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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 effort has been devoted 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 definite phase for the Cooper pair wavefunction; a signature of an unconventional superconducting state is the breaking of additional symmetries [3].Evidence for such broken symmetries include anisotropic pairing (such as d-wave in the high-T c cuprates) and the presence of multiple superconducting phases (UPt 3 and superfluid 3 He[4]). We have performed muon spin relaxation measurements of Sr 2 RuO 4 and observe a spontaneous internal magnetic field appearing below T c . Our measurements indicate that the superconducting state in Sr 2 RuO 4 is characterized by broken time reversal symmetry which, when combined with symmetry considerations indicate that its superconductivity is of p-wave (odd-parity) type, analagous to superfluid 3 He. Despite the structural similarity with the high T c cuprates, the origin of the unconventional superconductivity in Sr 2 RuO 4 is fundamentally different in nature.Sr 2 RuO 4 , which is isostructural to the high-T c cuprate La 1.85 Sr 0.15 CuO 4 , is to date the only known layered perovskite superconductor which does not contain copper. Although first synthesized in the 50's, [5] its superconductivity was only found in 1994[6]; T c 's of early samples were roughly 0.7 K but have increased to T c = 1.5 K in recent high quality single crystals [7]. Despite its low transition temperature, Sr 2 RuO 4 is of great interest as there is growing evidence for an unconventional superconducting state. In this system, strong correlation effects enhance the effective mass seen in quantum oscillation [8] and Pauli spin susceptibility measurements, in the same way as in 3 He [9]. Combining this feature with Sr 2 RuO 4 's expected tendency to display ferromagnetic spin fluctuations, Rice and Sigrist [10], and later Baskaran [11] argued that the pairing in Sr 2 RuO 4 could be of odd parity (spin triplet) type.The strong suppression of the superconducting T c by even non-magnetic impurities suggests non-s-wave pairing [7]. Specific heat [12] and NMR 1/T 1 [13] measurements indicate the presence of a large residual density of states (RDOS) at low temperatures (well within the superconducting state); in high quality samples, this RDOS as T→ 0 seems to approach half of the normal state value. Several authors [14,15] have proposed so-called non-unitary p-wave superconducting states for Sr 2 RuO 4 to account for this RDOS as well as the absence of a Hebel-Slichter peak in NMR measurements [13]. A finite RDOS is not a unique signature of unconventional superconductivity; for example it is observed in so-called gapless sup...

Nature © Macmillan Publishers Ltd 1998 8 letters to nature 658 NATURE | VOL 396 | 17 DECEMBER 1998 | www.nature.comT CO 317 K. Hence a conducting, magnetically ordered state is not found in Fe 2 OBO 3 as T C , T CO . The differences between the estimated activation energies for electron hopping in the chargedisordered (E a < 0 for T . T V ) and ordered (E a < 0:04 eV for T , T V ) 13 states of magnetite and those of Fe 2 OBO 3 (E a < 0:31 eV for E a < 0:35 eV for T . T CO are equal, showing that this small difference is essentially independent of spin alignment, although the ferromagnetic order in magnetite reduces both activation energies by 0.3 eV relative to those in paramagnetic Fe 2 OBO 3 .M

Polar Kerr effect in the spin-triplet superconductor Sr2RuO4 was measured with high precision using a Sagnac interferometer with a zero-area Sagnac loop. We observed non-zero Kerr rotations as big as 65 nanorad appearing below Tc in large domains. Our results imply a broken time reversal symmetry state in the superconducting state of Sr2RuO4, similar to 3 He-A.PACS numbers: 74.25. Gz,74.70.Pq,74.25.Ha,78.20.Ls Soon after the discovery of the layered-perovskite superconductor Sr 2 RuO 4 [1], it was predicted to be an oddparity superconductor [2,3]. Subsequently, a large body of experimental results in support of odd-parity superconductivity has been obtained [4], with the most recent one being a phase-sensitive measurement [5]. The symmetry of the superconducting state is related simply to the relative orbital angular momentum of the electrons in each Cooper pair. Odd parity corresponds to odd orbital angular momentum and symmetric spin-triplet pairing. While a priori the angular momentum state can be p (i.e. L = 1), f ( i.e. L = 3), or even higher order [6,7], theoretical analyses of superconductivity in Sr 2 RuO 4 favor the p-wave order parameter symmetry [2,8]. There are many allowed p-wave states that satisfy the cylindrical Fermi surface for a tetragonal crystal which is the case of Sr 2 RuO 4 (see e.g. table IV in [4]). Some of these states break time-reversal symmetry (TRS), since the condensate has an overall magnetic moment because of either the spin or orbital (or both) parts of the pair wave function. While an ideal sample will not exhibit a net magnetic moment, surfaces and defects at which the Meissner screening of the TRS-breaking moment is not perfect can result in a small magnetic signal [7]. Indeed, muon spin relaxation (µSR) measurements on good quality single crystals of Sr 2 RuO 4 showed excess relaxation that spontaneously appear at the superconducting transition temperature. The exponential nature of the increased relaxation suggested that its source is a broad distribution of internal fields, of strength ∼ 0.5 Oe, from a dilute array of sources [9,10]. While TRS breaking is not the only explanation for the µSR observations, it was accepted as the most likely one [4]. However, since the existence of TRS breaking has considerable implications for understanding the superconductivity of Sr 2 RuO 4 , establishing the existence of this effect, and in particular in the bulk without relying on imperfections and defects is of utmost importance. The challenge is therefore to couple to the TRS-breaking part of the order parameter to demonstrate the effect unambiguously.In this paper we show results of polar Kerr effect (PKE) measurements on high quality single crystals of Sr 2 RuO 4 . In these measurements we are searching for an effect analogous to the magneto-optic Kerr effect (MOKE) which would cause a rotation of the direction of polarization of the reflected linearly polarized light normally incident to the superconducting planes. PKE is sensitive to TRS breaking since it measures the existenc...

This review presents a summary and evaluations of the superconducting properties of the layered ruthenate Sr 2 RuO 4 as they are known in the autumn of 2011. This paper appends the main progress that has been made since the preceding review by Mackenzie and Maeno was published in 2003. Here, special focus is placed on the critical evaluation of the spin-triplet, odd-parity pairing scenario applied to Sr 2 RuO 4 . After an introduction to superconductors with possible odd-parity pairing, accumulated evidence for the pairing symmetry of Sr 2 RuO 4 is examined. Then, significant recent progress on the theoretical approaches to the superconducting pairing by Coulomb repulsion is reviewed. A section is devoted to some experimental properties of Sr 2 RuO 4 that seem to defy simple explanations in terms of currently available spin-triplet scenario. The next section deals with some new developments using eutectic boundaries and micro-crystals, which reveals novel superconducting phenomena related to chiral edge states, odd-frequency pairing states, and half-fluxoid states. Some of these properties are intimately connected with the properties as a topological superconductor. The article concludes with a summary of knowledge emerged from the study of Sr 2 RuO 4 that are now more widely applied to understand the physics of other unconventional superconductors, as well as with a brief discussion of relatively unexplored but promising areas of ongoing and future studies of Sr 2 RuO 4 .KEYWORDS: Sr 2 RuO 4 , ruthenate, spin-triplet superconductivity, topological superconductor Spin-Triplet Superconductors Candidates of spin-triplet superconductorsIn the last three decades, and particularly since the discovery of high-transition-temperature (high-T c ) superconductivity of the cuprates, 1) studies of ''unconventional'' superconductivity have been one of the main topics in condensed-matter physics. Here we designate the term ''unconventional'' as the pairing based on non-phonon mechanisms.2) The unconventional superconductivity is mainly found in heavy-fermion superconductors (since 1978), 3) Unconventional superconductivity is characterized by the anisotropic gap function or order parameter which is integrated to be zero or a small value due to the variations of the wave function ''phase'', in contrast to an ordinary s-wave state. In many of them, including high-T c cuprates and iron pnictides, the electrons are clearly paired in spinsinglet states. In this point of view, they are similar to conventional s-wave superconductors, in which the spindegrees of freedom is lost in the charged superfluids. Spintriplet superfluid states are fully established in the Fermi liquid 3 He, 7,8) for which spin and mass supercurrents emerge in the charge-neutral superfluids. The question is then whether or not spin-triplet superconductors exist, and what novel superconducting properties they may exhibit due to their charge and spin supercurrents.There are several classes of candidates of spin-triplet superconductors represented in Table I. W...

As liquids crystallize into solids on cooling, spins in magnets generally form periodic order. However, three decades ago, it was theoretically proposed that spins on a triangular lattice form a liquidlike disordered state at low temperatures. Whether or not a spin liquid is stabilized by geometrical frustration has remained an active point of inquiry ever since. Our thermodynamic and neutron measurements on NiGa2S4, a rare example of a two-dimensional triangular lattice antiferromagnet, demonstrate that geometrical frustration stabilizes a low-temperature spin-disordered state with coherence beyond the two-spin correlation length. Spin liquid formation may be an origin of such behavior.

The concept of quantum criticality is proving to be central to attempts to understand the physics of strongly correlated electrons. Here, we argue that observations on the itinerant metamagnet Sr3Ru2O7 represent good evidence for a new class of quantum critical point, arising when the critical end point terminating a line of first-order transitions is depressed toward zero temperature. This is of interest both in its own right and because of the convenience of having a quantum critical point for which the tuning parameter is the magnetic field. The relationship between the resultant critical fluctuations and novel behavior very near the critical field is discussed.