Pressure-induced magnetic phase transition in gold-phase SmS

Y. Haga,1,2 J. Derr,1 A. Barla,1 B. Salce,1 G. Lapertot,1 I. Sheikin,3 K. Matsubayashi,4 N. K. Sato,4 and J. Flouquet1

1Département de Recherche Fondamentale sur la Matière Condensée, CEA, 38054 Grenoble Cedex 9, France2Advanced Science Research Center, Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-1195, Japan

3Grenoble High Magnetic Field Laboratory, MPI-FKF/CNRS, Boîte Postale 166 38042 Grenoble Cedex 9, France4Department of Physics, Graduate School of Science, Nagoya University, Nagoya 464-8602, Japan

(Received 30 August 2004; published 17 December 2004)

Electrical resistivity and specific heat of SmS in its gold phase have been investigated. AbovePD=2 GPa,the resistivity is characteristic of a metallic heavy fermion compound. Ac calorimetry points out a phasetransition with the occurrence of a new ground state. Analyses of the resistivity and of the specific heat andcomparison with a microscopic probe(149Sm nuclear forward scattering) allow us to identify the onset ofantiferromagnetism. Discussion will be made on the interplay of gap closingsP, PDd, long-range magnetismsP. PDd, and valence state.

DOI: 10.1103/PhysRevB.70.220406 PACS number(s): 75.30.Kz, 75.30.Mb, 71.27.1a, 81.40.Vw

SmS is a key material to clarify the physics of stronglycorrelated electronic systems as the valence of Sm is directlycoupled to the release of a light 5d itinerant electron:Sm2+Sm3++5d. At zero pressure, the Sm ions are in adivalent insulating state, the so-called black phase. At veryhigh pressuresPd, the Sm will be in a trivalent metallic state.Between the two limits, the valencesvd of Sm is intermedi-ate. This transition occurs discontinuously from 2+ to anintermediate valence(IV ) value at the well known black-to-gold-phase transition that corresponds to a first-order linePB-GsTd extensively studied three decades ago.1–3 At roomtemperature,PB-G=0.65 GPa. At low temperature, the first-order transition is accompanied by a large hysteresis;PB-Granging between 1.4 down to 0.5 GPa.

In the gold phasesP. PB-Gd, the change of the valenceseems to occur continuously. PreviousLIII absorption spectraof Sm in SmS(Ref. 4) as well as recent experiments at theEuropean Synchrotron Radiation Facility5 show that the va-lence starts withv=2.6 at PB-G, goes through a maximum]v /]P of its pressure derivative forP, PD=2 GPa withv=2.7, and then smoothly increases. The trivalent state may bereached continuously atP3+.10 GPa. Near 2 GPa, Kelleretal.6 have already pointed out an abnormally large pressurederivative of the bulk modulus. Whatever is the pressure byrespect toPB-G, the cubic rock-salt structure is preserved.Phonon anomalies through the valence transition have beenreported in an inelastic x-ray scattering study.7 BetweenPB-Gand PD=2 GPa, all resistivity measurements8–11 agree thatthe system ends up in an insulating phase at low temperatureas observed for the other IV systems, such as TmSe, SmB6,or YbB12.

1 The magnetic susceptibility in this low-pressuregold phase does not show a Curie-Weiss divergence at lowtemperature. The IV state is a homogeneous nonmagneticelectronic state.3 Above PD=2 GPa, again all resistivity ex-periments indicate a metallic ground state. The resistivityincreases on cooling before reaching a maximum atTM andthen decreases. Another phase transition may occur belowTM. When the Sm ion will reach its trivalent state aboveP3+,a long-range magnetic ordering atTN must occur since Sm3+

is a Kramer’s ion with a 2J+1=6 degeneracy(the same an-

gular momentumJ=5/2 as Ce3+) and may be lifted into aG7doublet and aG8 quartet by the cubic crystal field. Thus,when P increases towardsP3+, long-range magnetism willappear above a critical pressurePc as discovered for theytterbium heavy fermion compounds,12 the hole analog ofthe cerium ones. The key questions are first, the localizationof Pc with respect toPB-G, PD, and P3+, then the nature ofthe phase transition(first or second order), and finally, theorigin of the ordered moments knowing that different chan-nels are possible with the Sm2+ and Sm3+ configurations.

At low temperature, the selection of the wave functionamong those of the Sm2+sJ=0d and Sm3+sJ=5/2d configura-tion is the result of a subtle balance. For the well-known IVcase of TmSe atP=0, the degeneracy of the paramagneticground state13 seems to be that of the doublet of theTm2+sJ=7/2d configuration, despite the fact that the valenceis near 2.7–2.8.1,14 Only aboveP=3 GPa, does the wavefunction seem to be that of a trivalent state.15

Single crystals of different origins were investigated. Allthe materials were grown by the Bridgman technique. Theywere taken from growths realized at Yorktown Height8,9 inGrenoble and Sendai.11 As no significant differences werefound in the electric and calorimetric behavior, we will notrefer later to the sample origin. Piston-cylinder pressure cellswere used for resistivity measurements up to 2.4 GPa at lowtemperature. Transverse magnetoresistance under pressurewas measured at the Grenoble High Magnetic Field Labora-tory up to 23 T. Specific heat was measured by an ac-calorimetry method in a diamond anvil cell(DAC) usingargon as transmitting medium.16 The sample is thermallylinked with a heat bath and heated up by a heater whosepower is modulated by a frequencyv. As a result the tem-perature of the sample oscillates with the same frequency.Assuming that the leakage of heat from the sample to theenvironment is characterized by a thermal conductivityk, theamplitude of the temperature oscillationTac is written as afunction of the specific heatCac of the sampleTac=Q/ sk+ ivCacd, where Q is an average of the power transmittedfrom the heater to the sample. Here it is also assumed thatthe thermal relaxation within the sample is faster than 1/v. A

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mechanically chopped laser light was used as a heater. Thetemperature difference between the sample and the heat bathwas measured using a AuFe-Au thermocouple directlybonded on the sample. Frequency around 800 Hz was appro-priate to cover the temperature range between 2 and 30 K.

Figure 1 shows the temperature dependence of the resis-tivity rsTd under several pressures above the black-gold tran-sition. Above PB-G, the resistivity at room temperature(around 200mV cm) is one order of magnitude smaller thanthat in the black phase and is almost the same as that ofmetallic Sm-based compounds. In agreement with previousdata,8–11 thersTd behavior up to 1.9 GPa is nonmetallic, i.e.,the resistivity increases with decreasing temperature. For ex-ample for P=1.9 GPa, two broad anomalies are seen ataroundTD9=2 K andTD8=10 K. Similar features were alsofound in Refs. 9 and 10, where bothTD9 and TD8 seem tocollapse nearPD=2 GPa. At 2 GPa, the low temperaturevariation of rsTd is characteristic of a heavy fermion com-pound(HFC) with a metallic conduction on cooling below amaximum ofrsTd at TM. With increasing pressure, the posi-tion of this peak shifts toward higher temperatures.8–11,17

We note that theT2 behavior of the resistivity is foundfrom 50 mK to 4 K. The quadratic coefficientA estimated for2 GPa is 0.9mV cm/K2. If we assume a Kadowaki-Woodsrelation,18 it corresponds to a heavy electronic state with aSommerfeld coefficientg,300 mJ/K2 mol. However, asshown in the inset of Fig. 1, theP dependence ofA isstrongly correlated with that of the residual resistivityr0. Fora given residual mean free path, that points out a change inthe carrier concentration. Indeed, a largeP dependence of theHall coefficientRH at 4.2 K has been reported with a changefrom a large positive value belowPD to a small negativecontribution slightly abovePD. These two concomitant fea-tures are a direct evidence of a large increase in electroniccarrier density.17,19

As the temperature increases above 4 K, the exponentaof the temperature termAaTa of rsTd increases, this extra

contribution is attributed to the spin wave scattering. In theparamagnetic state of HFC, the Fermi liquid termT2 is foundonly below a very low temperature regime. Above this tem-perature regime, the electronic contributionTa to the resis-tivity yields always an exponenta lower than two for non-magnetically ordered HFC. A value ofa greater than two isfound for AF ground states even close toPc.

20 The observa-tion of a positive departure fromr=r0+AT2 law is a firstsignature thatTM may be related to the Néel temperaturesTNd of an antiferromagnetic ground state. We have, ofcourse, checked if superconductivity appears near the criticalpressurePD by performing resistivity measurements down to50 mK; at least in the present stage of the sample quality nosuperconductivity has been detected.

Transverse magnetoresistance up toH=23 T at 2.4 GPahas been measured. The magnetoresistance is always verysmall. This weakH sensitivity has been confirmed for otherpressures up to 7 T. It contrasts with the huge negative mag-netoresistance observed in the black phase.21 Let us remarkthat the Sm-based cubic antiferromagnet SmSb appearsweakly sensitive to a magnetic field of 10 T.22 Having recon-firmed that the appearance of the resistive anomalyTM issample independent, we show specific heat measurementsunder high pressure.

Figure 2 shows the result of ac-calorimetric study underhigh pressures up to 8.1 GPa. The specific heatC has beenderived from the amplitude of the temperature oscillation.Because we do not know the exact power transmitted to thesample from the laser light, we could not obtain the absolutevalue of the specific heat. The specific heat value has beennormalized at 30 K, which is sufficiently higher than thetransition temperature. At 3.1 GPa, a prominent anomaly isseen atTN=17 K. This result shows directly the presence ofa phase transition in the gold phase of SmS. In parallel tothese calorimetric experiments, hyperfine interaction mea-surements on Sm nuclei using the nuclear forward scattering(NFS) technique show that, just abovePD, a hyperfine fieldHhf as well as a quadrupolar splitting appear below a tem-peratureTNFS.TN.23 Furthermore from both hyperfine sig-natures, the samarium state appears to be that of theG8 quar-tet of Sm3+. As TNFS.TM .TN, slow spin dynamics(electronic relaxation time is greater than 10−10 s) appearsalready far aboveTN (Fig. 3).

FIG. 1. Temperature dependence of electrical resistivity in gold-phase SmS under pressure. The quadratic coefficientA is plottedagainst residual resistivityr0 in the inset, for 2(h), 2.2(s), and 2.4(n) GPa.

FIG. 2. (Color online) Typical specific heat curves drawn by thetemperature variation ofCac/T for several pressures. The data arenormalized at 30 K.

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To see the evolution of the phase transition aroundPD, thesharpnessTN/DTN of the specific anomaly throughPD iscompared in Fig. 4 with the fractionf of magnetic sitesdetected by NFS(DTN was chosen by the temperature win-dow where the specific heat anomaly reaches half of itsmaximum). The simultaneous step increase ofy=TN/DTNand f at Pc=PD, demonstrates a drastic change from a para-magnetic short-range-ordered(SRO) phase and a long-range-ordered(LRO) phase. This statement is reinforced by the fastincrease of the calorimetric signal throughPD. From 2 up to4 GPa, the pressure variation ofTN is large: 15 K atPD, to 21K at 4 GPa. Above 4 GPa, the pressure dependence ofTN issmaller :TN=24 K at 8 GPa. The values ofTNFS are 30 K forP=2.35 GPa and 45 K forP=10 GPa. RoughlyTNFS andTNdiffer by a factor near two. The broadening of the calorimet-ric signal at high pressuresP.5 GPad appears to be an ex-

perimental artifact due to an attenuation of the thermocouplevoltage. Experiments on the highly documented systemTmSe up to 13 GPa have shown that the position of theordering temperature is well defined and in excellent agree-ment with published works, but the amplitude of the thermo-couple signal is strongly reduced at high pressure.24

Although our ac calorimetry in a DAC is semiquantita-tive, it appears that the specific heat behaves roughly asCac=gT+bT3. An antiferromagnetic ground state explainswell the second term, i.e., a spin-wave spectrum with van-ishing energy gap. By assuming that the entropy variation atTN corresponds to aG8 quartet ground state, a mean value of180 mJ/K2 mol is estimated. The occurrence of a heavy fer-mion behavior is confirmed. The invariance ofC/T at T→0 K is characteristic of a magnetically ordered HFC farfrom Pc with a strong interplay between Kondo energy andexchange interaction.25

The striking point is that a similarg value was also foundin the low pressure gold phase belowPD.26,27 From thebroadened calorimetric feature belowPD, strong magneticcorrelations coexist obviously with the localization of thecharge of the 5d electron involved in the balance of the twoSm2+ and Sm3+ states. Evidence of SRO exists in NFSexperiments:28 the NFS spectra for 1.6, P,2 GPa at lowtemperaturesT,2 Kd can only be fitted with a broad distri-bution of hyperfine parameters. The previousTD8 signaturein the r measurements was already associated to a possibleonset of magnetic correlations.11 The collapse of the broad-ened SRO’s feature occurs forP,1.3 GPa, i.e., near thepressure of the B–G transition. Let us stress that by theanalysis of the electron spin resonance ESR and susceptibil-ity measurements, a rather large ferromagnetic exchangecoupling(11 K) was found in the black phase of SmS;29 themagnetic ordering is precluded by the weakness of the mix-ing between theJ=0 andJ=1 configuration of Sm2+.

Obviously slow magnetic fluctuations appear far aboveTNfor P. PD. The precession of local moments around the nu-clei is observed for a pressure far belowP3+. Such a phe-nomenon has been reported recently in ESR experiments ofYbRh2Si2, despite the relatively large value given for itsKondo temperaturesTK =25 Kd.30 The divalent memory ofthe Tm ions in TmSe, almost up to the entrance in the triva-lent phase, has been already noticed. Furthermore, as for thelow-pressure gold phase of SmS, TmSe is an insulator up to3 GPa. In both cases, the normalization to the divalent ortrivalent configuration is coupled to the mode of the electricconduction reminiscent of the pure 2+ state(insulator) or ofthe pure 3+ state(metallic). A change in the localization ofthe 5d electrons leads to a switch in the microscopic natureof the magnetism(spatial shape of the 4f wave function) aswell as in its long-range appearance.

The present interplay between localization of the carrier,valence, and magnetism must push also to unravel the natureof the so-called magnetic quantum critical point and the re-lated possible Fermi surface instabilities in HFC. For thecerium cases as CeRh2Si2, there is already evidence of mag-netic quantum first-order transitions nearPC associated withdrastic modifications of the Fermi surface,31 the competitionbetween the Kondo energy, and the crystal field splitting ex-plains well the microscopic nature of the magnetism. Similar

FIG. 3. (Color online) Pressure dependence variation ofTNFS

(m), TM (P), andTN (j andl) detected in NFS, resistivitysrd andtwo independent calorimetric experimentssCd. Continuous lineshave been drawn for eyes abovePD. Below PD, the temperature ofthe maximum ofC has also been reported(h).

FIG. 4. (Color online) Zoom of the specific heat nearPD, inarbitrary units. The inset shows the normalized sharpnesss+d of thespecific heat anomaly defined byy=TN/DTN and the magnetic frac-tion f found by NFS(m).

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considerations for the fluctuations between 4f configurationsof different valence states are clearly required.

To summarize, atPD! P3+,10 GPa, the entrance in themetallic IV phase is coupled to the onset of long range mag-netismsPD=Pcd and to the switch to the renormalization ofthe wavefunction to the Sm3+ configuration. The insulating

low-pressure gold phase of Sm is a “sloppy” insulating mat-ter with short-range magnetic correlations.

Experimental developments onCacsT,Pd were supportedby “Region Rhône-Alpes / France” through the “Emergence”Grant No. 00 81 60 87/88.

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