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Kondo Effects and Multipolar Order in the Cubic PrTr2Al20 (Tr = Ti, V)

Nakatsuji Group

The Kondo effect, which screens magnetic dipole moments through the hybridization with conduction(c-) electrons, is known to provide a vast number of interesting phenomena such as heavy Fermions, quantum critical phenomena, and unconventional superconductivity. An interesting question is whether different type of Kondo effect is possible that screens orbital degree of freedom. Cox proposed such nonmagnetic version known as quadrupolar Kondo effect [1]. It was pointed out that quadrupolar Kondo effect arises if we consider orbital degree of freedom known as quadrupole moments of Γ3 crystal electric field ground state in cubic 4f2 configuration. Interestingly, over-compensation by c-electrons may lead to anomalous metallic state far different from Fermi liquid [1]. Motivated by this proposal, several experimental studies have been done in Heusler-type compounds such as PrInAg2 and PrMg3 [2], [3] and nonmagnetic heavy fermion states are suggested due to the nonmagnetic Kondo effect. However, the Heusler-type compounds are known to have random site exchange that may lift the orbital degeneracy essential for the Kondo effect. On the other hand, if a system exhibits a quadrupole ordering, orbital degeneracy is assured above the ordering temperature. Therefore, it is ideal to study a system that allows tuning of quadrupole ordering temperature by changing the hybridization strength.

Fig. 1. Temperature dependence of 4f electron contribution to the resistivity. Arrows indicate the quadrupole order at TO = 2.0 K (PrTi2Al20) and 0.6 K (PrV2Al20). –lnT dependence of resistivity is observed above Δ ~ 60 K (PrTi2Al20) and ~ 40 K (PrV2Al20), indicating the magnetic Kondo effect. In contrast with Fermi liquid behavior with T2 dependence (solid line) of the resistivity for PrTi2Al20, PrV2Al20 exhibits T1/2 dependence (solid line) of the resistivity, suggesting the anomalous metallic state due to the quadrupolar Kondo effect. (Left inset) Crystal structure of PrTr2Al20. 16 Al ions around Pr lead to strong c-f hybridization. (Right inset) Picture of typical single crystal PrTi2Al20.

Here, we report the low temperature thermal and transport properties of PrTr3Al20 (Tr = Ti, V) by using high quality single crystals [4]. We revealed that PrTr2Al20 (Tr = Ti, V) is the first system that allows us to tune the hybridization strength and the quadrupolar ordering temperature: (i) A lnT increase of resistivity ρ and large Weiss temperature θW of magnetic susceptibility χ indicate the Kondo effect, which is stronger in PrV2Al20 than PrTi2Al20. (ii) Quadrupolar ordering temperature TQ = 2.0 K in PrTi2Al20 becomes lower to TQ = 0.6 K in PrV2Al20. This hybridization difference can be attributed to (a) ~3 % unit-cell volume shrinkage by replacing Ti to V, and (b) additional 3d electron in V which should contribute to the conduction band. Moreover, anomalous metallic behaviors are observed in PrV2Al20 above TQ such as CP /T ~ T–3/2, χ ~ T1/2, and ρ ~ T1/2, most likely attributable to the quadrupolar Kondo effect. Further study is necessary to reveal how the quantum criticality appears by chemical substitution or applying pressure.


References
  • [1] D. L. Cox, Phys. Rev. Lett. 59, 1240 (1987).
  • [2] A. Yatskar, W. P. Beyermann, R. Movshovich, and P. C. Canfield, Phys. Rev. Lett. 77, 3637 (1996).
  • [3] H. Tanida, H. S. Suzuki, S. Takagi, H. Onodera, and K. Tanigaki, J. Phys. Soc. Jpn. 75, 07370 (2006).
  • [4] A. Sakai and S. Nakatsuji, J. Phys. Soc. Jpn. 80, 063701 (2011). Editor’s Choice
Authors
  • A. Sakai and S. Nakatsuji