Fermi surface reconstruction and multiple quantumphase transitions in the antiferromagnet CeRhIn5Lin Jiaoa, Ye Chena, Yoshimitsu Kohamab, David Grafc, E. D. Bauerb, John Singletonb, Jian-Xin Zhub, Zongfa Wenga,Guiming Panga, Tian Shanga, Jinglei Zhanga, Han-Oh Leea, Tuson Parkd, Marcelo Jaimeb, J. D. Thompsonb,Frank Steglicha,e, Qimiao Sif,1, and H. Q. Yuana,g,1

aCenter for Correlated Matter and Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310058, China; bLos Alamos National Laboratory, LosAlamos, NM 87545; cNational High Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32310; dDepartment of Physics, SungkyunkwanUniversity, Suwon 440-746, Korea; eMax Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany; fDepartment of Physics and Astronomy, RiceUniversity, Houston, TX 77005; and gCollaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

Edited by J. C. Séamus Davis, Cornell University, Ithaca, NY, and approved December 2, 2014 (received for review July 23, 2014)

Conventional, thermally driven continuous phase transitions aredescribed by universal critical behavior that is independent of thespecific microscopic details of a material. However, many currentstudies focus on materials that exhibit quantum-driven continuousphase transitions (quantum critical points, or QCPs) at absolutezero temperature. The classification of such QCPs and the questionof whether they show universal behavior remain open issues. Herewe report measurements of heat capacity and de Haas–van Alphen(dHvA) oscillations at low temperatures across a field-induced anti-ferromagnetic QCP (Bc0 ≈ 50 T) in the heavy-fermion metal CeRhIn5.A sharp, magnetic-field-induced change in Fermi surface is detectedboth in the dHvA effect and Hall resistivity at B*0 ≈ 30 T, well insidethe antiferromagnetic phase. Comparisons with band-structure cal-culations and properties of isostructural CeCoIn5 suggest that theFermi-surface change at B*0 is associated with a localized-to-itiner-ant transition of the Ce-4f electrons in CeRhIn5. Taken in conjunctionwith pressure experiments, our results demonstrate that at leasttwo distinct classes of QCP are observable in CeRhIn5, a significantstep toward the derivation of a universal phase diagram for QCPs.

heavy fermion | quantum phase transitions | superconductivity |Fermi surface reconstruction | localized-itinerant transition

Intermetallic heavy-fermion metals, the ground states of whichcan be tuned readily by control parameters other than temper-

ature, such as magnetic field, pressure, or chemical composition,form attractive systems for the study of quantum critical points(QCPs) (1, 2). Despite examples of QCPs in many heavy-fermionmaterials, their theoretical classification, analogous to that forthermally driven phase transitions, is yet to be achieved (2, 3). Anextension of the theory of thermally driven critical points to thezero-temperature limit predicts that only fluctuations of an orderparameter [for example, the sublattice magnetization of a spin-density wave (SDW)] are singular in space and time at a criticalvalue of the control parameter (4–6). The Fermi surface evolvessmoothly across the QCP. Although there is some experimentalsupport for this model of a QCP [e.g., in CeCu2Si2 (7)], thequantum critical response of some other heavy-fermion compoundsis clearly inconsistent with its predictions (8–10). Going beyond thisconventional Landau framework, a qualitatively different modelpredicts a sharp reconstruction of the Fermi surface while crossingthe QCP owing to the essential involvement of the electronicdegrees of freedom (11–13). Such an unconventional QCP hasbeen proposed to involve the critical destruction of the Kondoeffect, in addition to fluctuations of the order parameter (3). Be-havior that supports this type of QCP has been found in variousheavy-fermion systems, including UCu5-xPdx (8), CeCu6-xAux (9),and YbRh2Si2 (10). In each material, however, direct evidence fora change in Fermi surface is lacking. Besides the needs to verify thebasic predictions of this model of QCPs, a further test of its validityis the more restrictive observation of a change in the Fermi surfaceas a function of multiple tuning parameters.

CeRhIn5, a heavy-fermion antiferromagnet with a Néel tem-perature TN ≈ 3.8 K at ambient pressure (14), is very suitable forthis purpose. As shown in the schematic phase diagram at zerotemperature (Fig. 1A), application of pressure suppresses theantiferromagnetic (AF) order and induces superconductivity (15,16). In the presence of a modest magnetic field, sufficient tosuppress superconductivity, an AF QCP is exposed throughpressure tuning (15, 16). A distinct change of the Fermi surface isobserved across this pressure-induced QCP via dHvA oscillations(Fig. 1A, blue arrow) that find a large Fermi surface, like that ofCeCoIn5, above the QCP (17). In addition, the AF order ofCeRhIn5 is robust against magnetic field at ambient pressure(18). Thus, CeRhIn5 permits measurements of magnetic quan-tum oscillations across its field-tuned QCP at ambient pressure,providing a rare system in which the nature of QCPs can beprobed using more than one tuning parameter.Here, we report our study of the phase transitions in CeRhIn5

at ambient pressure using isothermal measurements of the acheat capacity and dHvA oscillations in pulsed magnetic fields ofup to 72 T (Fig. 1B), plus Hall resistivity and dHvA oscillations ina dc field of up to 45 T (SI Appendix). These experiments allowexplicit mapping of the magnetic field-temperature phase dia-gram and the investigation of the evolution of the Fermi surfaceas a function of magnetic field.

Significance

Conventional, thermally driven continuous phase transitions aredescribed by universal critical behavior that is independent ofmicroscopic details of a specific material. An analogous de-scription is lacking for phase transitions that are driven at abso-lute zero temperature by a nonthermal control parameter.Classification of quantum-driven phase transitions is a funda-mental but open problem that arises in diverse contexts andmultiple classes of materials. Here we report the first observation,to our knowledge, of a sharp Fermi surface reconstruction whileapplying a strongmagnetic field to suppress an antiferromagnetictransition to zero temperature. These experiments demonstratethat direct measurements of the Fermi surface can distinguishtheoretically proposed models of quantum criticality and point toa universal description of quantum phase transitions.

Author contributions: H.Q.Y. designed research; L.J., Y.K., Z.W., and H.Q.Y. performed thehigh-field measurements with assistance from D.G., J.S., and M.J.; Samples were grown byE.D.B., T.S., H.-O.L., and J.D.T.; L.J., Y.C., E.D.B., Z.W., G.P., J.Z., and T.P. characterized thesamples and partially prepared for the experiments; L.J., Y.C., Y.K., J.S., Z.W., and H.Q.Y.analyzed the experimental data; J.-X.Z. and Q.S. carried out theoretical calculations and ana-lyses; and L.J., F.S., Q.S., and H.Q.Y. wrote the manuscript with suggestions from J.S. and J.D.T.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence may be addressed. Email: hqyuan@zju.edu.cn or qmsi@rice.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1413932112/-/DCSupplemental.

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ResultsDetermination of the Magnetic Field-Temperature Phase Diagram.Fig. 2A displays the 3D plots of the heat capacity coefficientCp/T as a function of magnetic field and temperature forCeRhIn5 with B//c. Similar results were also observed for B//a (SIAppendix, Fig. S3). The pronounced maximum in Cp(B)/T marksthe onset position Bc(T) of the suppression of the Néel transitionby the magnetic field. The magnetic phase boundary TN(B) ofCeRhIn5 is then derived by projecting Bc(T) onto the B–T plane;the corresponding phase diagrams (B//a and B//c) are shown inFig. 2B. At low fields the boundaries are consistent with heat-capacity results in fields provided by a Physical PropertiesMeasurement System (PPMS) (Quantum Design). These heat-capacity data, along with the field dependence of the magneticsusceptibility (B//a) (Fig. 1B and SI Appendix, Fig. S4) yield a T =0 critical field Bc0 [≡Bc(T→0)] of about 50 T. In the low-tem-perature limit, the heat-capacity coefficient Cp(B)/T is sub-stantially enhanced in the paramagnetic phase (B > Bc) incomparison with that well inside the AF state (Fig. 2B, Inset).

Evidence for a Field-Induced Reconstruction of Fermi Surface. Wellinside the AF state a field-induced sharp change of Fermi sur-face is evidenced in the Hall resistivity ρxy(B) and the dHvAoscillations. Fig. 3A displays ρxy(B) at various temperatures.Here the field was applied along the c-axis; because of the flatsample geometry, it was difficult to measure the Hall resistivityfor fields applied within the ab plane. The jump in ρxy(B) aroundBM ≈ 18 T is attributed to a metamagnetic transition with thesample alignment slightly away from the c direction; BMincreases as a function of 1/cosθ when the field is tilted by θ from

[100] to [001], as found in other measurements (18). Upon fur-ther increasing the magnetic field the Hall resistivity ρxy(B)undergoes a sharp change at B* ≈ 31 ± 1 T, which disappears attemperatures above 1.4 K. Around B = B*, ρxy(B) changes slopesignificantly, suggesting a pronounced jump in the differentialHall coefficient RH = dρxy/dBjB = B*. For 20 T < B < 30 T, ρxy(B)decreases linearly with increasing field, indicating electron-typemajority carriers. For B > 33 T, the negative slope of ρxy(B) issubstantially reduced compared with that at B < 30 T, and thereis a significant change in the curvature at higher fields, typicalbehavior of a multiband conductor. The jump of Hall coefficientat B* suggests a sharp change of Fermi surface.In Fig. 3B we show Fourier transforms of the dHvA oscil-

lations obtained at T = 0.33 K for B//c, which were measured byusing a torque technique (CuBe cantilever) in dc fields of up to45 T. For B < 30 T several dHvA frequencies and their har-monics are well identified, which coincide with previous results(19). With increasing field new (or shifted) dHvA frequencies,labeled α1, α2, and β1, show up above B* ≈ 30 T. Fig. 3C plots thefield evolution of the dHvA amplitudes of the α1 branch atseveral temperatures; the α2 and β1 branches show similar be-havior. One can see that the dHvA amplitudes suddenly vanisharound B* ≈ 30 T at the lowest temperatures, providing a precisedetermination of the onset field B* for the Fermi surface re-construction. The dotted line shows a fit of the data to the

Fig. 1. Schematic phase diagram and field-dependent data for CeRhIn5. (A)Schematic magnetic field-pressure phase diagram of CeRhIn5 at zero tem-perature. Pressure suppresses the AF order and induces superconductivity(SC), leading to several ground states (i.e., AF order, SC, and their co-existence) in the phase diagram (15, 16). A pressure-induced change from asmall to a large Fermi surface and a diverging effective mass are observed atthe AF QCP for fields larger than the superconducting upper critical field(17). What happens as a function of magnetic field at ambient pressure is thesubject of the present study. (B) Heat capacity and dHvA oscillations in apulsed magnetic field. The magnetic susceptibility (T = 0.5 K) and the co-efficient of the ac heat capacity Cp/T (T = 0.9 K) of CeRhIn5 are shown asa function of magnetic field (B//a) up to 70 T and 53 T, respectively. Theydisplay a metamagnetic transition at BM ≈ 2.5 T, and a transition from AF toparamagnetic (P) phases at a higher field Bc(T ). The upturn in Cp/T vs.B below B = 15 T is due to the metamagnetic transition and also the back-grounds (SI Appendix).

Fig. 2. Temperature and magnetic-field dependence of the heat-capacitycoefficient Cp/T for CeRhIn5. (A) Magnetic-field dependence of Cp/T at vari-ous temperatures for B//c. (B) Field dependence of the Néel temperatureTN(B) for B//c (square) and B//a (circle). Both curves extrapolate to nearly thesame critical field Bc0 at T = 0; the red and yellow symbols represent con-sistent data obtained in a PPMS-16T and in pulsed fields, respectively. (Inset)Cp/T vs. B at 1.4 K for B//c.

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Lifshitz–Kosevich (LK) equation (20) for fields above 30 T. TheLK formula predicts that the high-frequency oscillations shouldcontinue to be observable (i.e., have an amplitude well above thenoise floor) to fields well below 30 T, which is inconsistent withour experimental data. With increasing temperature the dHvAamplitude is reduced and the critical field B* slightly shifts tohigher temperature. Above T ≈ 1.4 K, where the Hall jumpdisappears, the new dHvA oscillations also cannot be resolved.Thus, both the Hall data and the dHvA oscillations consistentlyprovide strong evidence of a Fermi surface reconstructionaround B* ≈ 30 T at our base temperatures, with no indication ofreconstruction with increasing temperature above T ≈ 1.4 K.Evidence for an isotropic reconstruction of Fermi surface can

be inferred from measurements with fields applied along thea axis. Fig. 4A shows the results of dHvA oscillations measuredwith a piezo-cantilever in quasistatic fields provided by a 45-Thybrid magnet (B//a). This measurement is extremely sensitive totiny changes of the magnetization of the sample and thus pro-vides a largely enhanced resolution. Unfortunately, owing toexperimental constraints, we could only measure the sample upto 38 T at one temperature (T = 0.31 K). After subtracting thebackground, a pronounced change of dHvA oscillations is seenclearly around B* ≈ 30.5 T (Fig. 4A, Upper Inset). In Fig. 4A,Lower Inset, we plot the dHvA signals as a function of 1/B nearthe maximum field, which demonstrate periodic oscillations witha rather large frequency of around 10,600 T. As an alternative

depiction, the main panel plots the amplitude of the high-fre-quency dHvA oscillations averaged over 2-T windows. Re-sembling that of B//c, the collapse of dHvA amplitude at B* ≈30.5 T marks an abrupt change of Fermi surface; the so-derivedvalue of B* is very close to that for B//c, demonstrating a ratherisotropic value of B* for both B//a and B//c.To further examine the field-induced reconstruction of Fermi

surface we used an induction method to extend the measure-ments of dHvA oscillations in a 75-T pulsed magnet (B//a).These higher fields provide a much broader window for theanalysis of Fourier transforms than that of the dc field data. Fig.4B shows Fourier transforms of the dHvA oscillations obtainedat T = 0.5 K for field windows of 10 T < B < 30 T (B < B*) and45 T < B < 70 T (B > B*), respectively. The peaks, labeled fa1–fa4, in the dHvA spectrum are located within the frequency range

Fig. 3. Evidence of Fermi surface reconstruction for B//c. (A) Hall resistivityρxy(B) at different temperatures. ρxy(B) shows a metamagnetic transition atBM ≈ 18 T and a rapid change of the differential Hall coefficient RH = dρxy/dBat B = B* ≈ 31 T; the latter suggests a sharp reconstruction of Fermi surface.Note that the metamagnetic transition at BM disappears upon rotating thesample by about 7°, suggesting a small deviation of the applied magneticfield from the c axis. (B) Fourier spectra of the dHvA oscillations at variousmagnetic fields (T = 0.33 K). Here a field window of ΔB = 5 T is used for theFourier analysis at each magnetic field and the Fourier spectra are shiftedaccordingly along the y axis. (C) dHvA amplitude of the α1 branch vs. mag-netic field at several selected temperatures. Note that it is difficult to resolvethe dHvA oscillations from the noise below the field of the first data pointfor each temperature. The dotted lines show fits to the LK equation (20); thefitting parameters of TD = 1.5 K and m* = 6.6 m0 represent the Dingletemperature and the effective mass, respectively.

Fig. 4. Evidence of Fermi surface reconstruction for B//a. (A) dHvA ampli-tude vs. magnetic field for the large dHvA frequency observed above B* =30.5 T. Data are obtained by averaging the oscillatory amplitudes over a fieldwindow of 2T centered at each presented field. Here the noise level is com-parable with the symbol size. The dotted line shows a fit to the LK formulawith TD = 1.0 K and m* = 9.3 m0. (Upper Inset) The dHvA oscillations aftersubtracting the background. The onset of a new dHvA oscillation at B* ≈ 30.5T is seen clearly here as well as in the main panel. (Lower Inset) Plot of theperiodic oscillations of dHvA signals on a 1/B axis. The data were measured ina 45-T hybrid magnet using a piezo-cantilever. (B) Fourier spectra of the dHvAoscillations over field windows of 10 T < B < 30 T and 45 T < B < 70 T, re-spectively. Four new dHvA frequencies are observed in the high field region.Here the data were obtained in a pulsed field up to 70 T at T = 0.5 K.

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200—1,000 T for fields of 10 T < B < 30 T. They coincide wellwith our preceding data obtained in the 45-T hybrid magnet aswell as with previous measurements (19) and are characteristic ofa “small” Fermi surface that does not include the 4f electrons ofCe. Several higher harmonics of the most pronounced dHvAfrequencies (fa4 ≈ 790 T) are observed. Four new dHvA branches(fa5–fa8) with much larger frequencies (7 kT < f < 15 kT) occur atB > B*; the frequency of fa7 is close to that obtained in a dc field.These new dHvA frequencies persist up to T = 0.8 K but becomedifficult to resolve around T = 1 K. It is noted that, owing to theirshort duration, pulsed experiments may give lower signal-to-noise ratios than equivalent dc field measurements. Hence, lowertemperatures are needed to resolve all the dHvA oscillations.

Summary and DiscussionFig. 5A presents the temperature–magnetic field phase diagramof CeRhIn5 for B//a and B//c derived from our experimentaldata. On applying a magnetic field the AF transition tempera-ture TN is suppressed continuously to the lowest accessibletemperature (T ≈ 0.4 K for B//a), providing strong evidence foran AF QCP around Bc0 ≈ 50 T. The field dependence of TN, thatis, TN ∼ (Bc0 − B)2/3, suggests an SDW-type QCP. Inside the AFphase the electronic system undergoes a sharp reconstruction ofFermi surface at B*(T), changing from a local-moment antifer-romagnetic order (AFS) to an SDW of the large Fermi surface(AFL). Further experiments are needed to determine whetherthe B* line eventually fades away in the paramagnetic state orterminates at a critical end point.High-frequency dHvA oscillations potentially could emerge

with increasing magnetic field owing either to the so-calledDingle damping factor or to magnetic breakdown (20). However,it is clear from Fig. 3 and Fig. 4A that the higher frequenciesappear suddenly at B*, rather than growing smoothly. If theDingle factor were responsible for their growth, each oscillationshould gradually become visible over differing ranges of field.The scenario of magnetic breakdown at B* also can be excludedbecause the new dHvA frequencies appear at indistinguishablefields for B//a and B//c; in an anisotropic band structure, such asthat of CeRhIn5, any breakdown fields also would be anisotropic.Thus, all these suggest that the sudden emergence of new dHvAfrequencies at B* corresponds to a field-induced reconstructionof Fermi surface in CeRhIn5.Modifications of the magnetic structure in a magnetic field

(e.g., a metamagnetic transition) may induce a reconstruction ofFermi surface. With the current resolution of our experimentswe cannot detect any thermodynamic phase transition at B = B*either in magnetic susceptibility or heat capacity (cf. Fig. 1B).Furthermore, the critical field of a metamagnetic transitionusually varies with the field orientation as shown for the transitionat BM. Our observations of an isotropic value of B* for B//a andB//c disfavor such a scenario. Therefore, it is unlikely that thefield-induced Fermi surface reconstruction in CeRhIn5 is causedby a change in magnetic structure. Nevertheless, it is desired toperform experiments (e.g., high-field NMR measurements) todirectly examine it.The delocalization of 4f electrons, resulting from Kondo

screening, expands the Fermi volume and may give rise to theemergence of larger dHvA frequencies above B* in CeRhIn5.This is supported by the following facts. First is evolution ofdHvA frequencies: For B < B*, previous dHvA studies haveshown that the Ce-4f electrons are localized in CeRhIn5 and donot contribute to the Fermi sea (18, 21). Our results are com-patible with this conclusion. Above B*(T) new dHvA frequenciesare observed for B//a and B//c at low temperatures. They arecomparable to both the ones measured in CeCoIn5 (ref. 22 andSI Appendix, Fig. S6) and calculations for CeRhIn5 under theassumption of itinerant 4f electrons (cf. SI Appendix, Fig. S5).Second is the change of the Hall coefficient: According to ref. 18,

the Fermi surface of LaRhIn5, which has no 4f electrons, isdominated by electron pockets; the Fermi surface of CeRhIn5will be similar if the 4f electrons are localized, accounting for thenegative Hall coefficient at fields below B*. However, inCeCoIn5 the 4f electrons are itinerant, and the Fermi surface ismore 3D; the volumes of electron and hole pockets are nearlycompensated (18). With delocalized 4f electrons the Fermi sur-face of CeRhIn5 would be of an analogous form, explaining themore complicated variation of the Hall coefficient above B*.We note that a change in magnetic structure (e.g., a metamagnetictransition as discussed above) may lead to a jump in the Hall

Fig. 5. Experimental temperature-field phase diagram and its relation toa multiparameter theoretical phase diagram. (A) Temperature–magneticfield phase diagram of CeRhIn5 at ambient pressure. Squares and circlesrepresent the characteristic temperatures for B//a and B//c, respectively. TheNéel temperature, TN(B), was determined from the heat capacity measuredin a PPMS with a dc field of 16 T (red) and in a pulsed field (yellow) as well asthe dHvA oscillations (light blue, B//a). The dashed line displays the fielddependence TN ∼ (Bc0 − B)2/3, expected for a 3D-SDW QCP (6). The field B*(T)is determined from a jump of the Hall resistivity (orange circles, B//c) and theonset of new dHvA frequencies in the Fourier transform spectra (whitesquare for B//a; white circles for B//c). The error bars were determined fromthe width of the Hall resistivity jumps and the field interval ΔB = 5 T used inthe Fourier transform analysis. The phases AFS, AFL, and PL represent AF orparamagnetic (P) states with large (L) or small (S) Fermi surfaces. (B)A schematic magnetic field-pressure phase diagram of CeRhIn5 at T = 0.A pressure-induced AF QCP exists at low field and is accompanied by a sharpchange of the Fermi surface, indicating a destruction of the Kondo effect atzero temperature (17). However, as shown in this work, a sufficiently strongmagnetic field at ambient pressure also continuously suppresses the AFphase at Bc0. In this case, the Kondo destruction takes place inside the AFstate, and the AF QCP is likely to be of an SDW type. Further measurementsare to be performed to determine experimentally the phase diagram in theregime of finite pressures and high magnetic fields.

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resistivity. However, the Hall number usually is unchangedacross a metamagnetic transition, as observed at BM for CeRhIn5(Fig. 3A). This adds further evidence against a change of mag-netic structure at B*. Third is enhancement of the heat-capacitycoefficient: In Fig. 2B, Inset, we have shown that the heat-capacity coefficient, Cp(B)/T, at low temperatures is substantiallyenhanced upon applying a magnetic field to suppress the AForder, suggesting the development of a Kondo-derived heavyelectron state in a magnetic field. The persistence of the largeFermi surface up to at least B = 70 T at low temperatures can beunderstood by a simple consideration of the magnetic field andtemperature scales. The temperature for the onset of Kondoscreening in CeRhIn5 is about 10 K (14), more than twice theNéel temperature. Given that the critical magnetic field Bc0 isabout 50 T, the single-ion Kondo field is expected to be sub-stantially larger than the presently accessible fields.The above analyses suggest that, upon increasing the magnetic

field at ambient pressure and zero temperature, (i) an abruptchange of Fermi surface associated with a localized-itineranttransition of the 4f electrons occurs at B* ≈ 30 T (i.e., inside theAF state of CeRhIn5), whereas (ii) the AF QCP at Bc0 ≈ 50 T ispresumably of the SDW type. This is in contrast to what happensas a function of pressure at relatively low magnetic fields, wherethe dHvA oscillations indicate a 4f-localized/itinerant transitionat the AF QCP (17). Our results are therefore twofold. First,there are at least two different types of quantum phase tran-sitions in CeRhIn5, one induced by tuning a magnetic field andthe other accessed with varying pressure. Moreover, under thetuning of these two parameters, a jump of Fermi surface occursinside the AF state and at the AF QCP, respectively.As a potential scenario, in Fig. 5B we present a schematic

magnetic field-pressure phase diagram for CeRhIn5 at zerotemperature. Such a phase diagram can be qualitatively inter-preted in terms of a global phase diagram of quantum-criticalheavy-fermion metals (23, 24). This model delineates the evo-lution of the zero-temperature AF transition and the Kondodestruction in a multiparameter phase space. While tuning thecompound by a magnetic field at zero pressure, the Kondoresonances are switched on at B0*[≡B*(T→0)] before the AForder is suppressed at Bc0, and the Fermi surface evolves smoothlyacross the latter transition. This is in contrast to the transitioncaused by pressure at relatively low field, at which the Kondodestruction and magnetic transition take place simultaneously,leading to a jump of the Fermi surface at the zero-temperaturecontinuous AF phase transition (17). We note that the dynamicalKondo effect makes the mass heavy even when the Fermi surfaceis small (3, 23). According to this model, the AF QCP associatedwith the pressure-induced superconducting dome is then likely tobe of the unconventional type. This indicates that heavy-fermionsuperconductivity not only arises in the vicinity of SDW-typeQCPs (7, 25) but can also be driven by electronic fluctuationsarising from such an unconventional QCP at which the Kondoeffect is destroyed.Our experimental results and understandings have implica-

tions beyond CeRhIn5. They can be connected to the disparateresults in a variety of heavy-fermion materials. Considerable

evidence already exists that pure YbRh2Si2 under magnetic-fieldtuning (10) and CeCu6-xAux under the variation of doping (9)feature Kondo destruction at their respective AF QCP. How-ever, there also is evidence for Kondo destruction inside the AFregion of Co-doped YbRh2Si2 (26) as well as in magnetic-field-tuned CeCu6-xAux (27) and Ce3Pd20Si6 (28). In CeIn3, dHvAfrequencies and the corresponding cyclotron masses of heavy-hole pockets undergo a sharp increase near 40 T, which is belowthe critical field needed to suppress AF order to a QCP (29).This suggests the possibility of a similar localization/itineranttransition inside its AF phase, even though dHvA oscillationsassociated with the large Fermi surface have not yet been ob-served at high fields. In a related vein, it has been suggested thatKondo destruction occurs outside the AF region in materialssuch as Ir-doped YbRh2Si2 (26) and Yb2Pt2Pb (30). Our Fermi-surface characterization of multiple quantum phase transitions ina single compound not only provides new understanding aboutCeRhIn5 but also strengthens the case that the quantum phasetransitions of the other electron-correlated materials may beplaced on the proposed global phase diagram.

MethodsA detailed description of the methods and materials is given in SI Appendix.Single crystals of CeRhIn5 were grown by a flux method. Room-temperaturepowder X-ray diffraction measurements revealed that all of the crystals aresingle-phase and crystallize in the tetragonal HoCoGa5 structure. The ori-entation of the crystal was determined by X-ray Laue diffraction (SI Ap-pendix, section 1). Heat capacity and dHvA oscillations were measured inpulsed field magnets at the Los Alamos National Laboratory Pulsed FieldFacility (SI Appendix, section 2). A typical sample size for this study is about1 mm × 0.5 mm × 0.1 mm. An ac calorimeter was used for heat capacitymeasurements at fields up to B = 53 T and temperatures down to T = 0.9 K.Subtractions of the field-independent addenda contributions from the totalheat capacity allow us to determine the absolute values of heat capacity forthe sample. Magnetic susceptibility was measured by an induction methodup to B = 72 T and at temperatures down to T = 0.4 K, obtained by pumpingon liquid 3He in a 3He bath cryostat. The transverse Hall resistivity ρxy(B) aswell as the dHvA oscillations based on a torque method were measured ina 3He cryostat and in fields to 45 T generated by the hybrid magnet at theNational High Magnetic Field Laboratory (SI Appendix, sections 3 and 4).Band structure calculations were performed using the full-potential linear-ized augmented plane wave method as implemented in the WIEN2k code(SI Appendix, section 5).

ACKNOWLEDGMENTS. We thank S. Kirchner and R. Daou for valuablediscussion. Work at Zhejiang University was supported by National BasicResearch Program of China (973 Program) Grants 2011CBA00103 and2009CB929104, Natural Science Foundation of China Grants 11174245 and10934005, the Fundamental Research Funds for the Central Universities,and Zhejiang Provincial Natural Science Foundation of China. Work at LosAlamos National Laboratory was performed under the auspices of the De-partment of Energy (DOE) and was supported by the DOE/Office of ScienceProject Complex Electronic Materials. Work at the National High MagneticField Laboratory is also supported by the National Science Foundation (NSF),the State of Florida, and the DOE Basic Energy Sciences Program Science in100 T. T.P. acknowledges support from National Research Foundation Grant220-2011-1-C00014. Work at Dresden was partially supported by the GermanResearch Foundation Research Unit 960 Quantum Phase Transitions. Work atRice University was supported, in part, by NSF Grant DMR-1309531 andRobert A. Welch Foundation Grant C-1411.

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