Time-Reversal Symmetry-Breaking Superconductivity in Heavy-FermionPrOs4Sb12Detec

Abstract

We report on muon spin relaxation measurements of the 4f 2 -based heavy-fermion superconductor filled-skutterudite PrOs4Sb12. The results reveal the spontaneous appearance of static internal magnetic fields below the superconducting transition temperature, providing unambiguous evidence for the breaking of time-reversal symmetry in the superconducting state. A discussion is made on which of the spin or orbital component of Cooper pairs carries a nonzero momentum.PACS numbers: 74.70. Tx, 76.75.+i, 74.70.Dd, 74.25.Ha Many unconventional superconducting (SC) states, as in Ce-and U-based heavy-fermion (HF) compounds or high-T c cuprates, appear in close proximity to magnetic instabilities when a certain parameter (pressure, atomic doping, or oxygen content) is varied [1,2,3]. This fact strongly suggests that the attractive interactions binding electrons into Cooper pairs are mediated by magnetic moment fluctuations. As another possible pairing glue, fluctuations of quadrupole moments-distorted shapes of the electronic clouds of ions, are theoretically considered to be possible [4,5]. An interesting question to be addressed is what is the nature of superconductivity in such a system. For this study, Pr-based compounds with a 4f 2 configuration are likely candidates, since nonmagnetic but quadrupolar active low-energy levels can be realized due to the crystalline-electric-field (CEF) effect; in 5f systems, CEF levels are less clear due to the tendency to be itinerant.One promising candidate material for this study is the recently found superconductor PrOs 4 Sb 12 [6], which is to date the only known Pr-based HF superconductor, with a superconducting transition temperature of 1.82 K (hereafter referred to as T c1 ). The estimated electronic specific heat coefficient γ = 350 − 700 mJ/K 2 mol [6,7] and the enhanced cyclotron-effective masses [8] reflect the existence of strong electron correlations. Specific heat (C), magnetic susceptibility (χ), and inelastic neutron studies provide evidence that PrOs 4 Sb 12 has a nonmagnetic ground state and a magnetic triplet excited state separated by ∆E CEF /k B = 8 K [7,9], which is 5 times larger than T c1 . In the temperature-versus-magneticfield (T -vs-H) phase diagram, a field-induced ordered phase (µ 0 H 4 T) [9] appears close to the superconducting phase (the upper critical field µ 0 H c2 = 2.2 T). It was recently proven to be an antiferro-quadrupolar ordered phase by elastic neutron scattering measurements [10]. This fact strongly indicates that quantum quadrupole fluctuations of the Pr ions play an important role in realizing the HF superconductivity in PrOs 4 Sb 12 , considering that the T -vs-H phase diagram is analogous to those for the HF and cuprate systems, where a magnetically ordered phase exists close to the SC phase in the T -vs-pressure, -atomic-doping, or -oxygen-content phase diagram. This scenario is further supported by the enhanced T c1 compared to T c = 0.74 K for a 4f 0 reference compound LaOs 4 Sb 12 [8,11].The remarkable unconventional SC properties ...

Simultaneous Measurements of Elastic Constant and Resistivity near the Tc of Non-BCS-Type Superconductor PrOs4Sb12

“…Taking into account intrasite hyperfine coupling between nuclear spin I = 5/2 and 4f -electron's J = 4 multiplet, the Γ 1 singlet CEF ground state can be regarded as a six degenerate new quantum state. This sextet will split, even in zero magnetic field, due to the second perturbation effect of mixing with the Γ (2) 4 triplet first excited CEF state. As a result, the ground sextet has a quadrupole degree of freedom, and this may be the origin of the softening.…”

“…The unconventional nature of this superconductivity (SC) has been proven by several studies [2,3]. The gap structure of the SC phase has been studied in the last decade, it has, however, not yet been fully understood [4,5].…”

A General Model of N/S Conductance Spectroscopy in Non-Unitary Superconductors Applied to PrOs4Sb12

“…Therefore the phase C 3 × K in the singlet channel offers the best explanation for point contact conductance [10] and low temperature thermal conductivity [5]; however it is inconsistent with µSR measurements [6] which indicate non-unitary superconductivity.…”

“…While broken symmetry may be detectable in measurements of elastic constants, it is often inferred by the presence of nodes that are required by symmetry. Non-unitary superconductivity, which is triplet pairing with broken time-reversal symmetry, has been inferred from µSR measurements [6]; iv) superconductivity occurs within more than one band: PrOs 4 Sb 12 has three Fermi surfaces [2] and multi-band superconductivity has been proposed [4,5].…”

Non-Fermi Liquid Regimes and Superconductivity in the Low Temperature Phase Diagrams of Strongly Correlated d- and f-Electron Materials

“…Of these compounds, PrOs 4 Sb 12 has received the most attention, owing largely to the fact that it is the first Pr-based heavy fermion superconductor, for which T c = 1.85 K and H c2 (0) = 2.5 T [27,28]. The superconducting state breaks time reversal symmetry [252], apparently consists of several distinct superconducting phases, some of which may have point nodes in the energy gap [253,254], and may involve triplet spin pairing of electrons [255]. Additionally, it has been shown that there likely are multiple superconducting bands [254,[256][257][258][259].…”