feodor v. kusmartsev et al- transformation of strings into an inhomogeneous phase of stripes and...
TRANSCRIPT
8/3/2019 Feodor V. Kusmartsev et al- Transformation of strings into an inhomogeneous phase of stripes and itinerant carriers
http://slidepdf.com/reader/full/feodor-v-kusmartsev-et-al-transformation-of-strings-into-an-inhomogeneous 1/6
2 October 2000
Ž .Physics Letters A 275 2000 118–123
www.elsevier.nlrlocaterpla
Transformation of strings into an inhomogeneous phase of stripesand itinerant carriers
Feodor V. Kusmartsev a,b, Daniele Di Castro c, Ginestra Bianconi d,Antonio Bianconi e
a Landau Institute, Moscow, Russia
bPhysics Department, Loughborough UniÕersity, Leicestershire LE 113 TU, UK
c Dipartimento di Fisica, UniÕersita di Roma La Sapienza, P. Aldo Moro 2, 00185 Roma, Italy`
d Department of Physics, Notre Dame UniÕersity, 46556 Indiana, USAe
Unita INFM, Dipartimento di Fisica, UniÕersita di Roma La Sapienza, P. Aldo Moro 2, 00185 Roma, Italy` `
Received 31 July 2000; accepted 7 August 2000
Communicated by V.M. Agranovich
Abstract
We discuss the transformation of a network of strings consisting of charges self-trapped by linear cooperative local lattice
distortions into an inhomogeneous phase of stripes and itinerant carriers in cuprate superconductors. This scenario is
observed by X-ray diffraction in oxygen doped La CuO where the doped charges at the critical doping 1r8 are self trapped2 4
into a crystal of ordered strings of finite length. Above this critical density in the superconducting phase the stripes co-existwith itinerant carriers. q 2000 Published by Elsevier Science B.V.
Doping drives a high correlated electronic system
toward a microscopic electronic phase separation as
it was first shown in doped magnetic semiconductorsw x1,2 . It has been recently shown that in the presence
of a strong electron lattice interaction the doped
charges have a tendency to create electronic stringsw x3–7 . Each string consists of M charged particles
that are self-trapped by local lattice deformation and
polarization in a linear array of N sites. The electron
correlation and in particular the antiferromagnetic
Ž . E-mail address: [email protected] F.V. Kusmartsev .
spin–spin interaction strongly enhance the tendency
to phase separation and to string formation. This
string is a generalization of the idea of the isolated
polaron to a system of many particles and high
density. In the range of physical parameters relevant
to the doped perovskites these strings have lowerw xenergy than isolated polarons 3– 5 .
The doped cuprate perovskites are strongly corre-
lated materials where the on site Coulomb repulsion
U ;6 eV forbids double hole occupancy on the
same Cu ions and holes are doped into oxygenw xorbitals 6,7 . At very low doping the doped holes
segregate into strings of charges that play the role of
domain walls between anti ferromagnetic domains
0375-9601r00r$ - see front matter q 2000 Published by Elsevier Science B.V.Ž .P I I : S 0 3 7 5 - 9 6 0 1 0 0 0 0 5 5 5 - 7
8/3/2019 Feodor V. Kusmartsev et al- Transformation of strings into an inhomogeneous phase of stripes and itinerant carriers
http://slidepdf.com/reader/full/feodor-v-kusmartsev-et-al-transformation-of-strings-into-an-inhomogeneous 2/6
( )F.V. KusmartseÕ et al.r Physics Letters A 275 2000 118–123 119
w x8 . At low doping the strings form a glassy phase.
At a critical doping d s 1r8 the doped holes form
an insulating crystal of strings where the charges arew xtrapped into mesoscopic linear domains 9,10 by the
w xpseudo Jahn–Teller electron lattice coupling 11 . At
higher doping the charges are self-trapped into aw xsuperlattice of stripes of a distorted lattice 12,13
that co-exist with 2D free charge carriers that give aw xquasi 2D Fermi surface 3,14 . In this scenario the
superconducting phase occur in a superlattice of w xquantum stripes 9,10,15– 19 .
It has been recently shown that the Jahn–Teller
electron–phonon coupling drives the formation of
strings where the doped charges are trapped by thew xcooperative local lattice distortions 20,21 also in
manganites. In the very low density limit we can
consider a system of non interacting strings where in
each string the elastic deformation Q is proportional
to the number of trapped charges M . The elasticenergy of the lattice is proportional to Q2
; M 2. The
electron kinetic energy of the self trapped particles
and therefore the lattice adiabatic potential of the
string state decreases as ; E M 2 where E is thep p
energy for trapping a single charged particle. This
localization energy is opposed by the Coulomb re-
pulsion between particles trapped by the string po-
tential well which energy has an additional factor log
M , so that the Coulomb energy is approximately
equal ;VM 2 log M where V is a constant of the
inter-site inter-electron Coulomb repulsion. A bal-ance between these energies which is determined by
a minimization of the total energy gives a stationary
many particles self trapped string state where thew xstring length is equal to 3,21 :
E 1p N ; M ;exp y . 1Ž .ž /V 2
Let us estimate the length of these strings in the
perovskite materials. We take the elastic modulas of
the order of c s 11=1010 ergrcm3, the inter-11
˚atomic distance is a s 4 A, then we get K ;4.1 eV.
The deformation potential may be approximated as
D;e2ra s 3.4 eV, then for the electron–phonon
coupling we obtain E s D2 K s 2.5 eV. Taking ap
dielectric constant of ´ s 5 for a doped system, we
get V s e2 ´ as 0.68 eV. This gives estimation for
the length of the string of the order of 10 inter-atomic
distances.
Increasing the doping the system of strings under-
goes into a kind of nematic liquid phase consisting
of these oriented ordered cigar shaped electronic
molecular strings that can constitute the underdoped
phase of cuprate perovskites. Each of these molecules
is a charged object and therefore by further increas-
ing the doping the long range inter-string Coulomb
repulsion increases and it is expected to stabilize an
ordered phase made of a crystal of strings that isw xexpected near the doping d s 1r8 12,13 .0
We have studied here the formation of this type of
liquid crystal of strings in oxygen doped La CuO at2 4
hole doping d near 1r8. We have focused our
interest to the superconducting L CuO system2 4q y
w x22–41 . The single crystal of La CuO was grown2 4q y
first as La CuO single crystal by flux method and2 4
then doped by electrochemical oxidation up to reachand average oxygen concentration y s 0.1 deter-
mined by the increase of molecular weight. Thew xoxygen ions are mobile above 200 K 36 and the
oxygen distribution al low temperature is known to
be non-homogeneous. Our crystal shows a spinoidal
macroscopic decomposition into two domains withŽ .about equal probability: phase 1 made of macro-
scopic domains with static antiferromagnetic orderw x Ž .below 40 K 41 and a second phase 2 made of
superconducting domains with a single supercon-
ducting transition T s 40 K where the hole densityc
is the same as in optimum doping in Sr doped
La CuO superconductors with d s 0.16 holes per2 4
w xCu site 23–25,38 .
Neutron diffraction data of our crystal show the
presence of two different sites for interstitial oxy-
gens. The first one are interstitial sites O4 at theŽ .1r4,1r4,1r4 lattice position within the LaO layers
Ž . w xwith probability y s 0.064 4 22 . The second site1
for the interstitial doped oxygen is in the LaO planeŽ Ž . Ž . Ž ..at the site O3 0.031 3 ,0.135 3 ,0.176 1 near the
Ž Ž ..apical oxygen at O1 0,0,0.1822 1 forming about
0.08 pairs of apical oxygens.
Therefore the stoichiometry of our crystal givenw xby neutron diffraction is O4 La O1 O3 -0.064 2 1.85 0.232
CuO .2
The first set of interstitial oxygen sites O4 are
associated with the insulating antiferromagnetic do-
mains with about d ;0.125 holes per Cu sites i.e., at
8/3/2019 Feodor V. Kusmartsev et al- Transformation of strings into an inhomogeneous phase of stripes and itinerant carriers
http://slidepdf.com/reader/full/feodor-v-kusmartsev-et-al-transformation-of-strings-into-an-inhomogeneous 3/6
( )F.V. KusmartseÕ et al.r Physics Letters A 275 2000 118–123120
the critical doping 1r8. The occupation of interstitial
sites O3 are associated with the formation of the
second metallic and superconducting domains with
hole doping d s 0.16 in the CuO plane. Therefore2
in the same crystal we can compare the structure of
insulating charge ordered phase and the supercon-
ducting phase at higher doping.
The charge ordering has been studied by tempera-
ture dependent diffraction data collected on the crys-
tallography beam-line at the synchrotron radiation
facility Elettra at Trieste. The X-ray beam emitted by
the wiggler source on the 2 GeV electron storageŽ .ring was monochromatized by a Si 111 double crys-
tal monochromator, and focused on the sample. The
temperature of the crystal was monitored with an
accuracy of "1 K. We have collected the data with˚a photon energy of 12.4 keV, wavelength l s 1 A,
using an imaging plate as a 2D detector. The sample
oscillation around the b-axis was in a range 0-f -308, where f is the angle between the direction of
the photon beam and the a-axis. We have investi-˚ y1gated a portion of the reciprocal space up to 0.6 A
momentum transfer i.e., recording the diffraction
spots up to the maximum indexes 3, 3, 19 in the a),
b), c) direction respectively. The orthorhombic lat-˚tice parameters of our crystal are a s 5.351 A, b s
˚ ˚5.418 A, c s 13.171 A. Thanks to synchrotron radia-
tion it has been possible to record a large number of
weak superstructure spots due to charge ordering
around the main peaks of the average structure. Theindexing of the superstructure has been conducted
taking into account the twinning of the crystal. The
oxygen ordering has been found to occur in the
temperature range 270–330 K. Charge ordering de-
velop below 190 K. At 100 K we have found the
competition and coexistence of two charge orderedŽ .modulation see Fig. 1 . The first one is character-
ized by 3D long range charge ordering and narrowŽ .resolution limited diffraction peaks with wavevec-
tor
q s 0.089 "0.0031 a) , 0 .244 "0.0024 b) ,Ž . Ž .1
0.495 "0.0046 c) .Ž .
This charge ordered phase shows the formation of a
crystal made of charge strings of finite length 11 a˚Ž . Žwhere a s 5.35 A , separated by R s 4 b where
Ž .Fig. 1. Scans along the Qs 0,k ,6q0.29 due to the diffuseŽ .scattering peaks of stage 3.5 superstructure 2 , squares, and along
Ž . Ž .the Qs 0,k ,6q0.5 squares due to the superstructure 1 .
˚ .b s 5.41 A and doubling of the unit cell along the
c-axis.The metallic superconducting phase shows a pat-
tern of diffuse spots due to a second superstructure,˚with a coherence length of about 350 A with
wavevector
q s 0.2080 "0.0016 b) , 0 .290 "0.0055 c) .Ž . Ž .2
This second wavevector q is associated to in plane2
superconducting stripe ordering. The length of the
stripes in the a direction becomes infinite or longer˚than 500 A. The transverse modulation of the super-
lattice of stripes in plane along the b-axis is the sameas the one found in superconducting Bi2212 and
characterized by diagonal stripes with wavevector of
0.208 b) indicating a separation between the stripes
of R;4.8 b in the b-axis direction. The period of of
the superlattice is 3.5 c in the c-axis direction.
The structure of the crystal of strings that we have
determined by X-ray diffraction in oxygen doped
L CuO at hole doping close to d s 1r8 is shown2 4q y
in Fig. 2.
At higher doping the crystal of strings shown in
Fig. 2 is unstable for the formation of an inhomoge-
neous phase where delocalized charge carriers co-ex-
ist with charges trapped into stripes as shown in Fig.
3. This phase is characterized by the diffuse short
range stripe fluctuations associated with the
wavevector q .2
Now we discuss the transformation of the crystal
of strings into an inhomogeneous phase where delo-
8/3/2019 Feodor V. Kusmartsev et al- Transformation of strings into an inhomogeneous phase of stripes and itinerant carriers
http://slidepdf.com/reader/full/feodor-v-kusmartsev-et-al-transformation-of-strings-into-an-inhomogeneous 4/6
( )F.V. KusmartseÕ et al.r Physics Letters A 275 2000 118–123 121
Fig. 2. Pictorial view of the striped charge ordered pattern at
doping d s1r8 in the CuO plane of oxygen doped La CuO2 2 4
forming a crystal of strings along the a-direction. The unit cell of
the crystal is orthorhombic with the a-axis shorter than the b-axis.
The strings of N ;11 sites are occupied by M ;10 charges run
along the a-axis. Each string is at distance R from its nearest
neighbor in the b-axis direction. The dashed line indicate thew xelastic antiferromagnetic scattering wavevector 41 .
calized charge carriers co-exist with charge trapped
into stripes at higher doping as shown in Fig. 3.
The total free energy of the crystal of stringsŽshown in Fig. 2 may be described as see, also for a
w x.comparison, in Ref. 1,2
F s F q F s F single inter single
1 n r y r n r X
y r Ž . Ž .Ž . Ž .X
q d r d r , 2Ž .H X2 ´ r y r
where F is the free energy per particle neededsingle
for a single string formation while the second term
F describes a contribution from inter-stringinter
Ž .Coulomb repulsion forces. The value n r describes
an inhomogeneous charge distribution associated with
the formation of liquid crystal of strings while the
value r is an average electron charge density associ-
ated with the doping.
We propose a very simple description of the free
energy per particle based on the assumption that the
electronic molecule is preserved at strong doping
while the molecule charge remains the same. At
doping n;1r8 such linear string molecules will be
ordered in the form presented in Fig. 2. Here dis-
tance between molecules R is determined from the
charge neutrality condition
Me y N r R q 1 e s 0, 3Ž . Ž .
whence from this equation we have that R s n r y 1
and we have used the definition that n s M N . The
inter-string Coulomb energy may be estimated withthe use of the electrostatics force law and it is equal
to
Q2
F s C , 4Ž .inter 1´ aR
where the string charge is equal to Q s Me y N r e
and the numerical factor C is related to a number of 1
strings which are interacting with each other within a
Debye screening radius. In other words, we have to
take into account an effective screening length j for
the inter-string Coulomb interaction. So, for exam-ple, for strings localized in a single CuO plane and
interacting via nearest neighbors, that is, with the
screening length j equal to an inter-string distance
R the value C s 1. When the next nearest neighbors1
are taken into account, i.e., when the screening
length j is equal to twice the inter-string distance,
2 R, the value C s 3r2. Analogously for the next1
Fig. 3. A crystal of charged strings of finite length is formed at
doping d ;1r8 in the phase diagram of the cuprate supercon-0
ductors while an inhomogeneous phase where a superlattice of
stripes coexists with the free carriers is formed by increasing the
density.
8/3/2019 Feodor V. Kusmartsev et al- Transformation of strings into an inhomogeneous phase of stripes and itinerant carriers
http://slidepdf.com/reader/full/feodor-v-kusmartsev-et-al-transformation-of-strings-into-an-inhomogeneous 5/6
( )F.V. KusmartseÕ et al.r Physics Letters A 275 2000 118–123122
nearest neighbors taken into account C s 11r6, and1
so on. In general this numerical factor may be esti-
mated with the use of the simple equation:
j 1C s .Ý1
k k s1
Using this expression for the free energy per particleassociated with the Coulomb inter-string interaction,
Ž .Eq. 4 we get the equation for the total free energy
equal to
F r Me2r n y r Ž . Ž .s y E q C , 5Ž .p 12 M ´ an
Žwhere E is the energy shift per particle or ap
.condensation energy associated with the formation
of individual strings. With the doping this value
changes slightly and it is of the order of a single
particle polaron shift. Therefore for the next consid-Ž .eration we put it as equal to a single particle polaron
shift. We also count the energy from the bottom of
the conduction band that we put equal to E s 0.c
From the obtained expression we may immedi-
ately determine the critical doping at which 2D free
charge carriers may appear and where they can
co-exist with localized string charges. Since in this
case at the value r )r the value of the free energyc
Ž .becomes positive F r )0, the critical value of the
doping may be found as equal to
E pr s . 6Ž .cVNC 1
Here we assume that the value r <n. Using theŽ .same parameters as in Eq. 1 , E s 2.5 eV andp
V s 0.68 eV, the number N s 11 obtained in ourŽ .experiment and also with the use of Eq. 1 and the
numerical factor 2.5-C -3 we apply the formula1
Ž . Ž .6 . Then with the use this formula 6 we obtain the
value for the critical hole doping as equal close to
0.1–0.12, which is in a remarkable agreement with
the present experimental findings.
Thus at the doping r )r the second subsystemc
associated with free charge carriers coexists with
charges trapped into stripes. The concentration of
these free particles is determined via a balance con-
trolled by the chemical potential m. For free fermions
the chemical potential is equal to the Fermi energy
m s E . Let the concentration of the free particles inF
the CuO plane be n , then the Fermi energy is2 F
equal to m s"2 n 4p ma2. Due to the conserva-F F
tion of charge the value of doping r s r q n ,s F
where the value of r is the part of the doping whichs
contributes to the formation of stripes. Thus theŽbalance between these two subsystems correlated
.Fermi liquid and stripes may be presented in the
form
"2 n M r n y r Ž .F s s
m s m s s y E q VC .F p 12 24p ma n
Since n s r y r then with the use of this equationF s
we obtain finally the equation to determine the con-
centration of free particles n or r in the form:F s
"2 n VC M F 1
s y E q r y n n q n y r .Ž . Ž .p F F2 24p ma n
7Ž .
The solution of this equation gives
2n a n a a r n s r y y q q y y r ,(F cž /2 2 b 2 2 b b
8Ž .
where a s"2 2 mp a2 and b s Me2 C ´ an2. From1
this equation one may see that there is a second
critical value for the doping r at which this chemi-c2
cal equilibrium can not be maintained. This second
critical value is equal to
2n a br s q y r . 9Ž .c2 cž /2 2 b a
Probably that at the higher densities r )r thec2
stripes disappear and only a correlated Fermi liquidŽ .or, more precisely, a system of correlated fermions
arises.
In conclusion this work provides a direct measure
of the instability of a crystal of strings at doping 1r8
into a superlattice of superconducting stripes in the
high T superconducting phase. The physical mecha-cnism driving the transformation of a phase made of
strings of finite length into the metallic striped phase
that gives high T superconductivity has been de-c
scribed. We show the presence of a phase for the
co-existence of free carriers and a superlattice of
stripes and we provide a new scenario for the forma-
tion of the high T superconducting phase.c
8/3/2019 Feodor V. Kusmartsev et al- Transformation of strings into an inhomogeneous phase of stripes and itinerant carriers
http://slidepdf.com/reader/full/feodor-v-kusmartsev-et-al-transformation-of-strings-into-an-inhomogeneous 6/6
( )F.V. KusmartseÕ et al.r Physics Letters A 275 2000 118–123 123
Acknowledgements
Thanks are due the A. Valletta and P. Radaelli for
help in the early stage of this work, to C. Chaillout
for neutron diffraction sample characterization and to
M. Colapietro for experimental help at the Elettra
X-ray diffraction beam line. This research has been
supported by Istituto Nazionale di Fisica della Mate-Ž .ria INFM in the frame of the progetto PAIS
AStripesB, the Ministero dell’Universita e della`Ž .Ricerca Scientifica MURST Programmi di Ricerca
Scientifica di Rilevante Interesse Nazionale coordi-
nated by R. Ferro, e Progetto 5% SuperconduttvitaŽ .del Consiglio Nazionale delle Ricerche CNR .
References
w x Ž .1 E.L. Nagaev, Sov. J. JEPT Lett. 16 1972 558.w x Ž .2 V.A. Kaschin, E.L. Nagaev, Zh. Exp. Teor. Phys. 66 1974
2105.w x Ž .3 F.V. Kusmartsev, J. Phys. IV 9 1999 10–321.w x Ž .4 F.V. Kusmartsev, Phys. Rev. Lett. 84 2000 530.w x Ž .5 F.V. Kusmartsev, Phys. Rev. Lett. 84 2000 5026.w x6 A. Bianconi, A. Congiu Castellano, M. De Santis, P. Rudolf,
P. Lagarde, A.M. Flank, A. Marcelli, Solid State Commun.Ž .63 1987 1009.
w x7 A. Bianconi, A. Congiu Castellano, M. De Santis, P. Delogu,Ž .A. Gargano, R. Girogi, Solid State Commun. 63 1987
1135.w x8 J.H. Cho, F.C. Chu, D.C. Johnston, Phys. Rev. Lett. 70
Ž .1993 222.w x Ž .9 A. Bianconi, Sol. State Commun. 91 1994 1.
w x Ž .10 A. Bianconi, Physica C 235–240 1994 269.w x11 Y. Seino, A. Kotani, A. Bianconi, J. Phys. Soc. Jpn. 59
Ž .1990 815.w x12 A. Bianconi, S. della Longa, M. Missori, I. Pettiti, M.
Ž .Pompa, A. Soldatov, Jpn. J. Appl. Phys. 32 1993 578,
Suppl. 32–2.w x Ž . Ž .13 A. Bianconi, M. Missori, J. Phys. I France 4 1994 361.w x14 A. Bianconi, N. L. Saini, A. Lanzara, M. Missori, T. Ros-
setti, H. Oyanagi, H. Yamaguchi, K. Oka, T. Ito, Phys. Rev.Ž .Lett. 76 1996 3412.
w x15 N. L. Saini, J. Avila, A. Bianconi, A. Lanzara, M. C.
Asenzio, S. Tajima, G. D. Gu, N. Koshizuka, Phys. Rev.
Ž .Lett. 79 1997 3467.w x16 N. L. Saini, J. Avila, A. Bianconi, A. Lanzara, M. C.
Asenzio, S. Tajima, G. D. Gu, N. Koshizuka, Phys. Rev.Ž .Lett. 82 1999 2619.
w x17 A. Perali, A. Bianconi, A. Lanzara, N.L. Saini, Solid StateŽ .Commun. 100 1966 181.
w x18 A. Valletta, G. Bardelloni, M. Brunelli, A. Lanzara, A.Ž .Bianconi, N.L. Saini, J. Supercond. 10 1997 383.
w x19 A. Bianconi, A. Valletta, A. Perali, N.L. Saini, Physica CŽ .296 1998 269.
w x20 F.V. Kusmartsev, in: Isaac Newton Institute for Mathemati-Ž .cal Sciences, Preprint NI00004-SCE 28 Apr 2000 .
w x21 F.V. Kusmartsev, to be published.w x22 C. Chaillout, J. Chenavas, S.W. Cheong, Z. Fisk, M. Marezio,
Ž .B. Morosin, E. Schirber, Physica C 170 1990 87.w x23 P.C. Hammel, A.P. Reyes, S.-W. Cheong, Z. Fisk, J.E.
Ž .Schriber, Phys. Rev. Lett. 71 1993 440.w x24 P.C. Hammel, A.P. Reyes, Z. Fisk, M. Takigawa, J.D.
Thompson, R.H. Heffner, S. Cheong, J.E. Schirber, Phys.Ž .Rev. B 42 1990 6781.
w x25 E.T. Ahrens, A.P. Reyes, P.C. Hammel, J.D. Thompson,Ž .P.C. Canfield, Z. Fisk, J.E. Schirber, Physica C 212 1993
317.w x26 J.C. Grenier, N. Lagueyte, A. Wattiaux, J.P. Doumerc, P.
Dordor, J. Etourneau, M. Pouchard, J.B. Goodenough, J.S.Ž .Zhou, Physica C 202 1992 209.
w x27 A. Demourges, F. Weill, B. Darriet, A. Wattiaux, J.C. Gre-
nier, P. Gravereau, M. Pouchard, J. Solid State Chem. 106Ž .1993 330.
w x28 M. Itoh, T. Huang, J.D. Yu, Y. Inaguna, T. Nakamura, Phys.Ž .Rev. B 51 1995 1286.
w x29 T. Kyomen, M. Oguni, M. Itoh, J.D. Yu, Phys. Rev. B 51Ž .1995 3181.
w x30 R.K. Kremer, E. Sigmund, V. Hizhnyakov, F. Hentsch, A.Ž .Simon, K.A. Muller, M. Mehring, Z. Phys. B 86 1992 319.¨
w x31 R.K. Kremer, V. Hizhnyakov, E. Sigmund, A. Simon, K.A.Ž .Muller, Z. Phys. B 91 1993 169.¨
w x32 N. Lagueyte, F. Weill, A. Wattiaux, J.C. Grenier, Eur. J.Ž .Solid State Inorg. Chem. 30 1993 859.
w x33 P.G. Radaelli, J.D. Jorgensen, A.J. Schultz, B.A. Hunter, J.L.Ž .Wagner, F.C. Chou, D.C. Johnston, Phys. Rev. B 48 1993
499.w x34 X. Xiong, P. Wochner, S.C. Moss, Y. Cao, K. Koga, N.
Ž .Fujita, Phys. Rev. Lett. 76 1996 2997.w x35 X.L. Dong, Z.F. Dong, B.R. Zhao, Z.X. Zhao, X.F. Duan,
L.-M. Peng, W.W. Huang, B. Xu, Y.Z. Zhang, S.Q. Guo,Ž .L.H. Zhao, L. Li, Phys. Rev. Lett. 80 1998 2701.
w x Ž .36 F. Cordero, R. Cantelli, Physica C 312 1999 213.w x37 P. Blakeslee, R.J. Birgenau, F.C. Chou, R. Christianson,
Ž .M.A. Kastner, Y.S. Lee, B.O. Wells, Phys. Rev. B 57 1998
13915.w x38 P.C. Hammel, B.W. Statt, R.L. Martin, F.C. Chou, D.C.
Ž .Johnston, S.-W. Cheong, Phys. Rev. B 57 1998 R712.w x39 Z.G. Li, H.H. Feng, Z.Y. Yang, A. Hamed, S.T. Ting, P.H.
Ž .Hor, Phys. Rev. Lett. 77 1996 5413.w x40 B.O. Wells, Y.S. Lee, M.A. Kastner, R.J. Christianson, R.J.
Birgeneau, K. Yamada, Y. Endoh, G. Shirane, Science 277Ž .1997 1067.
w x41 Y.S. Lee, R.J. Birgeneau, M.A. Kastner, Y. Endoh, S. Waki-
moto, K. Yamada, R.W. Erwin, S.-H. Lee, G. Shirane, Phys.Ž .Rev. B 60 1999 3643.