Six closely related YbT₂Zn₂₀ (T = Fe, Co, Ru, Rh, Os, Ir) heavy fermion compounds with large local moment degeneracy

Abstract

Heavy fermion compounds represent one of the most strongly correlated forms of electronic matter and give rise to low temperature states that range from small moment ordering to exotic superconductivity, both of which are often in close proximity to quantum critical points. These strong electronic correlations are associated with the transfer of entropy from the local moment degrees of freedom to the conduction electrons, and, as such, are intimately related to the low temperature degeneracy of the (originally) moment bearing ion. Here we report the discovery of six closely related Yb-based heavy fermion compounds, YbT₂Zn₂₀, that are members of the larger family of dilute rare earth bearing compounds: RT₂Zn₂₀ (T = Fe, Co, Ru, Rh, Os, Ir). This discovery doubles the total number of Yb-based heavy fermion materials. Given these compounds' dilute nature, systematic changes in T only weakly perturb the Yb site and allow for insight into the effects of degeneracy on the thermodynamic and transport properties of these model correlated electron systems.

Heavy fermion compounds have been recognized as one of the premier examples of strongly correlated electron behavior for several decades. Ce- and U-based heavy fermion compounds have been well studied, and in recent years a small number of Yb-based heavy fermions have been identified as well (1–3). Unfortunately, in part due to the somewhat unpredictable nature of 4f ion hybridization with the conduction electrons, it has been difficult to find closely related (e.g., structurally) heavy fermion compounds, other than of the ThCr₂Si₂ structure, especially Yb-based ones, that allow for systematic studies of the Yb ion degeneracy. Part of this difficulty is associated with the fact that the 4f hybridization depends so strongly on the local environment of the rare earth ion.

Dilute, rare earth (R) bearing, intermetallic compounds are ordered materials with <5 atomic percent rare earth fully occupying a unique crystallographic site. Such materials offer the possibility of investigating the interaction between conduction electrons and 4f electrons in fully ordered compounds for relatively low concentrations of rare earths. For the case of R = Yb or Ce, these materials offer the possibility of preserving low temperature, coherent effects while more closely approximating the single ion Kondo impurity limit. A very promising example of such compounds is derived from the family of RT₂Zn₂₀ (4) (T = transition metal), which has recently been shown to allow for the tuning of the nonmagnetic R = Y and Lu members to exceedingly close to the Stoner limit as well as allowing for the study of the effects of such a highly polarizable background on local moment magnetic ordering for R = Gd (5).

Discovery

Here, we present thermodynamic and transport data on six strongly correlated Yb-based intermetallic compounds found in the RT₂Zn₂₀ family for T = Fe, Co, Ru, Rh, Os, and Ir, effectively doubling the number of known Yb-based heavy fermions (compounds with linear coefficient of specific heat, γ, >400 mJ/mol K²; ref. 1). The RT₂Zn₂₀ compounds crystallize in the cubic CeCr₂Al₂₀ (Fd3̄m space group) structure (6, 7). Due to the relatively low concentration of rare earth, as well as transition metal, in these compounds, the four nearest neighbors as well as the 12 next-nearest neighbors of the rare earth ion are Zn atoms. The rare earth ion is coordinated by a 16-atom Frank–Kasper polyhedron and has a cubic point symmetry. This near spherical distribution of neighboring Zn atoms gives rise to the possibility of relatively low crystal-electric-field (CEF) split levels and also promises a large degree of similarity between this isostructural group of Yb-based heavy fermions. These compounds, then, not only greatly expand the number of known Yb-based heavy fermions, but, as will be shown below, also provide a route to studying how the degeneracy of the Yb ion at Kondo temperature, T_K, effects the low temperature-correlated state.

Thermodynamic and transport data taken on the six YbT₂Zn₂₀ compounds are presented in Figs. 1–3 and are summarized in Table 1. Whereas the temperature-dependent magnetic susceptibility, electrical resistivity, and specific heat for T = Fe, Ru, Rh, Os, and Ir are qualitatively similar, YbCo₂Zn₂₀ is, at first glance, somewhat different. Most conspicuously, instead of manifesting a clear loss of local moment behavior at low temperature (8), the temperature-dependent susceptibility continues to be Curie–Weiss-like down to 2 K (Fig. 1a Inset).

Fig. 1.

Low temperature thermodynamic properties of YbT₂Zn₂₀ compounds (T = Fe, Ru, Rh, Os, Ir). (a) Magnetic susceptibility (H = 0.1 T). (Inset) Temperature-dependent inverse susceptibility for YbCo₂Zn₂₀ and YbOs₂Zn₂₀. (b) Low temperature-specific heat, C, divided by temperature, as a function of T².

Fig. 2.

Temperature-dependent electrical resistivity of YbT₂Zn₂₀ compounds (T = Fe, Co, Ru, Rh, Os, Ir). (Inset) Low temperature electrical resistivity as a function of T² for T = Fe, Ru, Rh, Os, Ir; note separate axes for T = Os on top and right.

Fig. 3.

Low temperature electrical resistivity and C/T of YbCo₂Zn₂₀ as a function of T².

Table 1.

Summary of structural, thermodynamic, and transport data on YbT₂Zn₂₀ compounds (T = Fe, Co, Ru, Rh, Os, Ir)

T	a, Å	θ, K	μeff, μB	χ0, $\frac{{10}^{-3}c{m}^3}{mole}$	χmax, $\frac{{10}^{-3}c{m}^3}{mole}$	Tχmax, K	ρ0, μΩ cm	A, $\frac{\mu \Omega \mathrm{cm}}{K^2}$	RRR	γ, $\frac{\mathrm{mJ}}{\mathrm{mol}{K}^2}$	WR	KWR, $\frac{\mu \Omega \mathrm{cm}{\mathrm{mole}}^2{K}^2}{{\mathrm{mJ}}^2}$	N	TK, K
Fe	14.062	−22.6	4.5	58.0	65.1	14.0	2.1	5.4 × 10−2(T ≤ 11 K)	31.2	520	1.2	2.0 × 10−7	8	33
Co	14.005	−4.3	4.3	415.1			21	165 (T ≤ 0.2 K)	2.8	7,900		27 × 10−7	4	1.5
Ru	14.193	−15.5	4.5	58.9	65.4	13.5	5.3	6.8 × 10−2 (T ≤ 11 K)	10.9	580	1.1	2.0 × 10−7	8	30
Rh	14.150	−15.9	4.4	77.7	82.4	5.3	5.6	54 × 10−2 (T ≤ 6 K)	11.8	740	1.3	10.1 × 10−7	4	16
Os	14.205	−19.18	4.5	60.0	60.7	11.5	17	53 × 10−2 (T ≤ 1 K)	4.4	580	1.1	15 × 10−7	4	20
Ir	14.165	−23.8	4.4	55.9	56.3	6.5	8.8	33 × 10−2 (T ≤ 5 K)	8.9	540	1.2	11 × 10−7	4	21

Shown are cubic lattice parameter, a; paramagnetic Curie–Weiss temperature, Θ, and effective moment, μ_eff, obtained from fit to inverse susceptibility between ≈100 and 300 K (after substraction data from the nonmagnetic analogues, LuT₂Zn₂₀); low temperature magnetic susceptibility, χ₀ taken at 1.8 K; magnetic susceptibility at the maximum, χ_max and corresponding temperature, Tχ_max; residual resistivity, ρ₀, taken at T ≈20 mK; coefficient of the T² resistivity, A (with range of fit given below); residual resistivity ratio, RRR; linear coefficient of the specific heat, γ; Wilson ratio, WR; Kadowaki–Woods ratio, KWR; degeneracy, N; and estimated Kondo temperature, T_K.

Focusing initially on the five, apparently similar, YbT₂Zn₂₀ compounds (T = Fe, Ru, Rh, Os, Ir), Fig. 1 a and b demonstrates that each of these compounds appears to be an excellent example of a Yb-based heavy fermion with electronic specific heat, γ, values ranging between 500 and 800 mJ/mole K². [The modest rise in the ΔC(T)/T data below 2 K is most probably associated with a nuclear Schottky anomaly and, for this work, is simply ignored. This assumption is further supported by the data and analysis presented in Fig. 5 below.] The low temperature magnetic susceptibility correlates well with the electronic specific heat values leading to the Wilson ratio (1, 2) for these five compounds having values of 1.1 and 1.3 (see Table 1). The temperature-dependent electrical resistivity data (Fig. 2) for these five compounds are also remarkably similar at high temperature and manifest clear T² temperature dependencies at low temperatures (see Inset). Although resistivity data were taken down to 20 mK, no indications of either magnetic order or superconductivity were found for any of the YbT₂Zn₂₀ compounds.

Fig. 5.

Coqblin–Schrieffer analysis of magnetic specific heat data from YbFe₂Zn₂₀ (a) and YbRh₂Zn₂₀ (b) after subtraction data from the nonmagnetic analogues, LuFe₂Zn₂₀ and LuFe₂Rh₂₀, respectively. Data are shown as open symbols and best fits to J = 1/2, 3/2, 5/2, and 7/2 using formalism described in ref. 8 are shown in black, red, green, and blue lines, respectively. T_K values from these fits are ≈37 K and ≈15 for YbFe₂Zn₂₀ and YbRh₂Zn₂₀, respectively. For YbRh₂Zn₂₀, the Schottky contribution (ΔE₁ = 40 K) is shown as a dashed red line; the sum of Schottky and Rajan (J = 3/2) terms is shown as a solid black line.

The thermodynamic and transport properties of YbCo₂Zn₂₀ are somewhat different from the other five compounds. YbCo₂Zn₂₀ does not manifest the clear loss of local moment behavior, >1.8 K, in the susceptibility data (see Fig. 1a Inset) and the electrical resistivity and the specific heat only manifest Fermi-liquid-like behavior for T ≤ 0.2 K (Fig. 3). Although the higher temperature electrical resistivity of YbCo₂Zn₂₀ is similar to the other five YbT₂Zn₂₀ compounds, it manifests a much clearer example of a resistance minimum and lower temperature coherence peak.

Analysis

Some of the salient parameters extracted from these data are summarized in Table 1 and the coefficient of the T² resistivity (A) is plotted as a function of the linear coefficient of the specific heat (γ) in a Kadowaki–Woods (KW) (8–10) type plot (Fig. 4). Perhaps the most noteworthy point that becomes clear from this presentation of the data is that, whereas there is relatively little variation in the low temperature thermodynamic properties, or Wilson ratio, associated with the T = Fe, Ru, Rh, Os, Ir compounds, there is an order of magnitude variation in the value of the coefficient of the T² resistivity, A. This gives rise to a vertical spread of the KW data points.

Fig. 4.

Log–log plot of A versus γ (Kadowaki–Woods plot) of six new YbT₂Zn₂₀ heavy fermion compounds (T = Fe, Co, Ru, Rh, Os, Ir) shown with representative data from ref. 11 as well as data for YbBiPt (12, 13), YbNi₂B₂C (14), YbPtIn (15), YbAgGe (16), YbNiSi₃ (17), and YbIr₂Si₂ (18). The solid lines for degeneracies N = 2, 4, 6, and 8 are taken from ref. 11.

Recent theoretical work (11, 19, 20) has generalized the idea of a fixed KW ratio to one that can vary by over an order of magnitude, depending upon the value of the degeneracy of the Yb ion when it hybridizes. Fig. 4 shows, as solid lines, the four degeneracies possible for the Kramers, Yb³⁺ ion. The YbT₂Zn₂₀ data indicate that for T = Fe, Ru the Yb ion has a significantly larger degeneracy upon entering the Kondo-screened state than it does for the T = Rh, Os, Ir compounds. The data point for YbCo₂Zn₂₀ approaches the far extreme of the KW plot, being near to the point associated with the exceptionally heavy fermion, YbBiPt (12, 13).

As mentioned above, the sole Yb site is one of cubic point symmetry and is surrounded only by Zn in a shell of very high coordination number. Based on these facts, it is anticipated that the Yb ion's Hund's rule, ground state multiplet will split into a quartet and two doublet states with a small total splitting. If, indeed, the difference between YbFe₂Zn₂₀ and YbRu₂Zn₂₀ on one hand and YbRh₂Zn₂₀, YbOs₂Zn₂₀ and YbIr₂Zn₂₀ on the other is the degree to which the Hund's rule ground state degeneracy has been lifted by crystalline electric field splitting before the Kondo screening takes place, then there should be some indication of this in other data as well. If, as Tsujii et al. suggest (11), the ratio of T_K to T_CEF is of primary concern, then an examination of Fig. 1a in the light of the Coqblin–Schrieffer model (refs. 8 and 21, specifically figure 1 of ref. 8) indicates that the larger the ratio of the maximum susceptibility to the low temperature susceptibility, the larger is the degeneracy that remains in the Yb system at T_K. The ratios of the maximum susceptibility to the low temperature susceptibility for T = Fe and Ru are 1.12 and 1.11, respectively, whereas the ratios for T = Rh, Os, and Ir are 1.06, 1.01, and 1.01, respectively. These values are consistent with a difference in degeneracy of at least ΔN = 2 (see Fig. 4).

This analysis can be made even more thoroughly by performing a fit (8) to the magnetic component of the specific heat over a wide temperature range. This is shown in Fig. 5a for YbFe₂Zn₂₀, the compound with the largest degeneracy inferred from the KW plot (Fig. 4) as well as from the above analysis. The data are best fit (and very well fit) by the J = 7/2 (N = 8) curve. These data are particularly compelling because the height of the anomaly is not an adjustable parameter once N is chosen. This analysis further confirms the degeneracy inferred from Fig. 4 and confirms that the low temperature, greatly enhanced, electronic specific heat is due to Kondo screening of the large N, Yb ion. Fig. 5a Inset shows the magnetic entropy as a function of temperature. By 60 K, it rises past the J = 5/2 value. The fact that it does not reach the Rln8 anticipated is most likely due to (i) difficulties in accurately modeling the nonmagnetic contribution with LuFe₂Zn₂₀ at high temperatures and (ii) difficulties associated with taking the difference between two large, comparable values, as well as the fact that by 60 K a recovery of the full Rln8 is not expected (see fit to J = 7/2 in Fig. 5a).

Fig. 5b presents similar data from YbRh₂Zn₂₀, one of the compounds that the KW analysis predicts to have a lower degeneracy. The maximum in the magnetic specific heat data falls between the J = 3/2 and J = 5/2 values, indicating that the CEF splitting scheme will not allow the very simple type of analysis on which refs. 8 and 21 are premised: i.e., one that has the CEF levels either at T ≪ T_K or T ≫ T_K. These data can be well fit, though, by the addition of a Schottky anomaly associated with a T ≥ T_K CEF level. The low temperature part of the specific heat data can be well fit by assuming that a quadruplet is Kondo screened and that there is a doublet CEF level located at 40 K. The sum of the Kondo screened quadruplet and the Schottky anomaly associated with the 40 K doublet are shown as the solid line. Taken together, Figs. 4 and 5 indicate that the large electronic specific heat values shown in Fig. 1 are due to Kondo screening and that the degeneracies for the YbT₂Zn₂₀ compounds are most probably N = 8 for T = Fe, Ru and N = 4 for T = Os, Co, Rh, Ir.

Given the above analyses, Figs. 4 and 5 can be used to infer approximate degeneracies for the Yb ion in these YbT₂Zn₂₀ compounds (see Table 1). We can then infer a value of T_K by using T_K = (RlnN)/γ (22) or by using T_K = (N − 1)π²Rw_N/3Nγ (where w_N is a multiplicative factor that is a function of N as discussed in ref. 21). These expressions produce T_K values that are within 5% of each other for 2 ≤ N ≤ 8. It should also be noted that the T_K value estimated by this method is close to that found by fitting the whole C_p curve (see Fig. 5). As could be anticipated, T_K values for T = Fe and Ru are indeed larger than those found for T = Rh, Os, Ir.

Given that our earlier work on the RT₂Zn₂₀ families has shown that T = Fe and Ru compounds manifest anomalously high temperature, local moment ordering due to the fact that the Y and Lu host materials are close to the Stoner limit (5), it is noteworthy that for the YbT₂Zn₂₀ materials it is the T = Fe and Ru compounds that appear to be significantly different from the T = Rh, Os, and Ir compounds. Although we currently do not have enough data to conclude that this Stoner enhancement of the host material (if it even persists in the Yb based members) is responsible for the higher T_K/T_CEF ratio, such an enhancement certainly could be responsible for increased T_K values. This question is the focus of an ongoing dilution study.

Although at first glance the data for YbCo₂Zn₂₀ appear to be different from that of the other members of this family, at low enough temperatures, it too appears to enter into a Fermi liquid ground state and, as shown in Fig. 4, has an intermediate N value, similar to YbOs₂Zn₂₀. YbCo₂Zn₂₀ has a substantially lower T_K, and may be closer to a quantum critical point (QCP) than the other, T = Fe, Ru, Rh, Os, Ir members of the family: i.e., small perturbations to YbCo₂Zn₂₀ may lead to the onset of magnetic order, giving rise to a T = 0 phase transition controlled by a nonthermal (magnetic field, pressure, doping) tuning parameter. If YbCo₂Zn₂₀ is simply closer to a QCP, then, given that the unit cell dimensions for YbCo₂Zn₂₀ are the smallest of the family, this would imply that applications of modest pressure to other members of the YbT₂Zn₂₀ family may lead to several new Yb-based compounds for the study of quantum criticality.

Methods

Single crystalline samples of YbT₂Zn₂₀ were grown out of excess Zn using standard solution growth techniques (23). Initial ratios of starting elements (Yb:T:Zn) were 2:4:94 (T = Fe, Co), 2:2:96 (T = Ru, Rh), 1:0.5:98.5 (T = Os), and 0.75:1.5:97.75 (T = Ir). Crystals were grown by slowly cooling the melt between 1150°C and 600°C over ≈100 h. To reduce the amount of Zn transported to the top of the growth ampoule, all growths were sealed under ≈1/3 atmosphere of high purity Ar and were also slightly elevated from the hearth plate so as to ensure that the top of the ampoule was slightly hotter than the bottom. Residual Zn flux was etched from the surface of the crystals using diluted HCl (0.5 volume percent, T = Fe, Co) or acetic acid (1 volume percent, T = Ru, Rh, Os, Ir). As can be seen in Fig. 1, there is virtually no low-temperature Curie tail observed in any of the T = Fe, Ru, Rh, Os, Ir compounds, indicating little, or no local-moment-bearing impurities.

Magnetization measurements were performed for T ≥ 1.8 K in a Quantum Design MPMS unit with the applied magnetic field along the (111) crystallographic direction. Specific heat and transport measurements for T ≥ 0.4 K were performed in a Quantum Design PPMS system. Specific heat, C(T), data for 50 mK ≤ T ≤ 2 K were taken on YbCo₂Zn₂₀ in a dilution refrigerator insert for the Quantum Design PPMS system. Whereas all RT₂Zn₂₀ (R = Yb, Lu, Y; T = Fe, Co, Ru, Rh, Os, Ir) had θ_D values near 255 K, the linear component of the C(T) was low (50 mJ/mol K² or less) (5) for the Lu- and Y-analogues and greatly enhanced for the Yb-bearing materials. Transport data were taken for T down to 20 mK at the National High Magnetic Field Laboratory using an Oxford dilution refrigerator. Powder x-ray diffraction measurements were performed on a Rigaku Miniflex unit. The YbT₂Zn₂₀ (T = Fe, Co, Ru, and Rh) compounds had diffraction patterns and lattice parameters that agreed well with the data for the RT₂Zn₂₀ series presented in ref. 4. Although there are no prior reports on the ROs₂Zn₂₀ and RIr₂Zn₂₀ series, the diffraction patterns for YbOs₂Zn₂₀ and YbIr₂Zn₂₀ were easily indexed to the RT₂Zn₂₀ structure type. Room temperature unit cell parameters are given in Table 1.