Table Of ContentCoexistence of antiferromagnetism and superconductivity in heavy-fermions systems
Y. Kitaoka1, Y. Kawasaki1, T. Mito1, S. Kawasaki1, G. -q. Zheng1, K. Ishida1,
D. Aoki2, Y. Haga3, R. Settai2, Y. O¯nuki2,3, C. Geibel4, F. Steglich4
1Department of Physical Science, Graduate School of Engineering Science,
Osaka University, Toyonaka, Osaka 560-8531, Japan
2Department of Physics, Graduate School of Science,
Osaka University, Toyonaka, Osaka 560-0043, Japan
2 3Advanced Science Research Center, Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-1195, Japan
0 4Max-Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany
0 (Dated: February 1, 2008)
2
We report the novel pressure(P)−temperature(T) phase diagrams of antiferromagnetism (AF)
n
and superconductivity (SC) in CeRhIn5, CeIn3 and CeCu2Si2 revealed by the NQR measurement.
a IntheitineranthelicalmagnetCeRhIn5,wefoundthattheN´eeltemperatureTN isreducedatP ≥
J
1.23GPawithanemergentpseudogapbehavior. ThecoexistenceofAFandSCisfoundinanarrow
4 P range of 1.63 − 1.75 GPa, followed bytheonset of SCwith line-node gap overawide P window
2.1−5GPa. InCeIn3,thelocalizedmagneticcharacterisrobustagainsttheapplicationofpressure
l] uptoP ∼1.9GPa,beyondwhichthesystemevolvesintoanitinerantregimeinwhichtheresistive
e superconducting phase emerges. We discuss the relationship between the phase diagram and the
-
r magnetic fluctuations. In CeCu2Si2, the SC and AF coexist on a microscopic level once its lattice
t parameter is expanded. We remark that the underlying marginal antiferromagnetic state is due to
s
. collectivemagneticexcitationsinthesuperconductingstateinCeCu2Si2. AninterplaybetweenAF
t
a andSCisdiscussedontheSO(5)scenariothatunifiesAFandSC.WesuggestthattheSCandAF
m in CeCu2Si2 havea common mechanism.
- PACSnumbers:
d
n
o
I. INTRODUCTION in NQR frequencies of 3 ∼ 4 MHz. Therefore, this
c
[ marginal AFM state, that sets in at Tm ∼ 1.2 K well
Pressure-induced superconductivity was discovered in above Tc = 0.65 K, causes the wipe-out effect in NQR
1
intensity [6, 9, 10]. It was remarkedthat such extremely
v the magnetic heavy-fermion (HF) compounds, such as
low-frequency magnetic fluctuations are also reported in
0 CeCu2Ge2,CePd2Si2,CeIn3,CeRhIn5andUGe2[1,2,3,
4 4,5]. Thereis increasingevidencethatthe superconduc- high-TccupratesLa2−xSrxCuO4wherethewipe-outphe-
0 tivity in HF compounds takes place nearby a magnetic nomenonofCu-NQRintensitywasalsoreported[11,12].
1 Thereby,theemergenceofslowlyfluctuatingAFMwaves
phase or even coexists with it. By applying a pressure
0 seem to be one of characteristics for strongly correlated
(P), amagnetic orderis suppressedatacriticalpressure
2 electron systems nearby the AFM phase. Recently, this
P , where superconductivity is induced in the antiferro-
0 c
exotic magnetic and SC properties have been exten-
/ magentic (AFM)-HF compounds, such as CeCu2Ge2,[1]
t sively investigated through the transport, thermal, and
a CePd2Si2,[2], CeIn3,[3] and CeRhIn5 [4]. In order to
NQR measurements under P [10, 13, 14]. At pressures
m gain profound insight into a relationship between mag-
exceeding P ∼ 0.2 GPa, the HF-SC state with line-
netismandsuperconductivity inHF systems,systematic
-
d NMR/NQR experiments under P are important, since node gap is recovered, coincident with the suppression
n they can probe the evolution of the magnetic properties of the slowly fluctuating AFM waves in Ce0.99Cu2.02Si2
o [10]. Its normal state was well described in terms of the
toward the onset of SC phase and the character of spin
c self-consistentrenormalizedAFMspin-fluctuation(SCR)
fluctuations in the SC state.
:
v theory [15].
The superconductivity in underlying compound
i
X CeCu2Si2 isconsideredtooccurjustatthe borderofthe Onthe other hand,the Ge substitution forSi expands
r AFM phase at ambient pressure (P = 0) [1]. This was the lattice of the undoped sample to reduce a strength g
a alsocorroboratedby the existenceofthe magneticphase ofthehybridizationbetween4f electronsandconduction
(calledasA-phaseatzeromagneticfield)adjacenttothe electrons,correspondingto applying a negative chemical
SC state [6, 7]. Furthermore, when magnetic field (H) pressure[16]. Contrary to applying P to increase g, it
exceeds its upper critical field Hc2 , the H-induced nor- would be expected that magnetic (RKKY) interactions
malstateisreplacedbymagneticphase Aandsuccessive of4f moments become strongeras Ge content increases.
phase B with increasing H [8]. In fact, in the previous paper [17], we reported that the
From the Cu-NQR measurements [9], we showed that 2%GesubstitutionleadstotheemergenceofAFMorder
the A-phase at H = 0 behaves as a marginal AFM atT =0.75K,followedbytheSCtransitionat∼0.4K.
N
state, where slowly fluctuating AFM waves propagate The shape ofNQR spectrum, thatis significantly broad-
over a long distance and coexist with the SC state. It is ened below T , revealed that the AFM region are not
N
quite unusual that their characteristic frequencies range spatially separated from the non-AFM SC one. Thereby,
2
the coexistence of both was shown to occur on a micro- [21]. T monotonically decreases with P and supercon-
N
scopic level. Because of this, the T dependence of 1/T1 ductivity appearsbelowTc ∼ 0.2K ata criticalpressure
below T does not obey a T3 behavior,demonstrating to P = 2.55 GPa, but the onset of the superconductivity
c c
differfromtheline-node-gapstaterevealedintheHF-SC was observed only by the resistivity measurement and is
regime induced by applying P [10]. Persistence of mag- limited in a narrowP range of about 0.5 GPa [2, 3, 22].
neticexcitationsevenintheSCstatewasthusevidenced The previous In-NQR result on CeIn3 revealed that the
∗
from the significant enhancement in nuclear spin lattice AFM order disappears around P = 2.44 GPa close to
relaxation rate 1/T1 below Tc. Pc and the Fermi-liquid behavior was observed below 10
In the literature [17], we have proposed that (1) the K at P =2.74 GPa [23]. However, no SC transition was
exotic magnetic SC phases in Ce0.99Cu2.02Si2 which co- seen. Thus, the bulk nature of the P-induced SC state
exists with the marginal AFM state, (2) the microscopic in CeIn3 has not been confirmed yet by other measure-
coexistenceofAFMandSCphaseintheslightlyGesub- ments than resistivity. This is in contrast with the case
stituted compounds, and (3) the H-induced phase A are of CeRhIn5 where the bulk nature of the SC phase was
accounted for on the basis of the SO(5) theory that uni- fully established[20]whichcontinuesupto ∼5GPa[24].
fies superconductivity and antiferromagnetism [17, 18]. The interplay between magnetism and superconduc-
We believe that this model could shed light on current tivity is one of the typicaland fascinating examples that
ideasregardingthe magneticallymediatedmechanismof have revealed the incredible behavior of strongly corre-
the superconductivity in other strongly correlated elec- lated electrons in condensed matters. The NQR exper-
tron systems besides the high-T cuprates. In establish- iments under P is providing fruitful set of data on the
c
ingwhetherornotthesebelongtoanewphaseofmatter, evolution from the AFM to SC phase and the character
however, further experiments are needed. of spin fluctuations in the SC state. In this paper, we
compare systematically these P −T phase diagrams in
Remarkably, a recent µSR experiment has clearly
demonstrated that the singlet superconductivity in CeRhIn5, CeIn3 and CeCu2Si2 in order to present what
is the news.
Ce0.99Cu2.02Si2 coexists with the magnetic A-phase, or
the marginal AFM state in our terminology, and it
exhibits an intimate connection to the magnetism in
Ce0.99Cu2.02Si2 [19]. This result has strongly suggested II. CERHIN5
that the superconductivity and the A-phase magnetism
in CeCu2Si2 has a commonbackground. In other words, The T dependence of 1/T1T below 12 K is shown in
wemayremarkthatcollectivemagneticexcitationsinher- Fig.1 at P = 0, 0.46, 1 .23 and 2.1 GPa. At P = 0,
entto the unconventionalSC state existatthe magnetic 0.46 and 1.23 GPa [25], it is clearly seen that an AFM
critical point. order occurs at 3.8, 4.0 and 3.6 K, respectively, as indi-
Recently Hegger et al. found that a new HF mate- cated by a clear peak in 1/T1T due to critical magnetic
fluctuations toward the AFM ordering. This indicates
rial CeRhIn5 consisting of alternating layers of CeIn3 [4]
and RhIn2 reveals an AFM-to-SC transition at a critical
pressureP = 1.63GPalowerthanin allpreviousexam-
c
ples [1, 2, 3]. The SC transition temperature T = 2.2
c
K is the highest one to date amongP-inducedsupercon- TN CeRhIn5 ambient P
ductors [4]. This finding has opened a way to investi- 300 0.46 GPa
) 1.23 GPa
1
gate the P-induced evolution of both magnetic and SC -K 2.1 GPa
properties over a wide P range. The 115In NQR study -1c
of CeRhIn5 has clarified the P-induced anomalous mag- se 200
(
netism and unconventional superconductivity [20]. In T T
the AFM region, the N´eel temperature T exhibits a T1 c
moderate variation,while the internalfieldNHint atIn(1) 1 / 100
site in the CeIn3 plane due to the magnetic ordering is T
linearly reduced in P = 0−1.23 GPa, extrapolated to PG
0
zero at P∗ = 1.6±0.1 GPa. This P∗ is comparable to 2 4 6 8 10 12
Temperature (K)
P =1.63GPaatwhichtheSCsignatureappears,which
c
was indicative of a second-order like AFM-to-SC transi-
tion rather than the first-order one suggested previously FIG. 1: Temperature dependenceof 1/T1T in CeRhIn5. The
[4]. At P = 2.1 GPa, it was found that 1/T1 reveals solid, broken and dotted arrows indicate TPG, TN and Tc,
a T3 dependence below the SC transition temperature respectively.
T , which shows the existence of line-nodes in the gap
c
function [20]. thatT reducesatP =1.23GPaasP approachesP at
N c
On the other hand, CeIn3 crystallizes in the cubic which superconductivity sets in. This reductionin TN is
AuCu3 structureandordersantiferromagnetically(TN = not seen from the previous resistivity measurements [4].
10K)atP =0withanorderingvectorQ=(1/2,1/2,1/2) At P = 1.23 GPa, 1/T1T shows a broad peak around
3
T above T . This resembles the pseudogap behavior present experiment, we conclude that the P −T phase
PG N
found in the high-Tc copper oxide superconductors [26]. diagramand the nature of the SC phase in CeIn3 differs
∗
Namely, when P approaches the critical pressures P or from in CeRhIn5, in many aspects, reflecting their con-
P , the low-energy spectral weight of magnetic fluctua- trastingelectronicandmagneticproperties;wespeculate
c
tions is suppressed before an ordering occurs. We note that the SC phase in CeIn3 that accompaniesthe Meiss-
thatthepseudogapbehaviorhasbeenfoundineithertwo- nerdiamagnetism,ifany,isevennarrowerthansuggested
orlower-dimensionalstronglycorrelatedelectronsystems by the resistivity measurement [25].
[26]. Veryrecently,inCeRhIn5,anisotropicthreedimen-
sional AFM fluctuation was reported from neutron scat-
teringatP =0withanenergyscaleoflessthan1.7meV
IV. THE AF- AND SC-PHASE DIAGRAMS OF
for temperature as high as 3 T [27]. Onthe other hand,
c CERHIN5 AND CEIN5
asP furtherincreasesuptoP =2.1GPawherethebulk
SCtransitionappears,1/T1T continuestoincreasedown
to T = 2.2 K without any signature for the pseudogap TherespectiveP−T phasediagramsforCeRhIn5 and
c
behavior as seen in Fig.1. The T variation of 1/T1T is Ce∗In3 arepresentedinFigs.3aand3b[25]. ForCeRhIn5,
T , that is scaled to the bandwidth of HF state, slightly
consistent with the three dimensionalAFM Fermi-liquid
increases with increasing P up to 1.0 GPa, as does T
model of the self-consistent renormalized (SCR) theory N
which coincides with the previous result [4]. However,
for nearly AFM metals [20]. Thus the P-induced evolu-
T decreases above P = 1.23 GPa. At the same time,
tioninthemagneticfluctuations,fromamagneticregime N
a pseudogap behavior emerges below T ∼ 5.5 K. As
of reduced dimensionality to a more isotropic one, may PG
∗
P is further increased, T moderately increases with
take place in a narrowP window of1.2−2.1 GPa,when
dT∗/dP ∼8K/GPa. It is noted that T∗ is equivalent
the AFM order evolves into the SC one. Recent pre-
to the temperature T at which the resistivity ex-
cise NQR measurement in this P window has revealed max,ρ
hibitsamaximumvalueandalsodT∗/dP ∼dT /dP
a homogeneous coexistence of AFM and SC order on a max,ρ
[4]. We remark that these values are close to those in
microscopic level [28].
CeCu2Si2 [10] which is a superconductor at P = 0 and
reveals a SC state over a wide P region as well [29]. In
III. CEIN3 CeRhIn5,the anisotropic3D-AFMfluctuationsmaysur-
vive until the system is close to the SC state, where the
pseudogap behavior is emergent. Above P∗ or P where
Fig.2 indicates the T dependence of 1/T1T [25]. For c
the bulk superconductivity appears, the AFM spin cor-
all values of P, 1/T1T increases down to TN, giving no relations become more isotropic and the T dependence
indication for the pseudogap behavior. At P = 2.35
of1/T1T for T >Tc canbe explainedonthe basis ofthe
3D-SCR theory for nearly AFM metals [20]. While the
isotropicAFMfluctuationregimeisfullyestablished,the
300 (cid:3)
bulkSCisinsensitiveagainstP. ForCeIn3,thesteepin-
T CeIn
∗
N 3 creaseofT aboveP =1.9GPaindicatesanevolutionof
) ambient P the system into an itinerant magnetic regime where the
1
-1-ecK 200 122...436255 GGGPPPaaa nSoCrmstaalt-estbateecormeseisstievmiteyr,gρenitn.CMeIonr3eoavterlo,wcloTseistoalPsoc,cothne-
s
( sistentwiththe3D-AFMfluctuationmodel[3]. However,
T (cid:3)
T1 whenthepressureisfurtherincreasedabovePc,aFermi-
1 / 100 liquid behavior of the resistivity returns more rapidly in
CeIn3 than in CeRhIn5 and CeCu2Si2 [3]. This is also
corroborated by the observation of T1T = constant be-
0 havior at P = 2.65 GPa in CeIn3. We should remark
0 5 10 15 20 25 30 35 40 45 50 that an upper temperature scale T below which lo-
max,ρ
Temperature (K)
calmagneticfluctuationsareincreasinglyfrozenout,isas
highas 70−100K overthe P rangefrom0 to3 GPa[3].
∗
FIG. 2: Temperature dependence of 1/T1T in CeIn3. The This large difference between T and Tmax,ρ in CeIn3
solid arrows indicate TN. Dotted line is eye guide. contrasts strongly with the coincidence of the both in
∗
CeRhIn5,resultinginthesteeperchangeofT asafunc-
GPa where the zero resistance is observed, it has been tion of P in CeIn3 comparedwith those in CeRhIn5 and
confirmed that the magnetically ordering survives with CeCu2Si2. AreasonforsuchanarrowSCregioninCeIn3
a relatively high value of T = 5 K. The SC transi- is proposedas due to the small window for the 3D-AFM
N
∗
tion is, however, not found by the high-frequency ac- fluctuation regime because of its large rate of dT /dP.
susceptibility measurement down to 100 mK using the This small window for the 3D-AFM fluctuation regime
in-situ NQR coil, despite that a zero resistance was ob- against P in CeIn3 may be related to its cubic crystal
served in the same sample at T ∼ 0.15 K. From the structure which is more sensitive to external P than a
c
4
[34]. HereweexpectthataprimaryeffectoftheGedop-
ingistoexpandthelatticeandthatitschemicalpressure
is −7.6 GPa per 100% Ge doping as suggested from the
(a) 40
CeRhIn P dependence of νQ in CeCu2Ge2 and CeCu2Si2.[35] In
30 5
]
K
e [ 20 T * 0.3 0C.2eC0u.21(Si1–0xGex)2 K)
atur 150 T TPG 3 *T (
r N
e 4 20
p
m 3 Tc K) T*
Te 2 AF (m 2 0
T
(b) 010.0 0.5 1.0 1.5 2.0 S2C.5 3.0 T, T, Nc TN Tm TF*
K] 30 0.2 Tc (cid:3) CeIn3 1 AF Tc
25
[
ure 20 0.1 (cid:3) T * AF+SC SC
rat 15 0.02.0 2.2 2.4 2.6 2.8 3.0 0 0 1 2 3
pe (cid:3) T Pressure (GPa)
m 10 N SC
e 10T
T c FIG. 4: The AF and SC combined phase diagram for
5 AF CeCu2(Si1−xGex)2 and for Ce0.99 (x = 0) under pressure.
0 TN (closed squares) and Tc (open circles) are the AFM and
0.0 0.5 1.0 1.5 2.0 2.5 3.0 SC transition temperature, respectively. Also shown are the
Pressure [GPa] characteristic temperature to be scaled to the band width of
∗
HFstateT (opensquares)andTmbelowwhichthemarginal
AFMstateisdominant(opentriangles). ThedataforCe0.99
underpressureare cited from theprevious paper.[10]
FIG. 3: Pressure−temperature phase diagrams (a) for
fact, the recent NQR experiment under P has been car-
CeRhIn5 and (b) for CeIn3. (a) The open marks are deter- ried out on x = 0.02 where the AFM order below T ∼
mined from the resistivity measurements [24], and the solid N
0.75 K coexists with the superconductivity below T ∼
squares are determined from the ac-χ measurement [20]. (b) c
Theopen marks for TN and Tc are takenfrom theresistivity 0.4 K [34]. As indicated in Fig.5, at pressures exceed-
measurements[2,3,22]. Therestmarksaredeterminedfrom ing P = 0.56 GPa, the AFM order is suppressed and
the present work. The inset indicates the detailed P depen- concomitantly the unconventional SC state evolves into
dence of Tc in expanded scales. Dotted lines in both figures a typical HF one with the line-node gap. This result
are eye guides. demonstrates that the occurrence of the AFM order is
due to the lattice expansion caused by doping Ge and
that there exist gapless magnetic excitations in the un-
tetragonal structure. derlying coexisting state of AFM and SC order at P =
Based on magnetically mediated SC theoretical mod- 0.
els [30], it is predicted that 2D-AFM fluctuations are The characteristic temperature, T∗ which is scaled to
superior to 3D-AFM fluctuations in producing SC [31]. the bandwidth of HF state, increases continuously with
Therefore,theenhancementofTc inlayeredCeMIn5over decreasing x or applying P. TN is determined as the
CeIn3 has been suggested to be due to their quasi-2D temperature below which H (T) appears and at which
int
structure [4, 32, 33]. Here we propose that the small 1/T1 exhibits a peak [17, 34]. The AFM order suddenly
windowforthe spinfluctuationsregimeinCeIn3 may,at setsinoncex>0,whereas,atx=0,itbecomesmarginal
leastpartly,beresponsibleforitslowerTc ,whichshould withoutanytraceofHint downto0.012K.Themarginal
also be taken into account in modeling the SC in these AFM state develops below T in the ranges of 0 ≤ x <
m
compounds. 0.06 and 0< P < 0.2 GPa, which are shaded by a color
in Fig.4. The appearance of it is shown to be limited
to the border of the magnetic critical point at x ∼ 0.
V. THE AF AND SC PHASE DIAGRAM IN Approachingx=0,itisnoteworthythattheAFMorder
CECU2SI2 seems to disappear as a result of T approaching T .
N c
Nevertheless, the SC phase can coexist with either the
Fig.4showsthephasediagramdeterminedasfunctions marginalortheAFMstatein0≤x<0.06,characterized
ofGecontentxforCeCu2(Si1−xGex)2 andofP atx=0 by gaplessmagnetic excitations. This factindicates that
5
both magnetism and superconductivity has a common
TN 0 GPa
background.
102 Tc
In the P range 0 < P < 0.2 GPa, however, it should
0.91 GPa
bestressedthatsuchthemarginalAFMstateisexpelled
below Tc at H = 0, but when H turns on to suppress –1c) (fast)
the superconductivity, a first-order like SC to magnetic se
ispnuhpaPpser>eAss0ei.sd2inaGdnPudac,aedttht[e8h,eA1sF3a,Mm1e4m].taimWrgeii,tnhathlfuesrtHtahtFeersisiunpccoerrmecaopsnilnedtguelPcy- 1 / T (1 101 (slow) Intensity 65Cu 63Cu 0.546.2G PKa
tivity is recovered, exhibiting the line-node gap. In the 0.5 K
shadedzone,the exoticinterplayoccursbetweenantifer- 100
romagnetism and superconductivity. 0.18 K
Next, we shed further light on the coexisting state
3 f (MHz) 3.5
by comparing with the typical AFM-HF-SC compound
UPd2Al3 where the AFM order sets in below TN ∼ 14.5 10–1 100 101
Temperature (K)
K, followed by the onset of typical HF-SC transition be-
lowTc ∼1.98K[36,37,38]. InUPd2Al3,thecoexistence
of the AFM order with the superconductivity has been FIG. 5: Temperature dependence of 1/T1 at 0 and 0.91 GPa
established by various measurements [37, 39, 40, 41]. atx=0.02inCeCu2(Si1−xGex)2. Since1/T1 isnotbysingle
TheAl-andPd-NQRresultsshowedthat1/T1 decreases componentat0GPabelowTN,boththefast andslowrelax-
ation componentsare plotted. The inset shows NQRspectra
rapidlyduetoanopeninggapatapartoftheFermisur-
at 0.56 GPa, indicativeof nohyperfinebroadeningduetoan
face below TN and follows the 1/T1 ∝T3 below Tc, con- onset of AFM ordering.
sistent with the line-node gap.[39, 40] In UPd2Al3, note
that an average occupation of 5f electrons per U atom
is slightly less than three and larger than one in Ce HF
zone including in 0<P <0.2 GPa in Fig.4 may be new
systems [42]. With some relevance with this, nearly two
states of matter. In the literature [17], in fact, we have
localized 5f electrons are responsible for the AFM order
proposed that the microscopic coexistence of AFM and
with a relatively large spontaneous moment of 0.85µ
B SC phase in the slightly Ge substituted compounds, and
perUatom. Sincethe spin-waveexcitationsinthe AFM the magnetic field-induced phase A that was revealed in
state is gapped, the particle-hole excitations in HF state
the P range 0 < P < 0.2 GPa are accounted for on the
are dominant well below T , as actually evidenced from
N basis of the SO(5) theory that unifies superconductivity
the T1T =constant behavior typical for the Fermi-liquid andantiferromagnetism.[17,18]Thepresentresultshave
state. Therefore,the 1/T1 in the SC state is notaffected revealed, we believe, that the magnetic critical point is
by the magnetic excitations even in the coexisting state, located near x∼ 0 and the marginal AFM state existing
but reflectsits line-node SC gapstructure. However,the in 0 ≤ x < 0.06 below T may be identified as a collec-
c
situationin underlying CeCu2Si2 is completely different, tive magnetic mode in the coexisting phase, whereas it
because one 4f electron per Ce ion play vital roles for in0<P <0.2 GPaturns outto be competitive with the
both the magnetism and the superconductivity, leading
onset of SC phase at H = 0 [8, 10, 13, 14]. This latter
to the novel interplay between the magnetism and the fact is relevant to the emergence of a H-induced first-
superconductivity revealed in CeCu2Si2. order like SC to magnetic phase A transition [8, 13, 14].
Finally, we compare the present results with those on Concerningthe interplay betweenmagnetismandsuper-
Ce0.975Cu2Si2 (Ce0.975) where an AFM order was re- conductivity, we would propose that the marginal AFM
ported below TN ∼ 0.6 K [9, 43]. Unlike the Ge substi- state in the SC state at x = 0 may correspond to a
tutedsamples,however,anysignatureofsuperconductiv- pseudo Goldstone mode due to the broken SO(5) sym-
itywasnotobserveduptoP =2GPainCe0.975,andthe metry, and to the gapless magnetic excitations due to
AFM order persists [44]. This is in strong contrast with the broken spin symmetry in the coexisting state in the
that the superconductivity is robust against increasing range of 0 < x < 0.06. Due to the closeness to the
Ge content. Furthermore, the recent NQR result under magnetic critical point, the marginal AFM state in the
P at x = 0.02 has revealed that the AFM order is sup- SCstateshouldbesuchagappedmodethatischaracter-
pressedandtheHFsuperconductivitywiththeline-node izedbyextremelytinyexcitationenergy. Wethusbelieve
gap is recovered at P = 0.56 GPa as seen in Fig.5 [34]. that this SO(5) model could shed light on the intimate
These results indicate that the AFM order in Ce0.975 is interplay between magnetism and superconductivity in
driven by some disorder effect that destroys the super- CeCu2Si2 that is the long-standing issue over a decade.
conductivity. By contrast, the AFM order at x = 0.02 In order to get further insight into the marginal AFM
is primarily due to the lattice expansion. Therefore, the stateandthe suddenemergenceofAFMorderthatboth
magnetic order can coexist with the superconductivity coexist with the superconductivity, extensive NQR ex-
without destroying it. periments for Ge-doped system under pressure are now
The AFM and SC phases that emerge in the shaded in progress.
6
VI. CONCLUSION of phase segregationbetween a paramagnetic SC and an
AFM region. It is remarkable that when T approaches
N
In CeRhIn5 that is already in the itinerant magnetic Tc at the magnetic critical point (x ∼ 0), the AFM or-
regime at P = 0, T slightly increases with P at lower der suddenly disappears, indicative of a first-order like
N
pressureswhichisinaccordancewiththepreviousreport transition in the magnetic phase, in contrast with the
[4]. However,T startsto decreaseaboveP = 1.23GPa robustness of the SC one.
N
approaching the critical value at which superconductiv- The1/T1 result,thatdoesnotshowanysignificantre-
ity sets in. At the same time, the pseudogap behavior duction below Tc, has demonstrated that the SC state
emerges. By contrast, in CeIn3, the localized magnetic coexisting with the AFM order differs from that with
characterisrobustagainstthe applicationofP upto1.9 the line-node gap.@It reveals that the magnetic excita-
GPa, beyond which T∗, which marks an evolution into tions are gapless due to the coexistence of AFM and SC
an itinerant magnetic regime, increases rapidly. We re- phase. Apparently,thefactthatboththemarginalAFM
mark that the SC emerges in such the itinerant regime. stateandtheAFMordercancontinuetocoexistwiththe
The window for the 3D-AF fluctuation regime in CeIn3 superconductivity strongly suggests that both the mag-
is much narrower than in CeRhIn5. These results sug- netism and the superconductivity has a common mecha-
gestthatthe differentrobustnessofthe spinfluctuations nism.
regimeagainstP shouldbetakenintoaccountinexplain-
ing the difference of Tc in CeRhIn5 and CeIn3.
In CeCu2Si2, once its lattice parameter of x = 0 is Acknowledgements
slightlyexpanded,the AFMordersetsinatT ∼0.7K,
N
followed by the onset of superconductivity below T = We thank A. Koda, W. Higemoto, and R. Kadono for
c
0.5 K. This sudden emergence of AFM order due to the valuable discussions on µSR results. This work was sup-
slight 1%-Ge substitution reinforces the existence of the ported by the COE Research (10CE2004) in Grant-in-
marginal AFM state in the undoped Ce0.99Cu2.02Si2 (x Aid for Scientific Research from the Ministry of Educa-
=0)whereslowlyfluctuatingAFMwavespropagateover tion, Culture, Sports, Science and Technology of Japan.
alongdistance. ThemeasurementoftheNQRspectrum Oneoftheauthors(Y.Kawasaki)hasbeensupportedby
below T is a most reliable way to exclude the presence JSPS Research Fellowships for Young Scientists.
N
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