High-Tc superconductivity and antiferromagnetism in multilayer cuprates: 63Cu- and 19F-NMR on five-layer Ba2Ca4Cu5O10(F,O)2

2.1 MB·English

by  Sunao Shimizu

T
High- superconductivity and antiferromagnetism in multilayer cuprates:
c
63Cu- and 19F-NMR on five-layer Ba Ca Cu O (F,O)
2 4 5 10 2
∗
Sunao Shimizu, Shin-ichiro Tabata, Shiho Iwai, Hidekazu Mukuda, and Yoshio Kitaoka
Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
Parasharam M. Shirage, Hijiri Kito, and Akira Iyo
National Institute of Advanced Industrial Science and Technology (AIST), Umezono, Tsukuba 305-8568, Japan
(Dated: January 24, 2012)
2
1 We report systematic Cu- and F-NMR measurements of five-layered high-Tc cuprates
0 Ba2Ca4Cu5O10(F,O)2. It is revealed that antiferromagnetism (AFM) uniformly coexists with su-
2 perconductivity (SC) in underdoped regions, and that the critical hole density pc for AFM is ∼

n 0.11inthefive-layeredcompound. Wepresentthelayer-numberdependenceofAFMandSCphase
a diagrams in hole-doped cuprates, where pc for n-layered compounds, pc(n), increases from pc(1)
J ∼ 0.02 in LSCO or pc(2) ∼ 0.05 in YBCO to pc(5) ∼ 0.11. The variation of pc(n) is attributed
1 to interlayer magnetic coupling, which becomes stronger with increasing n. In addition, we focus
2 on the ground-state phase diagram of CuO2 planes, where AFM metallic states in slightly doped
Mott insulators change into the uniformly mixed phase of AFM and SC and into simple d-wave

] SC states. The maximum Tc exists just outside the quantum critical hole density, at which AFM
n
momentsonaCuO2 planecollapseatthegroundstate,indicatinganintimaterelationshipbetween
o
AFMandSC.ThesecharacteristicsofthegroundstateareaccountedforbytheMottphysicsbased
c
- on the t-J model; the attractive interaction of high-Tc SC, which raises Tc as high as 160 K, is an
r in-plane superexchange interaction Jin (∼ 0.12 eV), and the large Jin binds electrons of opposite
p spinsbetweenneighboringsites. ItistheCoulombrepulsiveinteraction U (>6eV)betweenCu-3d
u
electrons that playsa central role in the physicsbehind high-Tc phenomena.
s
.
t
a
m I. INTRODUCTION to the strength of interlayer magnetic coupling, which
would become stronger with an increase in the stacking
-
d Despite extensive research for more than a quarter number n of CuO2 layers in a unit cell. In addition to
n of a century, there is still no universally accepted the- that,itisexpectedthatdisordereffects,whichisinasso-
o ory about the mechanism of superconductivity (SC) in ciation with chemical substitutions, are enhanced when
c copper-oxidesuperconductors. Themaincontroversyex- nissmall[10,13,37,38],andthatsuchadisordermasks
[
ists over the attractive force that forms Cooper pairs, the intrinsic nature of CuO2 planes. In order to under-

2 which leads to a remarkable high SC transition temper- standtherelationshipbetweenAFMandSC,therefore,it
v ature T . It has been known that the hybridization be- isnecessarytoinvestigatethendependenceofelectronic
c
30 tween Cu(3dx2−y2) and O(2pσ) orbitals induces a large properties in underdoped regions.
in-planesuperexchangeinteractionJ ∼0.12eVor1300 Apical-fluorine multilayered high-T cuprates
4 in c
1 K in nondoped CuO2 planes, and that strong antifer- Ba2Can−1CunO2n(F,O)2 (02(n-1)nF) provide us
. romagnetic (AFM) correlations exist even in SC states. with the opportunity to investigate the n-dependent
1
Experiments have observed local magnetic moments in AFM-SC phase diagrams. 02(n-1)nF comprises a stack
0
2 metallic or SC regions [1–13], and theories have pointed of n CuO2 layers, as shown in Figs. 1(a)-1(d), and
1 outastrongrelationshipbetweenAFMandSCinunder- consists of inequivalent CuO2 layers: an outer CuO2
: doped regions [14–31]. Those reports have shown that plane (OP) in a five-fold pyramidal coordination and an
v
i AFMplaysa keyroleinthe mechanismofhigh-Tc SC in inner CuO2 plane (IP) in a four-fold square coordina-
X cuprates. tion. The substitution of oxygen O2− for apical fluorine
r We have reported on AFM and SC properties in mul- F1− results in doping hole carriers, increasing Tc from
a
tilayered cuprates [32–35], where long-range static AFM underdoped to optimally-doped regions [33, 35, 39–41].
orders uniformly coexist with SC in underdoped regions In this paper, we report the AFM and SC phase
[34]. Ontheotherhand,theuniformcoexistencehasnot diagram in five-layered Ba2Ca4Cu5O10(F,O)2 (0245F)
been observedin typical high-Tc cuprates such as single- by means of 63Cu- and 19F-NMR, and present the n-
layered La2−xSrxCuO4 (LSCO) [10, 36] and bi-layered dependence of the phase diagram from n=1 to 5. We
YBa2Cu3O6+y (YBCO) [7, 13]. The difference of the highlight the fact that the ground-state phase diagram
phasediagramsinvariouscupratesispossiblyattributed derivedfromthepresentstudyisingoodagreementwith
theoretical predictions based on the t-J model. This re-
sultsupportstheideathatthein-planesuperexchangein-
∗ E-mail: [email protected];Presentaddress: CorrelatedElectron teractionJin playsavitalroleasthegluetoformCooper
pairs or mobile spin-singlet pairs.
Research Group (CERG), RIKEN Advanced Science Institute
(ASI),Wako, Saitama351-0198, Japan The contents of this paper are as follows: after ex-
2
FIG. 1. (color online) Crystal structures of Ba2Can−1CunO2n(F,O)2 with (a) n=2 (0212F), (b) n=3 (0223F), (c) n=4 (0234F), and
(d) n=5(0245F). Here, n is the number of stacked CuO2 layers. The heterovalent substitution of F1− for O2− at apical sites decreases
the hole density p. Outer and inner CuO2 planes are denoted as OP and IP, respectively. Note that, in a precise sense, there are two
kindsofIPlayers: theinnermostinnerCuO2 plane(IP0)andthetwoadjacent innerones(IP1).
perimentaldetailsinSectionII,weprovideexperimental III. RESULTS
results and discussions; in Section III, we show system-
atic Cu- and F-NMR measurements on four 0245F sam-
A. Cu-NMR
ples,whichisevidenceoftheuniformcoexistenceofAFM
and SC; in Section IV, we present the n-dependence of
the AFM and SC phase diagrams in 02(n-1)nF, and fi- 1. 63Cu-NMR spectra and estimation of nuclear quadrupole
nally construct the ground-state phase diagraminherent frequency 63νQ
in hole-doped cuprates.
Figures 2(a), 2(b), 2(c), and 2(d) show typical 63Cu-
NMR spectra of the central transition (1/2 ⇔ −1/2)
II. EXPERIMENTAL DETAILS for 0245F(♯1), 0245F(♯2), 0245F(♯3), and 0245F(♯4), re-
spectively. The field-swept NMR spectra were measured
Polycrystallinepowdersamplesusedinthisstudywere with H perpendicular to the c axis (H ⊥c), and the
ex ex
prepared by high-pressure synthesis, as described else- NMR frequency ω0 was fixed at 174.2 MHz. As shown
where [39, 42]. Powder X-ray diffraction analysis shows in Fig. 1(d), 0245F has two kinds of CuO2 planes: an
thatthe samplescomprisealmostasingle phase. As dis- outer CuO2 plane (OP) and an inner plane (IP). There-
cussedlater,thesharpCu-NMRspectralwidthatT=300 fore, the two peaks in the NMR spectra correspond to
K assures the good quality of the samples. We prepared OP and IP. The assignment of NMR spectra to OP and
four samples of Ba2Ca4Cu5O10(FyO1−y)2 (0245F) and IP has been already reported in previous literature [44–
determined the values of T by the onset of SC diamag- 46]. Here, note that Cu-NMR spectra for the innermost
c
netismusingadcSQUIDmagnetometer. Thefour0245F IP (IP0 in Fig. 1(d)) and the two adjacent IP (IP1 in
samples exhibit a systematic decrease in T , as listed in Fig. 1(d)) overlap each other, which suggests that their
c
Table I, as the nominal amount of fluorine F1− (i.e., y) localdoping levelsarenot somuchdifferent[41]. Hence-
increases. The heterovalent substitution of F1− for O2− forth,wedonotdistinguishIP0 andIP1 inthispaper. In
atapicalsites (see Fig.1) decreasesthe hole density p in 0245F(♯1),the Cu-NMR spectra for both OP andIP are
apical-F compounds [33, 35, 39–41]. Note that it is dif- observed at T=280 K, whereas the IP’s spectrum disap-
ficult to investigate the actual fraction of F1− and O2− pearsatlowtemperatures,asshowninFig.2(a). Thisis
[40, 43]. For NMR measurements, the powder samples becauseAFMcorrelationsdevelopuponcoolingasinthe
were aligned along the c axis in an external field H of case of three-layered 0223F [35] and four-layered 0234F
ex
∼ 16 T and fixed using stycast 1266 epoxy. NMR ex- [33]. We have also reported on the loss of Cu-NMR in-
periments were performed by a conventional spin-echo tensity due to spin dynamics in a previous paper [32].
method in the temperature (T) range of 1.5 − 300 K. In 0245F(♯2), the Cu-NMR spectra are observed for OP
3
TABLE I. List of physical properties in Ba2Ca4Cu5O10(FyO1−y)2 (0245F) used in this study. The Tc values were determined
by the onset of SC diamagnetism using a dc SQUID magnetometer. Here, note that the amount of F1−, y, is nominal. It is
difficulttodeterminetheactualfractionofF−1 andO2− attheapicalsites[40,43]. Theholedensityp,thenuclearquadrupole
frequency 63νQ, and the full-width at half-maximum (FWHM) are separately evaluated for OP and IP from the Cu-NMR
measurements at T=300 K (see text).
0245F Tc y p(OP) p(IP) 63νQ(OP) 63νQ(IP) FWHM(OP) FWHM(IP)
♯1 85 K 0.6 0.126 0.066 13.6 MHz 8.3 MHz ∼ 300 Oe ∼ 110 Oe
♯2 75 K 0.7 0.106 0.062 13.1 MHz 7.8 MHz ∼ 230 Oe ∼ 60 Oe
♯3 65 K 0.8 0.083 0.053 11.9 MHz – ∼ 210 Oe –
♯4 52 K 1.0 0.060 0.046 11.6 MHz – ∼ 190 Oe –
than that for IP;OP is closerto the Ba-Flayer(see Fig.
1), which is the source of the disorder due to the atomic
substitution at apical-F sites. The values of FWHM for
OParelessthan∼300Oe,whichisnarrowerthanthose
for Bi- and Tl-compounds [47, 48]. On the other hand,
FWHMforIPislessthan∼110Oe,whichiscomparable
toorevennarrowerthanthoseforY-andHg-compounds
[49]. These NMRlinewidths pointto the goodqualityof
the present samples.
FIG. 2. (color online) Typical 63Cu-NMR spectra for (a)
0245F(♯1), (b) 0245F(♯2), (c) 0245F(♯3), and (d) 0245F(♯4). The
spectra were measured with Hex ⊥ c and at ω0=174.2 MHz. For
(a)0245F(♯1)and(b)0245F(♯2),thespectraofIPdisappearatlow
temperaturesduetothedevelopmentofantiferromagneticcorrela-
tions. For (c) 0245F(♯3) and (d) 0245F(♯4), no signal is obtained
forIPevenatT=300K.
and IP at T=300 K, as shown in Fig. 2(b). When de-
creasingT,however,notonlythespectrumofIPbutalso
that of OP disappears at low temperatures. Moreover, FIG. 3. (color online) NMR frequency ω0-dependence of Hres
in 0245F(♯3)and0245F(♯4),the IP’s spectra are not ob- plotted as (ω0−γNHres)/γNHres vs (γNHres)−2. According to
served even at T=300 K. These marked differences in Eq.(1),thevaluesof63νQ areestimatedaslistedinTableI.
the NMR spectra among the four samples suggest that
AFM correlations become stronger as p decreases from Accordingto the second-orderperturbationtheory for
0245F(♯1) to 0245F(♯4). The values of p for the present thenuclearHamiltonianwithHex ⊥c[50,51],the NMR
samples,listedinTable I,arediscussedlater. Here, note shiftsofthespectrainFig. 2consistoftheKnightshiftK
thatthefull-widthatthehalfmaximum(FWHM) ofthe and the second-order quadrupole shift. The NMR shifts
NMR spectra at T=300 K decreases from 0245F(♯1) to are expressed as
0245F(♯4), as presented in Table I. This is because the ω0−γNHres 3νQ2 1
disorder associated with the atomic substitution is re- =K+ , (1)
γ H 16(1+K)(γ H )2
duced with increasing y, i.e., decreasing the amount of N res N res
the O−2 substitution at the apical-F sites. In the same where γ is a nuclear gyromagnetic ratio, H is an
N res
sample,theNMRspectralwidthforOPismuchbroader NMR resonance field, and ν is a nuclear quadrupole
Q
4
frequency. In order to estimate 63ν for the present withdecreasingp. Inhigh-T cuprates,K comprisesaT-
Q c
samples, we have measured the ω0 dependence of Hres dependent spin part Ks(T) and a T-independent orbital
at T=300 K in a range of 110.2 - 176.2 MHz. The part K as follows:
orb
obtained data set of ω0 and Hres is plotted as (ω0 −
γNHres)/γNHres vs (γNHres)−2 in Fig. 3. Based on K =Ks(T)+Korb. (2)
Eq. (1), we estimated 63ν from the slope of the linear
line in the figure. The oQbtained 63ν values, listed in TheT-dependencesofKs(T)withHex ⊥cfor0245F(♯1),
Q 0245F(♯2), 0245F(♯3), and 0245F(♯4) are displayed in
Table I, are comparablewith those in other multilayered
cuprates [33, 44, 45, 52, 53]. As shown in Table I, 63ν Figs. 4(b), 4(c), 4(d), and 4(e), respectively. Here, Korb
Q was determined as ∼ 0.22 %, assuming K (T) ≃ 0 at a
decreasesfrom 0245F(♯1)to 0245F(♯4);this reductionof s
63ν showsthatpdecreasesfrom0245F(♯1)to0245F(♯4), T = 0 limit.
Q As shown in the figures, the room temperature value
as observed in other hole-doped cuprates[41, 54–58].
of K (T) decreases with decreasing p from 0245F(♯1) to
s
0245F(♯4). The values of p(OP) and p(IP), which are
2. 63Cu-NMR shift and estimation of hole density p summarized in Table I, are separately evaluated by us-
ing the relationship between K (300 K) and p [41]. The
s
quantity p(IP) is smaller than p(OP) because IP is far
from charge reservoir layers, which has been usually ob-
served in multilayered cuprates [44, 46, 59]. As for IP
in 0245F(♯3) and 0245F(♯4), it is impossible to directly
estimate p(IP) from K (300 K). Therefore, we tenta-
s
tively estimate p(IP) from Fig. 5. Figure 5 shows p(OP)
and p(IP) as functions of the average hole density p
av
for 0245F and another five-layered compound Hg1245
[32]. Here, p is defined as p =(2p(OP)+3p(IP))/5.
av av
As shown in the figure, p(OP) and p(IP) systemati-
cally decrease with the reduction of p , which allows
av
us to extrapolate p for 0245F(♯3) and 0245F(♯4) from
av
p(OP). As for 0245F(♯3), p =0.065 is expected from
av
p(OP)=0.083 on the linear line for p(OP) vs p . Fur-
av
thermore,theplotforp(IP)vsp givesatentativevalue
av
of p(IP)=0.053 from p =0.065. The value of p(IP) for
av
0245F(♯4) is also obtained by adopting the same proce-
dure. As summarized in Table I, p(OP) and p(IP) de-
crease with the increase of the fluorine content y, which
reduces T systematically.
c
TheT-dependenceofK (T)forthefour0245Fsamples
s
is different from that for paramagnetic superconductors,
suggesting a possible AFM order at low temperatures.
As an example of a paramagnetic multilayered com-
pound, we show in Fig. 4(a) the T-dependence of K (T)
s
for optimally-doped three-layered Ba2Ca2Cu3O6(F,O)2
(0223F) with T =120 K [35, 41]. As shown in Fig. 4(a),
c
K (T) decreases upon cooling down to T in association
s c
with the opening of pseudogap [60, 61]. The steep de-
crease of K (T) below T is evidence of the reduction in
s c
spin susceptibility due to the formation of spin-singlet
Cooper pairing. These behaviors in K (T) are common
s
in hole-doped cuprates that are paramagnetic supercon-
FIG.4. (coloronline)T-dependencesof63CuKnightshiftKs(T) ductors. On the other hand, in the case of 0245F(♯1),
with Hex ⊥ c for (a) 0223F (cited from Ref. [41]), (b) 0245F(♯1), Ks(T) in Fig. 4(b) shows a T-dependence totally differ-
(c)0245F(♯2), (d)0245F(♯3), and(e)0245F(♯4). ent from that in Fig. 4(a); K (T) for IP can not be de-
s
terminedbelow T ∼200K becauseofthe disappearance
According to Eq. (1), the Knight shift K for the Cu- ofCu-NMRspectra,andK (T)forOPshowsanupturn
s
NMR spectra in Fig. 2 is estimated by subtracting the at T ∼ 85 to 90 K. These unusual behaviors of K (T)
s
second orderquadrupole shift fromthe total NMR shift. suggest a possible AFM transition at IP in 0245F(♯1)
In order to estimate K, we use the 63ν values listed with the N´eel temperature T ∼ 85 K. A similar T-
Q N
in Table I. Here, 63ν (IP) ∼ 7.0 to 7.5 MHz is assumed dependence in K (T) has been reported in optimally-
Q s
for 0245F(♯3)and 0245F(♯4)since 63ν becomes smaller doped five-layeredHg1245 [32, 53], where K (T) for OP
Q s
5
FIG. 5. (color online) Plot of p(OP) and p(IP) as func-
tion of pav for 0245F(♯1), 0245F(♯2), 0245F(♯3), and 0245F(♯4).
Here, pav is the average value of p(OP) and p(IP), defined as
pav=(2p(OP)+3p(IP))/5. The data for Hg1245 is cited from
Ref. [32]. As for IP in 0245F(♯3) and (♯4), it is impossible to di-
rectly estimate p(IP) from Ks(300 K). Therefore, we tentatively
estimate p(IP) from the linear lines in the figure. As shown in
the figure, p(OP) and p(IP) systematically decrease with the re-
duction of pav, which allows us to extrapolate pav for 0245F(♯3)
and 0245F(♯4) from p(OP). As for 0245F(♯3), pav=0.065 is ex-
pected from p(OP)=0.083 on the linear line for p(OP) vs pav.
Furthermore, the plot for p(IP) vs pav gives a tentative value of
p(IP)=0.053 from pav=0.065 as shown by an open circle. The
valueofp(IP)for0245F(♯4)isalsoobtainedbyadoptingthesame
procedure. As summarized in Table I, p(OP) and p(IP) decrease
with the increase of the fluorine content y, which reduces Tc sys-
tematically.
shows an upturn at T ∼ 55 K with the AFM transition
at IP. In 0245F(♯2), the values of K (T) are unmeasur-
s
able for both OP and IP at low temperatures as shown
in Fig. 4(c). In 0245F(♯3) and 0245F(♯4), K (T) for OP
s
determinedonlyathightemperatures,andK (T)forIP
s
is not obtained in all measured T-ranges, as shown in
Figs. 4(d) and 4(e). These unusual behaviors of Ks(T) FIG. 6. (color online) (a) Cu-NQR spectrum at T=1.5 K for
suggest that AFM orders occur at both OP and IP in three-layered 0223F with Tc=120 K (cited from Ref. [34]). The
0245F(♯2), 0245F(♯3) and 0245F(♯4), and that T in- spectrumistypicalofparamagneticmultilayeredcompounds. (b)-
N
(e)Cu-NQRorzero-fieldNMRspectraatT=1.5Kfor0245F.The
creases with decreasing p from 0245F(♯2) to 0245F(♯4).
datafor0245F(♯4)in(e)iscitedfromRef.[34]. Thebarsrepresent
resonancefrequenciesestimatedbyusingEq.(3)withνQvaluesin
TableIandHintvaluesinTableII.ThecurvesinthefigureareCu-
B. Evidence for AFM order probed by Cu-NQR NMR spectral simulations for OP and IP based on the positions
and zero-field Cu-NMR of the bars, which represents resonance frequencies estimated by
usingEq. (3),andsimulationstothetotal Cu-NMRspectra.
As shown in Fig. 2, the 63Cu-NMR spectra for 0245F
are lost when T decreases. This is due to the marked
the nuclear-quadrupole interaction H as follows:
Q
development of AFM correlations, which suggests that
static AFM orders occur at low temperatures. NMR H=H +H
Z Q
measurements at Hex=0 T sensitively detect evidence of e2qQ
static AFM orders, as explained below. =−γN¯hI·H + 4I(2I−1)(3Iz2′ −I(I +1)), (3)
In general, the Hamiltonian for Cu nuclear spins (I =
3/2)with anaxialsymmetry is describedinterms ofthe where eQ is the nuclear quadrupole moment, and eq is
Zeeman interaction H due to a magnetic field H, and the electric field gradient at a Cu nuclear site. In H ,
Z Q
6
thenuclearquadrupoleresonance(NQR)frequencyisde- H isconvertedintoM ,aslistedinTableII,byus-
int AFM
fined as ν =e2qQ/2h. In paramagnetic substances, an ingtherelationofH =|A |M =|A−4B|M .
Q int hf AFM AFM
NQR spectrum is observed due to the second term in Here, A andB arethe on-site hyperfinefield andthe su-
Eq. (3) when H=H =0 T. On the other hand, in mag- pertransferred hyperfine field, respectively. A ∼ 3.7 and
ex
netically ordered substances, an internal magnetic field B ∼ 6.1 T/µ are assumed, which are typical values in
B
H is induced at Cu sites; in addition to the second multilayered cuprates in underdoped regions [41]. Here,
int
term, the first term in Eq. (3) contributes to the nu- wecommentonsomedistributionsofeachresonancefre-
clearHamiltonianevenif H =0 T.Therefore,the onset quency presented in Fig. 6. As mentioned above, the
ex
of a magnetically ordered state is observed as a distinct weakresolutionmaybeduetotheinhomogeneitiesofν
Q
change of the spectral shape at H =0 T. and H . However, a possibility of spin-glass states is
ex int
Figure 6(a) shows the Cu-NQR spectrum of three- ruled out in these compounds. It is reported that the
layered0223FwithTc=120K[34]asanexampleofpara- spin-glass phases cause Hint to largely distribute in as-
magnetic multilayered cuprates. The two peaks corre- sociationwith randomdirections of frozenmagnetic mo-
spond to OP and IP, and both peaks include two com- ments, which does not allowus to obtain zero-fieldspec-
ponents, 63Cu and 65Cu. It is assured that 0223F is a tra inlimited frequency regions. In fact, 19F-NMR stud-
paramagneticsuperconductorbecauseanNQRspectrum ies in the following section assure onsets of long-range
is obtained for OP and IP at H =0 T. Here, note that three dimensional AFM orders.
ex
an NQR spectrum similar to that in Fig. 6(a) should be
obtainedatH =0T when a measuredmaterialis para-
ex TABLE II.List of Hint, MAFM, and TN for 0245F. Weused
magnetic. The spectra obtained at Hex=0 T for five- Hint values presented below in order to obtain the bars in
layered0245Fare,however,totallydifferentfromthatof Fig. 6. The values of MAFM are deduced by using the re-
paramagnetic 0223F as shown in Figs. 6(b)-6(e). lation of Hint = |Ahf|MAFM = |A−4B|MAFM, where A
Figure6(b)showsthespectrummeasuredatH =0T andB aretheon-sitehyperfinefieldandthesupertransferred
ex
and T=1.5 K for 0245F(♯1). An NQR spectrum is ob- hyperfinefield, respectively. A ∼ 3.7 and B ∼ 6.1 T/µB are
served for OP, and the NQR frequency 63ν ∼ 14 MHz assumed, which are typical values in multilayered cuprates
corresponds approximately to the value estQimated from in underdoped regions [41]. The values of TN are estimated
from the upturn in Ks(T) for 0245F(♯1) and from F-NMR
Fig.3(seeTableI).Ontheotherhand,the spectrumfor
measurements for 0245F(♯2), 0245F(♯3), and 0245F(♯4) (see
IP is different from the NQR spectrum for IP in 0223F; text).
theresonancefrequencyofIPin0245F(♯1)issignificantly
larger than 63ν ∼ 8.3 MHz, which was estimated from
Fig. 3. AccordQing to Eq. (3), resonance frequencies in- Hint(OP) Hint(IP) MAFM(OP) MAFM(IP) TN
crease when Hint is induced at Cu sites by the onset of ♯1 0 T 2.3 T – 0.11 µB 85 K
AFM orders. The bars in Fig. 6(b) represent the reso-
nance frequencies estimated by using Eq. (3) on the as- ♯2 1.3 T 2.3 T 0.06 µB 0.11 µB 95 K
sumption of Hint = 0 T for OP and of Hint ∼ 2.3 T ♯3 2.1 T 3.3 T 0.10 µB 0.16 µB 145 K
(⊥ c) for IP. This reveals that H ∼ 2.3 T is induced
int ♯4 2.8 T 4.1 T 0.14 µB 0.20 µB 175 K
at IP by spontaneous AFM moments M due to the
AFM
AFM order. As shown in the figure, there are 63Cu and
65Cucomponents,andeachCucomponenthasonecenter
peak and two satellite peaks when H 6= 0. However,
int
due to the poor frequency resolution that is related to
a weak signal to noise ratio, those signals are not well C. F-NMR
resolved. The weak resolution may be also attributed to
the inhomogeneities of ν and of the size or direction of 1. 19F-NMR spectra
Q
M . Here, we tentatively represent spectra of the IP
AFM
by a single Lorentzian as shown in Fig. 6 (b). It is difficult to deduce the T dependences of
Figures6(c),6(d),and6(e)showthespectrameasured M (OP)andM (IP)fromthezero-fieldCu-NMR
AFM AFM
at H =0 T and T=1.5K for 0245F(♯2),0245F(♯3),and measurements because the nuclear spin relaxationat Cu
ex
0245F(♯4), respectively. In the three samples, the spec- sites is enhanced greatly as T approaches T . Instead,
N
tra for both OP and IP are totally different from the 19F-NMR is used to probe the T dependence of the in-
NQR spectra for 0223F shown in Fig. 6(a), which sug- ternal field H (F) at apical-F sites, which is induced
int
gests AFM orders at both OP and IP. With decreasing by M . Figure 7 shows the T dependences of 19F-
AFM
p from 0245F(♯2) to 0245F(♯4), the spectrum shifts to NMRspectraobtainedbysweepingfrequencieswithH
ex
higher frequency regions, as shown in the figures. As in (=4.245 T) parallel to the c-axis.
the caseofIPin0245F(♯1),the barsinthe figuresrepre- Figure 7(d) shows the T dependence of the F-NMR
senttheresonancefrequenciesestimatedbyusingEq.(3). spectrum for 0245F(♯4), which has the lowest T of the
c
Here,weusedthe valuesof63ν listedinTable Iandas- present samples. A sharp spectrum is observed with
Q
sumedthe values ofH listedinTable II.The quantity a single peak at T = 240 K, but the spectrum splits
int
7
FIG. 7. (coloronline)T dependences of19F-NMRspectrafor(a)0245F(♯1), (b)0245(♯2), (c)0245F(♯3), and(d)0245F(♯4). Here,Hex
is parallelto the c axis and isfixed at4.245 T. The spectra in(b)-(d) splitinto two at low temperatures, pointing to the onset of AFM
orders. Notethatthespectrumfor(a)0245F(♯1) exhibits asinglepeakinallmeasuredT ranges becauseOPisparamagnetic(seetext).
Thedashedlineindicates19Kc=0,andthesolidlinesarespectralsimulationstoestimateω,|Hint,c(F)|,and19Kc.
into two peaks at low temperatures. As discussed be- Figure 7(a) shows the T-dependence of the F-NMR
fore, 0245F(♯4) shows the AFM order with M (OP) spectrum in 0245F(♯1), which has the highest T in the
AFM c
∼0.14andM (IP)∼0.20atT=1.5K.Therefore,the present samples. The spectral shape is unchanged upon
AFM
spectralsplittingsuggeststhedevelopmentofH (F)in- cooling aboveT =85 K;the spectrum shifts to lower fre-
int c
ducedbyM . Figure8(c)presentstheT dependence quency regions due to the SC transition below T . As
AFM c
of the resonance frequency ω in the 19F-NMR spectra, showninFig.6(b)andlistedinTableII,OPin0245F(♯1)
which is deduced through spectral simulations shown by is paramagnetic at T=1.5K, whereas IP shows an AFM
solid lines in Fig. 7(d). As shown in Fig. 8(c), the F- order with M (IP) ∼ 0.11 µ . Therefore, the fact
AFM B
NMRspectrasplitbelowT=175K,suggestingthe AFM that the spectrum does not split at any temperature
ordering below the N´eel temperature T =175 K. shows that the F-NMR spectra with H parallel to the
N ex
c axis is not affected by M (IP), as we already dis-
AFM
Figures 7(b) and 7(c) show the T-dependences of the cussed in the previous report [34].
F-NMR spectra for 0245F(♯2) and 0245F(♯3), respec-
tively. As in the case of 0245F(♯4), the F-NMR spectra
split into two at low temperatures. Below T =75 K in
c 2. T dependence of internal field at apical-F site
0245F(♯2) and T =65 K in 0245F(♯3), however, the two
c
spectral peaks are blurred due to the spectral broaden-
Theresonancefrequencyω of19F-NMRwithH par-
ing related to vortex states in the SC phase. Note that ex
allel to the c-axis is expressed by
M in 0245F(♯2) and 0245F(♯3) is smaller than that
AFM
in0245F(♯4),andthatthevortex-relatedspectralbroad- ω ≃19γ H (1+19K )±19γ |H (F)|, (4)
N ex c N int,c
ening in 0245F(♯2) and 0245F(♯3) is larger than that in
0245F(♯4)duetothehigherT values. Therefore,incon- where H (F) is the component of H (F) along the
c int,c int
trastto0245F(♯4),itisdifficulttoseparatethetwopeaks c-axis, 19γ is the 19F nuclear gyromagnetic ratio, and
N
in0245(♯2)and0245F(♯3)belowT . TheT-dependences 19K is the Knight shift. The plus (minus) sign of
c c
ofω for0245F(♯2)and0245F(♯3)areshowninFigs.8(a) |H (F)|inEq.(4)correspondstoitsparallel(antipar-
int,c
and 8(b), suggesting the AFM transitions at T ∼ 95 K allel)componentalongthec-axis. AsshowninFigs.8(a)-
N
and ∼ 145 K, respectively. 8(c), the spectral splitting ∆ω increases below T due
N
8
FIG. 8. (color online) (a)-(c) T dependence of ω for0245F(♯2), 0245F(♯3), and 0245F(♯4). The values of ω are estimated from spectral
simulations in Fig. 7. For (a) 0245F(♯2) and (b) 0245F(♯3), it is impossible to determine ω below Tc owing to the marked spectral
broadening,whichisinassociationwiththedistributionofvorticesintheSCmixedstate. (d)-(f)T dependence of|Hint,c(F)|estimated
from∆ω=2×19γN|Hint,c(F)|. Here,∆ωisthewidthofthespectralsplittinginF-NMRspectra. ThesolidlineisHint,c(F)∝MAFM(T)=
MAFM(0)(1−T/TN)0.5, which is ingood agreement with the experiment down to Tc. (g)-(i) T dependence of Knight shift19Kc. The
decreasein19Kc belowTc isassociatedwithSCdiamagneticshifts. Thedatain(c),(f),and(i)for0245F(♯4) arecitedfromRef.[34].
to the development of H (F), which is in proportion in the figure, |H (F)| evolves upon cooling following
int,c int,c
to M (OP). If the direction of M (OP) were in the solid line M (T) = M (0)(1 − T/T )0.5.
AFM AFM AFM AFM N
the basal CuO2 planes with a wave vector Q = (π,π), Below Tc=65 K, however, it is difficult to determine
H (F) would be cancelled out at the apical-F site; |H (F)| because the spectral peaks are blurred, as
int,c int,c
the F ions are locatedat a magnetically symmetric posi- shown in Fig. 7(c). The same situation is also true
tion. WehavereportedthatH (F)isinducedbecause in 0245F(♯2); |H (F)| develops below T =95 K as
int,c int,c N
M (OP)isdirectedoutoftheplaneswithinafewde- shown in Fig. 8(d), but the F-NMR spectral peaks are
AFM
greesofthecantingangle[34]. RefertoRef.[34]formore blurred below T =75 K. Here, note that the T values
c N
detailed discussions on the origin of |H (F)|. areexpected to be the same in OP and IP because three
int,c
Figure 8(f) shows the T-dependence of dimensional AFM interactions determine TN. In other
|Hint,c(F)| for 0245F(♯4), which is obtained from words,weexpectthatMAFM(OP)andMAFM(IP)show
∆ω=2×19γ |H (F)|. In order to focus on the the same T dependence, althoughF-NMR spectra probe
N int,c
T evolution of M , M (T), the relationship the development of the staggered moment at OP below
AFM AFM
Hint,c(F) ∝ MAFM(T) = MAFM(0)(1 − T/TN)0.5 is TN.
displayed as the solid line in Fig. 8(f). This power-law
variation of M (T) is in good agreement with the
AFM
experiment down to T = 52 K, which suggests the 3. 19F-NMR shift evidence for SC transition in AFM
c
three-dimensional long-range order of M . The background
AFM
same T-dependence of M (T) has been reported in
AFM
slightly-doped LSCO compounds which exhibit AFM Here, we deal with the SC properties in 0245F. The
ground states [62]. It is also possible to reproduce the T T dependence of 19K is displayed in Figs. 8(g)-8(i).
c
dependence down to T =52 K by another relationship The values of 19K are estimated from the gravity cen-
c c
H (F) ∝ M (T) = M (0)(1 −(T/T )3/2)0.5 ter of the 19F-NMR spectra. In all samples, 19K is T-
int,c AFM AFM N c
(not shown), which has been theoretically predicted independent upon cooling down to T , which is different
c
on an itinerant AFM metal [63]. In any case, the T from the Knight shift K (T) of 63Cu shown in Fig. 4.
s
evolution of M assures that three dimensional The reason that 19K is T-independent above T is that
AFM c c
AFM orders set in below T . Figure 8(e) shows the the spin component in 19K is small owing to the small
N c
T-dependence of |H (F)| for 0245F(♯3). As shown hyperfine coupling between 19F nuclei and Cu-3d spins
int,c
9
asreportedintheliterature[64]. WhendecreasingT be- phase, T listed in Table II is plotted against p(IP). We
N
low T , 19K markedly decreases due to the appearance assumethatT isdeterminedbyIP,consideringthefact
c c N
of SC diamagnetism. Here, note that the reduction of that M (IP) is larger than M (OP). The data
AFM AFM
19K , which is in association with the onset of high-T point for T =0 K at p ∼ 0.126 corresponds to OP in
c c N
SC,takesplaceunderthebackgroundoftheAFMorder; 0245F(♯1), which is paramagnetic even at T=1.5 K.
these observations provide firm evidence for the uniform This phase diagram demonstrates that in 0245F, the
coexisting state of AFM and SC at a microscopic level. AFMmetallicphaseisrobustuptop∼0.11to0.12,and
In 0245F(♯4), |H (F)| additionally increases below that the three-dimensional long-range AFM order coex-
int,c
T as shown in Fig. 8(f). It is likely that the onset of istswithhigh-T SCinanunderdopedregion. Suchaco-
c c
high-T SC decreases the size of M (OP) due to the existence phase has been also reported in three-layered
c AFM
formation of coherent spin-singlet states over the sam- 0223F [35] and four-layered 0234F [33]. Note that the
ple. Therefore,theadditionalincreasein|H (F)|may coexistence of AFM and SC is not a phase separation
int,c
not be attributed to an increase of M (OP) but an between magnetic and paramagnetic phases; AFM and
AFM
increase of the out-of-plane canting angle in the AFM- SC uniformly coexist in a CuO2 plane. We have dis-
SC mixed state. In any case, this finding demonstrates cussed the AFM ordering based on the zero-field NMR
an intimate coupling between the SC order parameter spectrashowninFig. 6, where no paramagneticsignalis
and MAFM [34]. The same behavior is expected for observed for CuO2 layers in AFM states. Here, we de-
0245F(♯2) and 0245F(♯3) as well, although the F-NMR termine the critical hole density p for the AFM order
c
spectralpeaksareblurredduetothespectralbroadening as p ≃ 0.11. The value of p is expected to exist be-
c c
in vortex states below T . tween p(OP) ∼ 0.106 in 0245F(♯2) and p(OP) ∼ 0.126
c
in 0245F(♯1), because OP in 0245F(♯1) is paramagnetic,
but OP in 0245F(♯2) is antiferromagnetic.
D. Phase diagram of AFM and SC in five-layered
Ba2Ca4Cu5O10(F,O)2
IV. DISCUSSIONS
A. Layer number dependence of AFM-SC phase
diagram in hole-doped cuprates
Figure 10 shows the phase diagram of hole-doped
cuprates with the different stacking number n of CuO2
layers. Figure 10 (a) is a schematic phase diagram for
LSCO with n=1; figs. 10(b)-10(e) show the phase dia-
gramsofBa2Can−1CunO2n(F,O)2 (02(n-1)nF)withn=2
[41], n=3 [35], n=4 [33, 65], and n=5, respectively. The
datainFig.10(e)correspondtothoseinFig.9,andthose
inFigs.10(b)-10(d)havebeenreportedinpreviousNMR
studies [33, 35, 41]. Here, note that the data of YBCO
[7, 13] is cited as the AFM phase in Fig. 10(b). There
are no data for the AFM phase of 0212F at present.
Figures10(a)-10(e)showthe variationofthe p values
c
for n-layered compounds, p (n): p (1) ∼ 0.02 [10, 36],
c c
p (2) ∼ 0.055 [7, 13], p (3) ∼ 0.075 [35], p (4) ∼ 0.09
c c c
FIG.9. (coloronline)AFMandSCphasediagramoffive-layered [33,65], andp (5)∼ 0.11. This increaseofp (n) is qual-
c c
0245F. Solid and open squares correspond to OP and IP, respec-
itatively explained as a result of the fact that the inter-
tively. The values of p are determined from the room T values of
layer magnetic coupling becomes stronger with increas-
Cu-NMR Knight shift in Fig. 4, and those of TN are from the
T-dependence of |Hint,c(F)| in Fig. 8 ( see text for detail). The ing n. The mother compounds of high-Tc cuprates are
solidlinesinthefigureareguidestotheeye. characterized by a large in-plane superexchange interac-
tionJ ∼1300Kbetweennearest-neighboringCu-spins
in
Figure 9 shows the phase diagram of AFM and SC [66–69]. In addition to J , an interlayer magnetic cou-
in
in five-layered 0245F, which is derived from the present plingalongthec-axisplaysacrucialroleinstabilizingan
NMR study. For the SC phase, T is plotted against AFM order since no long-range AFM order occurs in an
c
p(OP).IthasbeenreportedthatOPandIPhaveunique isolated two-dimensionalsystem at a finite temperature.
T values,andthatthehigheronedeterminesthebulkT The effective interlayer magnetic coupling of n-layered
c c
[52]. Here,itisexpectedin0245Fthatthe bulkT listed cuprates is given as pJ J (n), where J is a magnetic
c c out c
in Table I corresponds to T (OP). Both OP and IP are coupling between OPs through CRL (charge reservoir
c
in underdoped regions, and p(OP) is larger than p(IP); layer), and J (n) is that in a unit cell, as illustrated
out
therefore, T (OP) is larger than T (IP). For the AFM in Fig. 11(a). It is considered that J is independent of
c c c
10
FIG. 11. (Color online) Schematic illustrations of magnetic cou-
plingsinn-layeredcuprates. (a)Interlayermagneticcouplingalong
c-axis. Jc is the magnetic coupling between OPs through CRL,
which is independent of n; Jout(n) is the magnetic coupling in a
unit cell, which increases with n. (b) In-plane superexchange in-
teraction Jin between nearest Cu spins in two-dimensional CuO2
plane. The quantity Jin is as large as 1300 K in undoped AFM-
Mott insulators [66–69]. It is considered that Jin does not de-
pendonn;therefore,itistheeffectiveinterlayermagneticcoupling
(pJcJout(n))thatincreasespc withincreasingn(seetext).
[70].
FIG. 10. (color online) (a) Schematic phase dia-
grams of LSCO. (b)-(e) AFM-SC phase diagrams of
Ba2Can−1CunO2n(F,O)2(02(n-1)nF). The data plot for (b) B. Ground-state phase diagram of CuO2 plane
0212F, (c) 0223F, and (d) 0234F are cited from Ref. [33, 35, 41].
The data for (e) 0245F are the same with those in Fig. 9. The
Figure12(a)showsM atT=1.5KandtheSCen-
n dependence of the phase diagram reveals the variation of the AFM
ergygap∆ asafunctionofp. Thedatainclude0245F
pc(n) values: pc(1)∼ 0.02 [10, 36], pc(2)∼ 0.055 [7, 13], pc(3)∼ SC
0.075[35],pc(4)∼0.09[33,65],andpc(5)∼0.11. and the previous reports for 0212F, 0223F, and 0234F
[33–35, 41]. The values of M are estimated from
AFM
zero-fieldNMR measurements, andthose of ∆ are as-
SC
sumed to be proportional to T . We also plot M
c AFM
n,andthatJ (n)increaseswithincreasingn;therefore,
out for Y123 [13] in the figure instead of that for bi-layered
the weakness of J (n) suppresses the static long-range
out 0212F since the AFM phase of 0212F has not been re-
AFM orders in LSCO and YBCO at such small doping
ported. Note that, in contrast to Fig. 10, this figure
levels.
focuses on the ground state of CuO2 planes, which gives
Whilep (n)increaseswithn,itseemstosaturateat∼ us an opportunity to compare the experimental results
c
0.14to0.16eveninthestronglimitofinterlayermagnetic with theoretical outcomes.
couplingexpectedforinfinite-layeredcompounds;M The AFM phase in Fig. 12(a) is characterized by the
AFM
atthegroundstateisextrapolatedtozeroatp∼0.14to fact that M exists up to the quantum critical hole
AFM
0.16,asdiscussedinthenextsection(seeFig. 12). These density p ∼ 0.14 to 0.16, at which M disappears
qcp AFM
resultssuggestthattheuniformcoexistenceofAFMand evenatthegroundstate. Itisworthnotingthatirrespec-
SC is a universal phenomenon in underdoped regions, tive of n, the maximum of ∆ (i.e., T ) is around p ∼
SC c
when the interlayer magnetic coupling is strong enough 0.16, which is close to p ∼ 0.14. This implies an inti-
qcp
to stabilize an AFM ordering. A recent report seems to materelationshipbetweentheSCandAFMorderparam-
support this conclusion from a theoretical point of view eters. We also point out that at finite temperatures, no