 12, 2006 4639 that 7 T is not a significant field to induce saturation of the magnetic moments in TbRhIn 5 .These values are significantly smaller than the full Hund's saturation moment of 9 µ B expected for a Tb 3+ ion.The temperature dependence of the electrical resistivity of a single crystal of TbRhIn 5 is shown in Figure 5. TbRhIn 5 is metallic (dF/dT > 0) and has a residual resistivity ratio (RRR) of 6.A kink in the resistivity is observed near the ordering temperature at 48 K, consistent with a reduction in the spin-disorder scattering.Above T N , the resistivity increases linearly with temperature.The small downturn at 3.4 is caused by some residual In flux in the sample.
Figure 6 shows the temperature dependence of the specific heat, C p , for TbRhIn 5 .At zero field, a large cusp is observed at ∼48 K which is consistent with the antiferromagnetic transition observed in the susceptibility.The specific heat can be described by the equation C p ) γT + RT 3 , where γ is the Sommerfeld coefficient and R is the phonon contribution to the total specific heat.The phonon contribution is negligible at low temperatures, which allows the electronic contribution to the specific heat to be determined experimentally.The f electron contribution to the specific heat, C/T m (Figure 6), is obtained by subtracting the phonon contribution C/T of LaRhIn 5 .Since LaRhIn 5 does not contain any f electrons, it is a good approximation of the lattice contribution to the specific heat.The specific data in TbRhIn 5 is similar to other antiferromagnetic LnMIn 5 materials.Several mechanisms act simultaneously to produce the specific heat data as shown in Figure 6.There is a large nuclear Schottky contribution at low temperatures (below 2K).It results from the hyperfine interaction between the 4f electrons and the Tb 3+ nuclei, which carry a nuclear spin moment of I ) 3/2.There is a possible Schottky anomaly resulting from the crystalline electric field (CEF) at 11 K as shown in Figure 7, and there is a large peak at 48 K from    In summary, TbRhIn 5 has been synthesized using flux methods and is isostructural to the well-studied CeRhIn 5 .The magnetic moments of CeRhIn 5 form an incommensurate spiral along the c axis, 26,35 and although CEF anisotropy energetically favors the moments to point along the c axis, the magnetic moments have been found to lie in the a-b plane. 36Thus there may be competition between the two magnetic interactions, since we observe a 50% decrease in T N for CeRhIn 5 in comparison to the parent compound CeIn 3 .
In contrast, the easy axis of magnetization in TbRhIn 5 (T N ) 47 K) is along the c axis; therefore, T N is enhanced nearly 24% compared to that in TbIn 3 (T N ) 36 K). 37 In addition, the enhanced T N indicates that RKKY interactions are more dominant than the Kondo effect in this compound because we observe more interaction between the uncompensated rare-earth ions.The magnetic susceptibility of GdRhIn 5 is only significantly anisotropic below T N showing an easy axis of magnetization in the plane.Furthermore, CeRhIn 5 becomes superconducting under 16 kbar of mechanical pressure, but the superconducting state diminishes at ∼25 kbar.The size of the atomic radii of Ce 3+ versus Tb 3+ decreases by ∼3.4% because of lanthanide contraction.Multiplying 16 kbar by 3.4% gives an estimated molecular pressure for TbRhIn 5 of ∼25 kbar, at which point the superconducting state diminishes in CeRhIn 5. 21 The magnetic-ordering temperature of TbRhIn 5 scales in accordance with the de Gennes factor [(g J 2 -1)][J(J + 1)] of LnRhIn 5 (Ln ) Ce, Nd, Sm, Gd) for a ground-state multiplet, J, through the rare earths, with a T N of 3.8-48 K for the Ce and Tb analogues.Although TbRhIn 5 is not a heavy fermion superconductor, it does have strong antiferrromagnetic correlations resulting in an ordering temperature much higher than its heavy fermion analogue CeRhIn 5 .It would be interesting to do a doping study by substituting Ce for Tb in TbRhIn 5 to observe how the heavy fermion superconducting state develops out of a strong antiferromagnet.

Table 3 .Figure 2 .
Figure 2. Structure of TbRhIn5 consisting of layers of TbIn3 cuboctahedra (gray).alternating with layers of RhIn2, in which the Rh and In atoms are designated as black and white closed circles, respectively.

Figure 3 .
Figure 3. Temperature-dependent magnetic susceptibility (χ) of TbRhIn5 along the a-b plane (open circles) and c axis (closed circles) measured at 1000 G.

Figure 4 .
Figure 4. Field-dependent magnetization of TbRhIn5 along the a-b plane (open circles) and c axis (closed circles) measured at 2 K.

Figure 6 .
Figure 6.Specific heat of TbRhIn5 (closed circles) and LaRhIn5 (open circles).The f electron contribution of Tb is denoted with open triangles.

Table 2 .
Atomic Positions and Thermal Parameters of TbRhIn5