4f -based heavy-fermion (HF) systems have attracted much attention with interesting phenomena such as unconventional superconductivity and non-Fermi-liquid (NFL) behavior found in the vicinity of quantum critical points. Our recent studies have found the first Yb- (4f ¹³) based HF superconductivity with the transition temperature T_c = 80 mK in the compound β-YbAlB₄ [1, 2]. Pronounced NFL behavior above T_c and its magnetic field dependence indicate that the system is a rare example of a pure metal that displays quantum criticality at ambient pressure and close to zero magnetic field [1]. Furthermore, the T/B scaling found in our recent high-precision magnetization measurements clarifies its unconventional zero-field quantum criticality without tuning [3], which cannot be explained by the standard theory based on spin-density-wave fluctuations. In contrast to the canonical quantum critical materials, hard x-ray photoemission spectroscopy (HXPES) measurements have revealed a strongly intermediate valence of Yb^+2.75 [4], providing an example of quantum criticality in a mixed-valence system. Whether the valence fluctuation is relevant for the mechanism of quantum criticality and superconductivity is an interesting open question.

Fig. 1. Crystal structure of A) α-YbAlB₄ and B) β-YbAlB₄.

Fig. 2. Temperature dependence of the in-plane and c-axis resistivity ρ_ab and ρc of α-YbAlB₄ and ρ_ab of β-YbAlB₄. The magnetic part of the resistivity ρ_m is obtained by subtracting the nonmagnetic contribution estimated by ρ_ab of α- and β-LuAlB₄ (solid and dash-dotted lines, respectively) or ρc of α-LuAlB4 (dashed line). The inset shows the temperature dependence of the ratios ρ_ab/ρc for α-YbAlB₄ and α-LuAlB₄.

Here, we measured the specific heat, magnetization, and resistivity of α-YbAlB₄ down to very low temperature [5]. This compound is the locally isostructural polymorph of β-YbAlB₄ with a different arrangement of distorted hexagons made of Yb atoms [space groups Pbam(α-YbAlB₄) and Cmmm(β-YbAlB₄), see Fig. 1]. According to the HXPES measurement [4], α-YbAlB₄ also has an intermediate valence of Yb^+2.73. The results indicate a Fermi-liquid (FL) ground state for α-YbAlB₄ in contrast to the unconventional quantum criticality observed in β-YbAlB₄. Interestingly, both systems exhibit Kondo lattice behavior with a small renormalized temperature scale of T* ∼ 8 K, although both of them have a large valence-fluctuation scale of ∼200 K. Below T*, α-YbAlB₄ forms a heavy-Fermi-liquid state with an electronic specific heat coefficient γ ∼ 130 mJ/mol K² and a large Wilson ratio greater than 7, which indicates a ferromagnetic correlation between Yb moments. A Kadowaki- Woods ratio is found that is similar to those found in the normal Kondo lattice systems and considerably larger than mixed valence systems. Furthermore, the resistivity of α-YbAlB₄ exhibits one of the strongest anisotropies in heavy fermions (Fig. 2). The ratio between in plane and c-axis resistivity ρ_ab and ρ_c, ρ_ab/ρ_c, reaches 11 at low temperatures below T*. This strongly suggests anisotropic hybridization between 4f and conduction electrons which is stronger in the ab-plane. This is the key to understanding the mechanism of heavy-fermion formation as well as the Kondo lattice behavior found in the intermediate-valence system. Thus the system should be one of the best systems to study for elucidating the effects of anisotropic hybridization.

References

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• [2] K. Kuga, Y. Karaki, Y. Matsumoto, Y. Machida, and S. Nakatsuji, Phys. Rev. Lett. 101, 137004 (2008).
• [3] Y. Matsumoto, S. Nakatsuji, K. Kuga, Y. Karaki, N. Horie, 
Y. Shimura, T. Sakakibara, A. H. Nevidomskyy, and P. Coleman, Science 331, 316 (2011).
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A. Chainani, Y. Takata, M. Yabashi, K. Tamasaku, Y. Nishino, T. Ishikawa, K. Kuga, N. Horie, S. Nakatsuji, and S. Shin, Phys. Rev. Lett. 104, 247201 (2010).
• [5] Y. Matsumoto, K. Kuga, T. Tomita, Y. Karaki, and S. Nakatsuji, Phys. Rev. B 84, 125126 (2011).

Authors

• Y. Matsumoto, K. Kuga, T. Tomita, Y. Karaki^a, and S. Nakatsuji
• ^aUniversity of the Ryukyus