Superconductivity in the Ferroquadrupolar State in the Quadrupolar Kondo Lattice PrTi₂Al₂₀

Abstract

The cubic compound PrTi 2 Al 20 is a quadrupolar Kondo lattice system that exhibits quadrupolar ordering due to the non-Kramers À 3 ground doublet and has strong hybridization between 4f and conduction electrons. Our study using high-purity single crystals reveals that PrTi 2 Al 20 exhibits type-II superconductivity at T c ¼ 200 mK in the nonmagnetic ferroquadrupolar state. The superconducting critical temperature and field phase diagram indicates clean limit superconductivity with moderately enhanced effective mass of m à =m 0 $ 16. Orbital degree of freedom in strongly correlated electron systems leads to rich variety of nontrivial phenomena, such as colossal magnetoresistance, orbital ordering, 1) and spinorbital disordered states.2) In particular, for the study of topical subjects of d-electron systems including hightemperature superconductivity and frustrated magnetism, orbital arrangement has been found to provide an important basis to understand the underlying electronic and spin structures. This is because of the strong coupling between orbital, spin and charge degrees of freedom, which, on the other hand, makes it hard to study purely orbital-driven effects.Interestingly, however, f -electron systems may provide a rare example of nonmagnetic ground states that have mainly orbital degree of freedom known as quadrupolar moments, i.e., irreducible tensor operators of the total angular momentum J.3) In particular, cubic Pr and U based compounds with 4f 2 configuration are known to sometimes exhibit a nonmagnetic ground state with the À 3 quadrupolar degree of freedom. In comparison with the uranium compounds, Pr based materials have been found to exhibit rich variety of electronic ground state due to quadrupole moments, such as ferro-and antiferroquadrupolar states, e.g., in PrPtBi and PrPb 3 , [4][5][6] and superconductivity in a quadrupolar phase in PrIr 2 Zn 20 . 7,8) Moreover, for these nonmagnetic states, the hybridization between the 4f and conduction electrons is expected to lead to two competing interactions. One is the indirect RKKY type intersite coupling between quadrupole moments, which may sometimes induce incommensurate modulated structure as observed in PrPb 3 .6) The other is the two-channel (quadrupolar) Kondo effect that quenches the orbital degrees of freedom and stabilize an anomalous metallic state. [9][10][11] For Ce and Yb based compounds described as Kondo lattice systems, it is known that the competition between the Kondo effect and RKKY interaction gives rise to quantum criticality and related phenomena such as unconventional superconductivity and non-Fermi liquid behavior. In analogy, novel quantum criticality and exotic superconductivity might arise as a result of the competition between the quadrupolar Kondo effect and RKKY interaction.In the search for the novel screening effects, pioneer works on the cubic 4f 2 À 3 systems PrInAg 2 and PrMg 3 have found that these compounds do not exhibit any long-range order 12,13) and suggested a nonmagnetic heavy fermion state due to the qu...

Classical Monte Carlo Study for Antiferro Quadrupole Orders in a Diamond Lattice

“…20, the magnitude of this anisotropy is about ∼1 K in Pr-based 1-2-20 compounds, and this is comparable to the transition temperature for the quadrupole orders. [7][8][9][10][11] Another point we should mention is the coupling to magnetic fields. Since the quadrupoles are nonmagnetic degrees of freedom, they do not couple to magnetic fields in the linear order.…”

“…Most of them are considered to be antiferro quadrupole ordered phases. An exception is PrTi 2 Al 20 , 10,11) and the neutron scattering 15) and ultrasound experiments 16) suggest a ferro * E-mail: hattori@tmu.ac.jp quadrupole order in this compound. Anisotropy in the orbital sector in these systems is manifested in the strong anisotropy of the critical field and the phase diagram strongly dependent on the field direction.…”

Heavy-Fermion Superconductivity in the Quadrupole Ordered State ofPrV2Al20

“…At ambient pressure, PrTi 2 Al 20 superconducts at T c = 0.2 K in the ferroquadrupole ordered state [21]. Effective mass estimated from the upper critical field is moderately enhanced with m * /m 0 ∼ 16.…”

“…Due to the anisotropic character, quadrupole moments normally form a excitation gap in the ordered state. Indeed, PrTi 2 Al 20 displays the exponential decay of the specific heat and resistivity below T Q [21,29]. In PrV 2 Al 20 , however, the temperature dependence of C 4f below T Q shows the T 4 power law behavior.…”

Field-insensitive heavy fermion features and phase transition in the caged-structure quasi-skutterudite Sm3 Ru4 Ge13

“…The caged structure are also known for field-insensitive heavy fermion state [7,8] and mixed-valence [9,10]. For example, the filled-skutterudites of chemical formula RT 4 X 12 (R = rare earth, T = transition metal and X = P, As or Sb) display heavy fermion superconductivity, multipole ordering and unusual field-insensitive features in specific heat and in resistivity [11,12,7] which are also observed in the Frank-Kasper type caged structure intermetallics, RT 2 X 20 [13,14,15]. Both RT 4 X 12 and RT 2 X 20 display puzzling physics especially when R = Sm [16,17,18,5,7,19].…”