Recently, one of the most interesting topics has been the ground state properties of heavy fermion compounds located close to a magnetic Quantum Critical Point (QCP). Applying pressure or magnetic field controls the electronic configuration, and thus anomalous behaviors appear at around magnetic QCP, such as an unconventional superconductivity and non-Fermi liquid state. In the case of Yb based heavy fermion compounds, it is known that YbCo₂Zn₂₀ is a prototypical compound of the pressure-induced QCP from a paramagnetic state to an antiferromagnetic. The high temperature magnetic susceptibility shows the Curie-Weiss law with the effective moment close to the value of Yb³⁺ ( μ_eff = 4.5 μB), although there is no indication of magnetic order down to 20 mK. The low temperature electrical resistivity and specific heat follows ρ = ρ₀ + AT² and C/T = const : which indicates the Fermi-liquid behavior: the values of A and γ are 165 Ωcm/K² and 7900 mJ/moleK², respectively. These large values of A and γ are due to the small Kondo temperature, suggesting the closeness to the pressure induced magnetic order. According to the resistivity, specific heart and neutron diffraction measurements under pressure, magnetic ordered phase appears around critical pressure P_c = 1 GPa. Figure 1 shows the pressure phase diagram of YbCo₂Zn₂₀ [1]. The applying pressure stabilizes the magnetic Yb³⁺ configuration and resulting in the appearance of a magnetically ordered state. It is worth noting that the critical pressure of YbCo₂Zn₂₀ is lower than that of other Yb based compounds such as YbNi₂Ge₂ (P_c = 5 GPa) and YbCu₂Si₂ (P_c = 8 GPa). Therefore YbCo₂Zn₂₀ has an advantage of investigating the behavior of Yb based compounds near QCP.

Fig. 1. Pressure–temperature phase diagram of YbCo₂Zn₂₀. T_max and TFL are suppressed by applying pressure, and thus, the nonmagnetic Fermi-liquid state vanishes around P_c. T_M appears to abru ptly develop above P_c, where T_max decreases. Assuming that the observed T_max in the resistivity is proportional to T_K, the value of T_K decreases with an increase in the pressure. According to a theoretical study, the suppression of valence fluctuations leads to a decrease in T_K. It is generally accepted that the magnetic instability results from the competition between the RKKY and the Kondo interactions. By applying pressure, the RKKY interaction becomes more dominant with a reduction in the Kondo interaction.

Fig. 2. Temperature dependence of the electronic contribution of the specific heat for YbCo₂Zn₂₀ at selected magnetic field (H // [110]). Arrow indicates the onset temperature of the Fermi liquid behavior. Here, the electronic contribution to the specific heat C_e of YbCo₂Zn₂₀ was obtained by subtracting that of LuCo₂Zn₂₀. At lower temperature, C_e/T increases logarithmically and tends to saturate below T_FL ~ 0.2 K, coinciding with the T² dependence in the resistivity, namely Fermi-liquid behavior as observed in the previous report. Inset : Field dependence of C_e/T at selected temperature. Two peak structure, which has local minimum point at H_m, was observed at around 0.6 T.

More interestingly, it is reported that a metamagnetic crossover occurs at H_m ~ 0.57 T by M. Ohya et al. The origin of this metamagnetic behavior is not fully understood, however relevance to the valence fluctuation is considered by S. Watanabe and K. Miyake. To shed light on the nature of the metamagnetic behavior, the specific heat of YbCo₂Zn₂₀ single crystal under magnetic field has been measured at ambient pressure. Figure 2 shows the temperature dependence of the electronic contribution of the specific heat C_e/T under magnetic field on a logarithmic temperature scale. At zero- field, C_e/T exhibits a broad shoulder structure at around 2 K due to the combined effect of the Kondo effect and the Schottky anomaly associated with the crystalline electronic field (CEF) splitting. With increasing magnetic field, the T_FL is gradually suppressed to a lower temperature. It is worth noting that C_e/T diverges more rapidly than a logarithmic dependence at H_m ~ 0.6 T, which corresponds to the metamagnetic field. With further increasing magnetic field, the temperature dependence changes to a peak structure as typical behavior of Kondo systems under magnetic field. C_e/T as a function of magnetic field at selected temperature has been plotted to see the field variation in inset of fig. 2. The most intriguing feature obtained here is the two peak structure which has local minimum point at H_m ~ 0.6 T. Although the double peak structure becomes weaker with increasing temperature, the minimum point is temperature independent. Similar feature is also observed in the prototypical heavy fermion compound CeRu₂Si₂ which shows metamagnetic transition at H_m ~ 7.7 T by J. Flouquet et al. In the case of CeRu₂Si₂, the field dependence of C_e/T exhibits the double peak structure above 1 K, and thus that changes to a single peak structure at lower temperatures. Here we compare the characteristic energy scales of YbCo₂Zn₂₀ to those of CeRu₂Si₂. It is obvious that the values of Hm and T_max of YbCo₂Zn₂₀ are ten times smaller than that of CeRu₂Si₂, i.e. the characteristic energy scale of YbCo₂Zn₂0 is much smaller than that of CeRu₂Si₂. Considering the difference of the energy scale, it is expected that the double peak structure in YbCo₂Zn₂0 may evolve into a single peak structure at lower temperature, suggesting the development of the critical fluctuation. Further experimental and theoretical studies are needed to clarify the origin of the metamagnetic behavior and the relationship with the pressure-induced magnetically ordered state of YbCo₂Zn₂0.

References

• [1] Y. Saiga, K. Matsubayashi, T. Fujiwara, M. Kosaka, S. Katano, M. Hedo, T. Matsumoto and Y. Uwatoko, J. Phys. Soc. Jpn. 77, 053710 (2008).

Authors

• R. Yamanaka, K. Matsubayashi, Y. Saiga^a, T. Kawae^b, and Y. Uwatoko
• ^aHiroshima University
• ^bKyushu University