Orbital degree of freedom provides a various interesting phenomena such as colossal magnetoresistance, orbital ordering, and quantum spin-orbital liquid states. Although orbital degree of freedom strongly couples to spin and charge degrees of freedom in d-electron systems, f-electron systems with 4f² configuration, such as cubic Pr and U based compounds, sometimes exhibit nonmagnetic ground state with a pure orbital degree of freedom known as quadrupole moments. In analogy with magnetic Kondo lattice systems, two competing interactions, RKKY type intersite coupling and quadrupolar Kondo effect, can be induced in quadrupolar Kondo lattice systems due to hybridization between 4f quadrupole and conduction(c-) electrons, which may lead to novel quantum criticality of quadrupole order.

Fig. 1. Temperature dependence of the resistivity below 2.5 K in PrTi₂Al₂₀ (solid circle). Arrows indicate the ferro-quadrupole transition temperature T_Q = 2.0 K and superconducting transition temperature T_c = 0.2 K. Inset: T dependence of the real part of the ac-susceptibility (solid line) and dc-susceptibility for zero field cooled (ZFC, solid circle) and field cooled (FC, open circle).

Recently, we revealed that PrTr₂Al₂₀ (Tr = transition metal) is the first ideal quadrupolar Kondo lattice system that allows us to tune the hybridization strength and the quadrupolar ordering temperature [1]. Among them, PrTi₂Al₂₀ is the best studied and established to have nonmagnetic Γ₃ crystal electric field ground doublet with ferroquadrupolar ordering at T_Q = 2.0 K [1-4] as well as strong c-f hybridization [1, 5].

Here, we report the heavy fermion superconductivity at T_c = 0.2 K in the ferroquadrupolar ordered state of PrTi₂Al₂₀. The temperature dependence of critical field B_c2 and weak differential paramagnetic effect indicate type-II superconductivity. Estimated effective mass m* from B_c2 and Sommerfeld coefficient γ is ~16 m₀, indicating moderately enhanced m* by hybridization. The positive ∂²B_c2/∂T² at ~T_c and sensitivity of T_c to sample quality suggest the multi-gap nature of the superconductivity. These features provide an interesting counterpart to the superconductivity at T_c = 
50 mK in the antiferro-quadrupole ordered state of PrIr₂Zn₂₀ [7, 8], where in contrast 4f electrons are well localized. More enhanced T_c and B_c2 in PrTi₂Al₂₀ should come from the mass enhancement due to the strong hybridization between 4f and c-electrons.

References

• [1] A. Sakai and S. Nakatsuji, J. Phys. Soc. Jpn. 80, 063701 (2011).
• [2] T. J. Sato, S. Ibuka, Y. Nambu, T. Yamazaki, A. Sakai, and S. Nakatsuji, arXiv0301828.
• [3] T U. Ito, W. Higemoto, K. Ninomiya, H. Luetkens, C. Baines, A. Sakai, and S. Nakatsuji, J. Phys. Soc Jpn. 80, 113703 (2011).
• [4] M. Koseki, Y. Nakanishi, K. Deto, G. Koseki, R. Kashiwazaki, F. Shichinomiya, M. Nakamura, M. Yoshizawa, A. Sakai, and S. Nakatsuji, J. Phys. Soc. Jpn. 80, SA049 (2011).
• [5] M. Matsunami, M. Taguchi, A. Chainani, R. Eguchi, M. Oura, A. Sakai, S. Nakatsuji, and S. Shin, Phys. Rev. B 84, 193101 (2011).
• [6] A. Sakai, K. Kuga, and S. Nakatsuji, J. Phys. Soc. Jpn. 81, 083702 (2012).
• [7] T. Onimaru, K. T. Matsumoto, Y. F. Inoue, K. Umeo, Y. Saiga, Y. Matsushita, R. Tamura, K. Nishimoto, I. Ishii, T. Suzuki, and T. Takabatake, J. Phys. Soc. Jpn. 79, 033704 (2010).
• [8] T. Onimaru, K. T. Matsumoto, Y. F. Inoue, K. Umeo, T. Sakakibara, Y. Karaki, M. Kubota, and T. Takabatake: Phys. Rev. Lett. 106, 197201 (2011).

Authors

• A. Sakai, K. Kuga, and S. Nakatsuji