SUPERCONDUCTIVITY

Emergence of superconductivityin the canonical heavy-electronmetal YbRh2Si2Erwin Schuberth,1,2* Marc Tippmann,1,3 Lucia Steinke,1,2 Stefan Lausberg,2

Alexander Steppke,2 Manuel Brando,2 Cornelius Krellner,2,4 Christoph Geibel,2

Rong Yu,5,6 Qimiao Si,7* Frank Steglich2,8,9*

The smooth disappearance of antiferromagnetic order in strongly correlated metalscommonly furnishes the development of unconventional superconductivity. The canonicalheavy-electron compound YbRh2Si2 seems to represent an apparent exception from thisquantum critical paradigm in that it is not a superconductor at temperature T ≥ 10millikelvin (mK). Here we report magnetic and calorimetric measurements on YbRh2Si2,down to temperatures as low as T ≈ 1 mK. The data reveal the development of nuclearantiferromagnetic order slightly above 2 mK and of heavy-electron superconductivityalmost concomitantly with this order. Our results demonstrate that superconductivity inthe vicinity of quantum criticality is a general phenomenon.

Unconventional (i.e., nonphonon-mediated)superconductivity, which has been attract-ing much interest since the early 1980s, isoften observed at the border of antiferro-magnetic (AF) order (1). As exemplified

by heavy-electron (or heavy-fermion) metals,the suppression of the AF order opens up a wideparameter regime where the physics is con-trolled by an underlying quantum critical point(QCP) (2, 3). A central question, then, concernsthe interplay between quantum criticality andunconventional superconductivity in strongly cor-related electron systems such as heavy-electronmetals. In many heavy-electron metals, supercon-ductivity turns out to develop near such a QCP(2–5). However, the absence of superconductivityin the prototypical quantum critical materialYbRh2Si2 (6) has raised the question as towhetherthe presence of an AF QCP necessarily gives riseto the occurrence of superconductivity. BecauseYbRh2Si2 exists in the form of high-quality singlecrystals, we are able to address this issue at verylow temperatures without seriously encoun-tering the limitations posed by disorder. YbRh2Si2exhibits AF order below a Néel temperature TAF =70 mK. When applied within the basal plane ofthe tetragonal structure, a small magnetic field of

B = 60 mT continuously suppresses the magneticorder and induces a QCP. Along with those ofCeRhIn5 (7–9) and CeCu6–xAux (10, 11), the QCPin YbRh2Si2 has been exclusively demonstrated(12, 13) to be of the unconventional type withKondo breakdown (14–16). Electrical resistivitymeasurements down to 10 mK have failed toshow any indications for superconductivity (6).Because a critical field of 60 mT is likely todestroy heavy-electron superconductivity with asuperconducting transition temperature (Tc) ofless than 10 mK, a different means of suppress-ing the antiferromagnetism is needed to even-tually reveal any potential superconductivity atits border. We note that the application of pres-sure does not facilitate realization of a QCP inan AF Yb-based material, as increased pressurewill strengthen the magnetic order—contraryto the case of Ce-based systems where magnet-ism usually becomes weakened by pressure.Compared to Ce, which does not exhibit a nuclearspin, two of the Yb isotopes have finite nuclearspin values [see below and section F of thesupplementary materials (17)].We have carried out magnetic and calori-

metric measurements on high-quality YbRh2Si2single crystals, using a nuclear-demagnetizationcryostat with a base temperature of 400 mK (17).Figure 1, A andB, display the temperature depen-dence of the field-cooled (fc) dc magnetizationM(T), measured upon warming at various mag-netic fields B ranging from 0.09 to 25 mT, ap-plied within the basal plane of the YbRh2Si2single crystals. The curves display peaks at 70mK,which is the well-established Néel tempera-ture for the AF order, as well as additional low-temperature anomalies. There is a second peak inM(T)/B at Tc ≃ 2 mK, which indicates an almost-simultaneous onset of a nuclear-dominated AForder (“A phase”) and the Meissner effect (seebelow). It is visible above 1 mK up to 23mT andhad already been observed previously (18). In

addition, there is a shoulder around TB ≈ 10 mK,as defined in Fig. 1C. Below TB, the results ofthe fc and zero-field-cooled (zfc) measurementsbecome different. This divergence, which is as-cribed to superconducting fluctuations [sectionF of (17)], can be followed as a function of themagnetic field, up to the limit of our setup (B =0.5 mT) for measurements of the dc magnetiza-tion cooled at zero field.At T ≃ 2 mK, the zfc dc M(T)/B (0.012 mT)

shows a sharp increase upon warming, startingfrom negative values (Fig. 1C). This indicatesa substantial shielding signal due to supercon-ductivity. Raising the temperature further, thezfc M(T)/B slowly increases until it meets the fccurve at 10mK. To verify this finding, we carriedout measurements of the ac susceptibility, cac,under nearly zero-field conditions [section D of(17)]. Its real part, c′ac(T), displays an even morepronounced diamagnetic signal (Fig. 1D), largerthan what was found for the canonical heavy-electron superconductor CeCu2Si2 (19), againconfirming the occurrence of superconductingshielding. In addition, the reduction of the fcmagnetization upon cooling below 2 mK reflectsflux expulsion from the sample (Meissner effect).The relatively small Meissner volume of ≈3% ismost likely due to strong flux pinning [section Cof (17)]. As shown in fig. S7, the superconductingphase transition is of first order. This suggeststhat superconductivity does not coexist on amicroscopic basis with AF order, as previouslyobserved for A/S-type CeCu2Si2 [compare withsection D of (17)].In Fig. 2A, the specific heat is displayed as

C(T)/T at B = 2.4 and 59.6 mT, respectively. Asthe electronic specific heat can be completelyneglected below T ≈ 10mK (20), C(T) denotes thenuclear contribution in this low-T regime. Thesolid lines show the calculated nuclear specificheats at various fields from (20), which includethe quadrupolar as well as the Zeeman terms. Atzero field, the nuclear specific heat is completelydominated by the nuclear quadrupole states, towhich the Zeeman terms due to the nuclear spinstates add at B > 0. In Fig. 2B, we display DC(T)/T,where DC marks the difference between the spe-cific heat measured at the lowest field B = 2.4 mTand the nuclear quadrupole contribution calcu-lated for B = 0 (20). Our DC(T)/T results clearlyreveal a peak at T ≈ 1.7 mK. Assuming a con-tinuous phase transition, the transition temper-ature can be obtained by replacing the high-Tpart of this peak by a sharp jump while keepingthe entropy unchanged. This yields a jump heightof ~1000 J/K2 mol and TA ≈ 2 mK (B = 2.4 mT),almost coinciding with Tc (Fig. 1). Because theeffect of the magnetic field on the quadrupolecontribution to the nuclear specific heat is ofhigher order only, we can use the DC(T)/T dataof Fig. 2B to estimate the nuclear spin entropy(at B = 2.4 mT), SI(T) [section F of (17)]. SI;tot ≃1:35 Rln2 (whereR is the gas constant), the totalnuclear spin entropy of YbRh2Si2 for B = 2.4mT,is reachedatT≈ 10mK,whereDC(T) vanisheswithinthe experimental uncertainty (Fig. 2C).Uponcoolingto T = TA, SI(T) decreases to ~0.94SI,tot—that is,

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1Walther Meissner Institut für Tieftemperaturforschung derBayerischen Akademie der Wissenschaften, 85748 Garching,Germany. 2Max Planck Institute for Chemical Physics ofSolids, 01187 Dresden, Germany. 3Physikdepartment,Technische Universität München, 80333 München, Germany.4Physics Institute, University of Frankfurt, 60438 Frankfurt,Germany. 5Department of Physics, Renmin University ofChina, Beijing 100872, China. 6Department of Physics andAstronomy, Collaborative Innovation Center of AdvancedMicrostructures, Shanghai Jiaotong University, Shanghai200240, China. 7Department of Physics and Astronomy, RiceUniversity, Houston, TX 77005, USA. 8Center for CorrelatedMatter, Zhejiang University, Hangzhou, Zhejiang 310058,China. 9Institute of Physics, Chinese Academy of Sciences,Beijing 100190, China.*Corresponding author. E-mail: steglich@cpfs.mpg.de (F.S.);eschuber@ph.tum.de (E.S.); qmsi@rice.edu (Q.S.)

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most of this nuclear spin entropy must be re-leased below the phase transition temperatureTA. The entropy of the

103Rh and 29Si spins is tem-perature independent at T > 1 mK, but the Yb-derived spin entropy SYb(T) decreases by 26%

upon cooling from 10 to 2 mK [compare withsection F of (17)]. This indicates substantial short-range order, consistent with a second-order(antiferro)magnetic phase transition. We stressthat this very large entropy at ultralow temper-

atures (Fig. 2C) can only be understood if theordering transition at TA involves the Yb-derivednuclear spins to a substantial degree.To explore the role of the nuclear spins in

the phase diagram [(3, 6) and Fig. 3], we take

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Fig. 1. Temperature dependence of the dc magneti-zation and ac susceptibility for YbRh2Si2. (A) Field-cooled (fc) dc magnetization curve of YbRh2Si2 takenat B = 0.09 mT applied within the basal plane. Threemain features are clearly visible: the AF phase tran-sition at TAF = 70 mK, a shoulder in magnetization atTB ≈ 10 mK, and a sharp peak at Tc = 2 mK. (B) Seriesof fc magnetization data taken at fields of 0.10, 1.13,1.13, 5.01, 7.48, 10.12, 15.01, 20.04, 22.42, and 25.02 mT.(C) Zero-field-cooled (zfc) and fc dc magnetizationtraces taken at selected small magnetic fields.The tracesat 0.028, 0.055, and 0.418 mTwere shifted upward forbetter visibility. For the smallestmagnetic field of 0.012mT,a sharp diamagnetic shielding signal is observed, sug-gesting a superconducting phase transition. (D) The acsusceptibility was measured using a superconductingquantum interference device magnetometer by modu-lating a primary coil around the pickup coils. Here weshow the in-phase signal c′ac(T) (at 17 Hz), havingcompensated the Earth field. The features seen at TAF,TB, and Tc in the dc magnetization curve are also de-tected by the ac susceptibility. The large negative val-ues of the zfc dc magnetization at B = 0.012 mT (Fig.1C) and of c′ac(T) indicate superconducting shielding,whereas the low-temperature peak in the fc dc mag-netization (Fig. 1, A to C) signals the onset of theMeissner effect. Measurements in (A) to (D) were per-formed on samples 1, 2, 3, and 4, respectively.

5

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1 10 100

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100 0

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M/B

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-6m

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)

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-6m

3 /mol

)

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0

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T (mK)

TB

B ⊥ c (mT)0.4180.0550.0280.012

-0.8

-0.4

0

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1 10 100

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SI)

T (mK)

Tc

B = 0

0.1

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1000

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1 10 100

C/T

(J/

K2 m

ol)

T (mK)

YbRh2Si2

B ⊥ c

TA

µYb /µB

0.150.050.010.00

B (mT)59.62.4

0.8

0.9

1

0 2 4 6 8 10 12

SI /

SI,t

ot

T (mK)

0

500

1000

1500

1 2 3 4 5 6

∆ C/T

(J/

K2 m

ol)

T (mK)

B = 2.4 mT

TA

Fig. 2. Nuclear specific heatand entropy of YbRh2Si2.(A) The temperature depen-dence of the specific heat C(T)of YbRh2Si2 divided by T isshown for B = 2.4 and 59.6 mT[section E of (17)]. The 2.4-mTdata extend down to 1.4 mK.The solid lines denote the cal-culated nuclear specific heatfrom (20), which is the sumof the quadrupolar term andthe Zeeman term with three

selected field-induced Yb-derived ordered magnetic moments: 0.01, 0.05, and 0.15(mYb/mB).The large errors at temperatures above 10 mK are due to the uncertainty in the subtractionof the addendum [section E of (17)]. (B) DC(T)/Twas obtained by subtracting the nuclearquadrupolar contribution calculated for B = 0 from the data at B = 2.4 mT. A peak in DC(T)/Toccurs at ≈1.7 mK. Assuming the transition to be of second order, an equal-area constructionyields a nuclear phase transition temperature TA ≈ 2 mK. This coincides with the peak

position found in the dc magnetization (compare with Fig. 1)—that is, the superconducting critical temperature Tc at 2.4 mT.The associated jump of DC(T)/Tis on the order of 1000 J/K2 mol. The error bars reflect the statistical error in the measurements of the specific heat by using a quasi-static heat-pulsetechnique, as well as the relaxation method. In the latter case, the error bar contains the statistical error in determining both the relaxation time and the heatconductivity of the weak link. In total, two runs have been performed for each field; therefore, four sets of data at the same temperature were used fordetermining the specific heat. Each data point was weighted by its reciprocal error. At the lowest temperatures, the error associated with the relaxationmethod is essentially smaller than that of the heat-pulse measurement. (C) From DC(T)/T (Fig. 1B), a rough estimate can be made for the nuclear spinentropy SI(T) at B = 2.4 mT (see text). We have normalized SI(T) to SI,tot, the total nuclear spin entropy in YbRh2Si2 at B = 2.4 mT, reached at ~10 mK. Bysubtracting from SI(T) the contribution of the nuclear Si and Rh spins, which is temperature independent at T ≥ 1 mK, we obtain the corresponding valuesSYb(T) for the nuclear Yb spins. Measurements were performed on sample 3.

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advantage of the early recognition that hyper-fine coupling to nuclear spins can considerablyinfluence the electronic spin properties near aquantum phase transition (21). Furthermore, mea-surements on PrCu2 and related compounds havedemonstrated a large coupling between the elec-tronic and nuclear spins in rare-earth–basedintermetallics at temperatures up to 50mK (22,23). These considerations raise the possibility ofusing the presence of nuclear spins to weakenthe electronic AF order, thereby enabling theformation of a superconducting state. We havewritten down a Landau theory of the interplaybetween the magnetic orders of the electronicand nuclear spins. Consider the electronic AForder, with an order parameter mAF at the AFwave vectorQAF, as well as two bilinearly coupledorder parameters, mJ and mI, the staggeredmagnetizations of the electronic and nuclearspins at another finite wave vectorQ1 ≠ QAF. Thebilinear coupling arises from the hyperfine cou-

pling between the two order parameters havingthe same wave vector. The Landau theory willthen have the following free-energy functional

f ¼ 1

2rAFf

2AF þ

1

4uAFf

4AF þ

1

2rJf

2J þ

1

4uJf

4J þ

1

2rIf

2I þ

1

4uIf

4I − lfJfI þ

1

2ef2AFf

2I þ

1

2hf2Jf

2AF

where fAF, fJ, and fI are, respectively, thenormalized order parametersmAF,mJ, andmI;the r terms are quadratic couplings; the uterms as well as e and h are the intracompo-nent as well as intercomponent quartic cou-plings; and l is the bilinear hyperfine couplingbetween two normalized order parameters[section G of (17)].Under suitable conditions (17), this can lead to

two stages of phase transitions (Fig. 4). Thephase transition at TAF corresponds to the pri-maryAForder setting inat~70mKand isnotmuch

affected by the nuclear spins. In a suitable pa-rameter range of the Landau theory, the nuclear fIorder dominates over the electronic fJ order and,furthermore, suppresses the primary electronicfAF order. A second transition occurs at Thyb,which represents a hybrid electronic-nuclear spinorder. The component that is associated with thenuclear spins generates substantial entropy forthe transition, which explains the large nuclearspin entropy that is experimentally observed (Fig.2C) [section E of (17)]. In addition, the effectiveg-factor (geff) is on the order of gelfJ=fI (wheregel is the electron g-factor), which is substantiallysmaller than the bare g-factor for the 4f elec-trons. This explains the geff < 0.1 observed in ourexperiment.We thus conclude that the A phase forming at

TA ≃ 2 mK is an electronic-nuclear hybrid phasedominated by the Yb-derived nuclear spin order-ing. We estimate that the small (1 to 2%) 4f elec-tronic component contributes about one-third ofthe decrease inM(T) below TA [section C of (17)].As the nuclear phase transition cannot be resolvedbecause of the very small nuclear moment, themajor part of this reduction ofM(T) (i.e., the othertwo-thirds) must be due to the Meissner effect[section C of (17)]. A measurement of the fc dcmagnetization at very low fields reveals two sep-arated phase transitions close to T = 2 mK: TAand Tc (fig. S3B). Upon increasing the field to ~3to 4mT, however, TA and Tc appear tomerge with-in the experimental uncertainty (fig. S3C). Asmen-tioned previously, this peak in the fc dc M(T)curve remains visible (above 1mK)up toB ≃ 23mT(Fig. 1B). By analyzing magnetization data takenbetween 0.8 and 540 mK at a field of 10.1 mT(fig. S4), we conclude that superconductivity islikely to exist and coincide with the A phase at

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K)

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B ⊥ c

AF

PM

A + SC

B

YbRh2Si2

0

0.5

1.8 2

B (m

T)

T (mK)

A + SC

Fig. 3. Generic Tversus B phase diagram of YbRh2Si2.This phase diagram (shown on semi-logarithmicscales) is obtained from dc magnetization and ac susceptibility measurements in several magnetic fields.Four samples were measured, and no sample dependence was found. AF indicates the electronic AF order(TAF = 70 mK); PM indicates the paramagnetic state. All data points used to illustrate the AF-PM phaseboundary TAF(B) were obtained in the present study.The hatched light-blue area indicates the onset ofA-phase fluctuations, which give rise to a reduction of the staggered magnetization and a splitting ofthe zfc and fc dc magnetization curves (i.e., the beginning of shielding due to superconducting fluc-tuations) (Fig. 1C). The two data points (gray triangles) determined via field sweeps of the dc mag-netization between 3.6 and 6.0 mK (fig. S4) are most likely not related to these A-phase fluctuations. TheA + SC phase represents the concurring (dominantly) nuclear AF order and superconductivity, at least atfields below 3 to 4 mT. Only at B = 0 is nearly full shielding observed. The low-temperature limit of ourexperiment is ~800 mK; therefore, we cannot detect the fc dcM(T) peaks above 23 mT.The two red dashedlines mark the range within which the A-phase boundary line may end. At low fields (B < 4 mT), thetransition at ~2 mK is split into two parts (compare with fig. S3). The green circle indicates the su-perconducting transition temperature seen in the ac susceptibility at B = 0 (compare with Fig. 1D),whereas the yellow circles (partially covered by the green point) result from the shielding signals in the zfcdc magnetization (Fig. 1C). (Inset) These shielding transitions are shown separately on an enlarged scale.The superconducting phase boundary Tc versus B is extremely steep at low fields,with−dBc2=dTTc ≈ 25 T/K,consistent with results for the canonical heavy-electron superconductor CeCu2Si2 [section A of (17)]. Ifsuperconductivity exists at higher fields,Bc2(T) extrapolates to 30 to 60mT (at T=0)—that is, close to thecritical field of the primary electronic AF phase.

TTAFThyb

TAFT I

A hf

T

Thyb TAF T

ΨSCmAF

Fig. 4. Phase transitions at TAF and Thyb. (A)Sketch of the two phase transitions associatedwith electronic and nuclear spin orders. (Top line)Without any hyperfine coupling (Ahf), the electronicand nuclear spins are ordered at TAF and TI, re-spectively. (Bottom line)With a hyperfine coupling,TAF is not affected, but a hybrid nuclear and elec-tronic spin order is induced at Thyb ≫ TI . (B) Tem-perature evolution of the primary electronic spinorder parameter (mAF) and the superconductingorder parameter fSC. fSC is developed whenmAF issuppressed by the formation of hybrid nuclear andelectronic spin order directly below Thyb.

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elevated fields, consistent with the evolution of theM(T) peak as a function of field [section C of (17)].Figure 4 describes a possible scenario for the

two stages of transitions. Below TAF, the Néelorder develops. We speculate that the growth ofthe Néel order parameter mAF is arrested as thetemperature is lowered past Thyb, due to theonset of the nuclear spin order. A diminishedmAF would place the electronic phase in theregime close to the QCP that underlies the pureelectronic system in the absence of any hyperfinecoupling. This quantum criticality effectively in-duced by the nuclear spin order at zeromagneticfield would naturally lead to the development ofa superconducting state [section I of (17)]. Asinferred from the experimental results (Fig. 1C),fluctuations of the A phase are already set in nearTB and lead to a substantial reduction of the stag-geredmagnetization and the emergence of super-conducting fluctuations well above the A-phaseordering temperature [section I of (17)].The large initial slope of the superconducting

upper critical field Bc2(T) at Tc ≃ 25 T/K, ex-tracted from both shielding (Fig. 3, inset) andMeissner measurements (fig. S3C), correspondsto an effective charge-carrier mass of several hun-dred me (where me is the rest mass of the elec-tron), which implies that the superconductingstate is associatedwith the Yb-derived 4f electrons(heavy-electron superconductivity). Extrapolatingthe positions of the low-temperature fc M(T)peak to zero temperature, the critical field of theAphaseBA =B(TA→0) is found to be 30 to 60mT,which corresponds to geff = kBTA(B = 0)/mBBA =0.03 to 0.06 (where kB is the Boltzmann constantand mB is the Bohr magneton). This value of geff ismuch smaller than the in-plane electronic g-factor3.5 (24) but is a factor of 20 to40 larger than in caseof a purely nuclear spin ordering transition. Wecan understand this geff if the ordered momentis a hybrid of the electronic and nuclear spinswith, at most, 2% of the ordered momentsbeing associated with the 4f electron–derivedspins.The very large entropy near TA ≥ 2 mK is one

of the most pronounced features in our observa-tion. An alternative possibility for this entropy isthe involvement of a “nuclear Kondo effect”—that is, the formation of a singlet state betweenthe nuclear and conduction electron spins. Theresulting superheavy fermions may be assumedto form Cooper pairs and cause a superconduct-ing transition at Tc ≈ 2mK that would be probedby the magnetic and specific-heat measurements.Though our estimates of the nuclear Kondo tem-perature and the quasi-particle effective massreveal discrepancies with this picture [section Eof (17)], further theoretical and experimental workis needed to investigate the possible role of thenuclear Kondo effect in generating superconduc-tivity in YbRh2Si2.It is likely that the coupling of electronic and

nuclear spin orders, as well as the concomitantemergence of new physics, is not exclusive toYbRh2Si2 [section H of (17)]. Systematic studiesof other heavy-electron antiferromagnets atultralow temperatures are needed to find out

whether a hybrid electronic-nuclear order is amore general phenomenon. In addition, a com-parative study would be highly welcome to eval-uate whether superconductivity is truly absentin isotopically enriched YbRh2Si2 without Yb-derived nuclear spins, similar to the compoundstudied in (25).Our ultralow-temperature measurements on

the unconventional quantum critical materialYbRh2Si2 reveal heavy-electron superconductivitybelow Tc = 2 mK. This observation strongly sup-ports the notion that superconductivity near anAF instability is a robust phenomenon.

REFERENCES AND NOTES

1. P. A. Lee, N. Nagaosa, X.-G. Wen, Rev. Mod. Phys. 78, 17–85(2006).

2. H. Löhneysen, A. Rosch, M. Vojta, P. Wölfle, Rev. Mod. Phys.79, 1015–1075 (2007).

3. P. Gegenwart, Q. Si, F. Steglich, Nat. Phys. 4, 186–197(2008).

4. N. D. Mathur et al., Nature 394, 39–43 (1998).5. O. Stockert et al., Nat. Phys. 7, 119–124 (2011).6. J. Custers et al., Nature 424, 524–527 (2003).7. H. Shishido, R. Settai, H. Harima, Y. Ōnuki, J. Phys. Soc. Jpn.

74, 1103–1106 (2005).8. T. Park et al., Nature 440, 65–68 (2006).9. G. Knebel, D. Aoki, J.-P. Brison, J. Flouquet, J. Phys. Soc. Jpn.

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14547–14551 (2010).14. Q. Si, S. Rabello, K. Ingersent, J.-L. Smith, Nature 413,

804–808 (2001).

15. P. Coleman, C. Pépin, Q. Si, R. Ramazashvili, J. Phys. Condens.Matter 13, R723–R738 (2001).

16. T. Senthil, M. Vojta, S. Sachdev, Phys. Rev. B 69, 035111(2004).

17. Supplementary materials are available on Science Online.18. E. Schuberth, M. Tippmann, C. Krellner, F. Steglich, Phys. Stat.

Solidi B 250, 482–484 (2013).19. F. Steglich et al., Phys. Rev. Lett. 43, 1892–1896

(1979).20. A. Steppke et al., Phys. Stat. Solidi B 247, 737–739

(2010).21. H. M. Rønnow et al., Science 308, 389–392

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(2013).24. J. Sichelschmidt, V. A. Ivanshin, J. Ferstl, C. Geibel, F. Steglich,

Phys. Rev. Lett. 91, 156401 (2003).25. G. Knebel et al., J. Phys. Soc. Jpn. 75, 114709

(2006).

ACKNOWLEDGMENTS

We thank K. Andres, P. Coleman, P. Gegenwart, S. Paschen, andS. Wirth for useful discussions. Part of the work at the Max PlanckInstitute for Chemical Physics of Solids was supported by theDeutsche Forschungsgemeinschaft Research Unit 960 “QuantumPhase Transitions.” Q.S. was supported by NSF grant DMR-1309531and Robert A. Welch Foundation grant C-1411. E.S., Q.S., and F.S.thank the Institute of Physics, Chinese Academy of Sciences, Beijing,for hospitality. Q.S. and F.S. acknowledge partial support from theNSF under grant 1066293 and the hospitality of the Aspen Center forPhysics. We declare no competing financial interests.

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/351/6272/485/suppl/DC1Materials and MethodsSupplementary TextFigs. S1 to S9References (26–65)

23 February 2015; accepted 16 December 201510.1126/science.aaa9733

GEOPHYSICS

Periodic slow slip triggersmegathrust zone earthquakes innortheastern JapanNaoki Uchida,1* Takeshi Iinuma,2† Robert M. Nadeau,3 Roland Bürgmann,4 Ryota Hino1

Both aseismic and seismic slip accommodate relative motion across partially coupled plate-boundary faults. In northeastern Japan, aseismic slip occurs in the form of deceleratingafterslip after large interplate earthquakes and as relatively steady slip on uncoupled areasof the subduction thrust. Here we report on a previously unrecognized quasi-periodicslow-slip behavior that is widespread in the megathrust zone. The repeat intervals of theslow slip range from 1 to 6 years and often coincide with or precede clusters of large[magnitude (M) ≥ 5] earthquakes, including the 2011M 9 Tohoku-oki earthquake.These resultssuggest that inherently periodic slow-slip events result in periodic stress perturbationsand modulate the occurrence time of larger earthquakes.The periodicity in the slow-slip ratehas the potential to help refine time-dependent earthquake forecasts.

Slow (or aseismic) slip is a process by whichfaults displace rocks like earthquakes do,but muchmore slowly and without gener-ating seismic waves (1, 2). Slow fault-slipevents increase stress in adjacent areas

andmay trigger damaging earthquakes (3). Fore-

shocks are sometimes related to precursory slowslip (4–6), and some slow-slip events revealedby geodetic measurements are accompanied byseismicity rate changes (7). However, the rela-tionship between large earthquakes and aseismicslip is not well understood because of the poor

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2Si2Emergence of superconductivity in the canonical heavy-electron metal YbRh

Christoph Geibel, Rong Yu, Qimiao Si and Frank SteglichErwin Schuberth, Marc Tippmann, Lucia Steinke, Stefan Lausberg, Alexander Steppke, Manuel Brando, Cornelius Krellner,

DOI: 10.1126/science.aaa9733 (6272), 485-488.351Science 

, this issue p. 485Scienceall. Almost simultaneously with superconductivity, another order appeared that showed signatures of nuclear spin origin.measurements at extremely low temperatures and magnetic fields and found that it does become superconducting after

performed magnetic and calorimetricet al., which undergoes a magnetic QPT. Schuberth 2Si2being the material YbRhpressure are varied. In heavy fermion compounds, superconductivity often accompanies QPTs, a seeming exception

Quantum phase transitions (QPTs) occur at zero temperature when parameters such as magnetic field orGoing to extremes to find superconductivity

ARTICLE TOOLS http://science.sciencemag.org/content/351/6272/485

MATERIALSSUPPLEMENTARY http://science.sciencemag.org/content/suppl/2016/01/27/351.6272.485.DC1

REFERENCES

http://science.sciencemag.org/content/351/6272/485#BIBLThis article cites 63 articles, 6 of which you can access for free

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is a registered trademark of AAAS.ScienceScience, 1200 New York Avenue NW, Washington, DC 20005. The title (print ISSN 0036-8075; online ISSN 1095-9203) is published by the American Association for the Advancement ofScience

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