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Time-Reversal Symmetry Breaking Superconductivity in Sr2RuO4

Submitted to Nature 1

Time-Reversal Symmetry Breaking Superconductivity in Sr 2RuO 4

a r X i v :c o n d -m a t /9808159v 1 [c o n d -m a t . s u p r -c o n ] 14 A u g 1998

G. M. Luke ∗, Y. Fudamoto ∗, K. M. Kojima ∗, M. I. Larkin ∗, J. Merrin ∗, B. Nachumi ∗, Y. J. Uemura ∗, Y. Maeno †, Z. Q. Mao †, Y. Mori †, H. Nakamura ‡, M. Sigrist §

Dept. of Physics, Columbia University, New York, NY 10027, U.S.A. †

Dept. of Physics, Kyoto University, Kyoto 606-8502, Japan. ‡

Dept. of Material Science and Engineering, Kyoto University, Kyoto 606-8501, Japan. §

Yukawa Instutute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan.

In addition to its importance for existing and potential applications, superconductivity[1]is one of the most interesting phenomena in condensed matter physics. Although most superconducting materials are well-described in the context of the Bardeen Cooper and Schrieffer(BCS)theory[2],considerable efforthas been de-voted to the search for exotic systems whose novel properties cannot be described by the BCS theory. Conventional superconductors break only gauge symmetry by selecting a def-inite phase for the Cooper pair wavefunction; a signature of an unconventional supercon-ducting state is the breaking of additional symmetries[3].Evidence for such broken symmetries include anisotropic pairing (suchas d-wave in the high-T c cuprates) and the presence of multiple superconducting phases (UPt3and superfluid3We have per-formed muon spin relaxation measurements of Sr 2RuO 4and observe a spontaneous internal magnetic fieldappearing below T c . Our measurements indicate that the supercon-ducting state in Sr 2RuO 4is characterized by broken time reversal symmetry which, when combined with symmetry considerations in-dicate that its superconductivity is of p-wave (odd-parity)type, analagous to superfluid3

He. Despite the structural similarity with the high T c cuprates, the origin of the un-conventional superconductivity in Sr 2RuO 4is fundamentally differentin nature.

Sr 2RuO 4, which is isostructural to the high-T c cuprate La 1. 85Sr 0. 15CuO 4, is to date the only known layered perovskite superconductor which does not contain copper. Although firstsynthesized in the 50’s,[5]its superconductivity was only found in

1994[6];T c ’sof early samples were roughly 0.7K but have increased to T c =1. 5K in recent high quality single crystals[7].Despite its low transition temperature, Sr 2RuO 4is of great interest as there is growing evidence for an unconventional supercon-ducting state. In this system, strong correlation ef-fects enhance the effectivemass seen in quantum oscillation[8]and Pauli spin susceptibility measure-ments, in the same way as in 3Combining this feature with Sr 2RuO 4’sexpected tendency to display ferromagnetic spin fluctuations,Rice and Sigrist[10],and later Baskaran[11]argued that the pairing in Sr 2RuO 4could be of odd parity (spintriplet) type. The strong suppression of the superconducting T c by even non-magnetic impurities suggests non-s-wave Specificheat[12]and NMR 1/T1[13]mea-surements indicate the presence of a large residual density of states (RDOS)at low temperatures (wellwithin the superconducting state); in high quality samples, this RDOS as T →0seems to approach half of the normal state value. Several authors[14,15]have proposed so-called non-unitary p-wave super-conducting states for Sr 2RuO 4to account for this RDOS as well as the absence of a Hebel-Slichter peak in NMR measurements[13].A finiteRDOS is not a unique signature of unconventional superconductiv-ity; for example it is observed in so-called gapless superconductors with isotropic s-wave pairing as a re-sult of impurity scattering (althoughthis is unlikely in the specificcase of Sr 2RuO 4where the finiteRDOS apparently remains in the cleanest samples). It could also be explained with a multi-band hypothesis[16]where differentgaps are associated with two types of bands. Therefore, further studies are required for a definitivedetermination of the pairing symmetry in Sr 2RuO 4.

One aspect of the pairing symmetry, the breaking of time reversal symmetry (TRS)can be probed di-rectly. If the superconducting state has a degenerate representation (asis possible for some triplet super-conducting states) then TRS can be broken, whereas it cannot be broken for non-degenerate representa-tions (thecase for all singlet states). When spin or-bit coupling is small, the pair wave function can be written as a product of the orbital part and the spin part. Non-zero angular momentum of either the or-bital or the spin part could result in TRS breaking, although there are many such cases with conserved TRS, such as d-wave states in the high-T c cuprates. TRS breaking is also possible in the case of strong spin orbit coupling. In general, pairing states can be further classifiedin terms of gap functions attached to irreducible representations of a point group for a given crystal lattice symmetry of the system[3].TRS

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