Table Of ContentPeierls Instability Induced Ferromagnetic Insulator at Orbital Order Transition
J. H. Wei,1,∗ D. Hou,1,2 and X. R. Wang3
1Department of Physics, Renmin University of China, Beijing 100872, China
2Department of Physics, Shandong University, Jinan 250100, China
3Department of Physics, Hong Kong University of Science and Technology, Kowloon, Hong Kong
(Dated: January 11, 2010)
TheoriginofferromagneticinsulatingstateofLa7/8Sr1/8MnO3isinvestigated. Basedonthetight-
binding model, it is shown that this state can be attributed to the Peierls instability arisen from
0 theinterplayofspinandorbitalordering. Theimportanceofthehole-orbiton-phononintercoupling
1 in doped manganites is revealed. This picture explains well the recent experimental finding of the
0 reentranceof ferromagnetic metal state at low temperature[Phys. Rev. Lett. 96, 097201 (2006)].
2
n PACSnumbers: 71.30.+h,75.47.Lx,75.30.Et
a
J
I. INTRODUCTION metal (V) at temperature T 30K. Phase V is a reen-
1 R
≃
1 trance of FM metallic (FMM) state through the FMI
] R1−xAxMnO3 (R being rare-earth ions and A for di- pmhaagsneetinicTreRso<nanTce<tecThOnOiq,unee8w.lTyhdeisccroyvsteareldstrbuyctnuurcelbeaer-
i valent ions, e.g. A= Ca, Sr, Ba or Pb) have been in-
c lowT isstillunknown. Table1listsallfivephases,char-
R
s tensively studied for more than a decade because of its acterized by four critical temperatures. So far, phases
- rich physics, such as unusual colossal magnetoresistance
l I-III have been widely studied and well understood in
r (CMR)1, interesting ferromagnetic (FM) and antiferro-
t terms of crystalstructure, magentic and transportprop-
m magnetic (AFM) phases, and charge and/or orbital or-
erties.
dering. Despite intensive research and progress made so
.
at far in understanding the system, the origin of the fer-
m romagnetic insulating (FMI) phase observed in lightly TABLE I: Phase transitions of La7/8Sr1/8MnO3:
doped La Sr MnO 2 is still controversial and un- P−Paramagnetic, FM−Ferromagnetic, I−Insulator and
- 7/8 1/8 3
d known. CMR can be qualitatively understood in terms M−Metallic
n of the celebrated double exchange (DE) model3, which Phase Temperature Structure Magnetism Transport
o
means the simultaneous appearance of ferromagnetism
c I T >TJT Orthorhombic P I
andmetallicbehavior. Thus,FMIisnotcompatiblewith
[ II TC <T <TJT Monoclinic P I
theDEmodel,atleastnotinadirectway. Althoughitis
2 generallyrecognizedthattheFMIstatemayrelatetothe III TOO<T <TC Monoclinic FM M
v interplay of charge, spin and orbital degrees of freedom, IV TR <T <TOO Triclinic FM I
9 no concrete picture is available. Finding such a picture V T <TR Unknown FM M
1
is the focus of this paper.
0
2 It shall be useful to first summarize the experimental In order to explain the FMI state of La7/8Sr1/8MnO3,
1. observed phases of La7/8Sr1/8MnO3 solid. Lowering the manydifferentmodelswereproposedintheliterature,in-
1 temperature,thefirststructuralphasetransitionfromor- cluding chargepolaronsorder9, checkerboard-likecharge
8 thorhombic to monoclinic orders occurs at T 283K. order10, orbital order without charge order11, etc. Most
JT
0 Thesystemisintheorthorhombicparamagnetic∼insulat- of them are not consistent with the recent resonant X-
v: ing phase (phase I) above TJT, and monoclinic param- rayscattering(RXS)experiments,whichobservedanor-
i agnetic insulating phase (phase II) below T but above bital polaron lattice (OPL) in phase IV12. This obser-
X JT
ferromagnetic (FM) transition temperature T 183K. vation is the basis of FMI orbital polaron model, pro-
ar The second structural phase transition from mCo∼noclinic posed by Kilian and Khali−ullin13. Orbital polarons can
to triclinic orders occurs at T 150K, separating the be viewedas chargecarriers(holes) dressedby the inter-
OO
monoclinic ferromagnetic metall∼ic phase4,5 (phase III) connected orbital states. At light doping magnanites,
from the triclinic FMI state (phase IV) having a super- one Mn4+ site is surrounded by six neighboring Mn3+
structure with unit cell 2ac 4bc 4cc (ac bc cc sites, equivalent to one hole (with eg orbits unoccupied)
is the unit cell of the high-t×emper×ature orth×orhom×bic surroundedby six (occupied) eg orbits. The stronghole-
phase)6. The FMI state of phase IV is supported by orbital coupling will polarize those eg orbits and make
thermalactivatedexponentialT-dependence2,7 ofthere- them point towards the hole to minimize the interaction
sistivity that increases rapidly with the decrease of tem- energy as well as the kinetic energy13. The formation
perature for T < TOO, and the metallic nature of phase of OPL in La7/8Sr1/8MnO3 emphases the importance of
III is confirmed by the fact that the resistivity decreases hole-orbital interaction for the FMI state12–14.
with temperature below T 2. The system undergoes an- Obviously the genuine mechanism of the FMI state
C
othermetal-insulatortransitionfromFMinsulatortoFM should explain following experimental features: 1) the
2
measuredρ T curves2,7;2)thegiantphononsoftening15;
and 3) the −reentrance of the FMM state (IV V)8. It is
difficult for orbital polaron model to explain→feature 1) 3+ 4+ 3+ 4+ 3+
Mn Mn Mn Mn Mn
and 3). The reasons are as follows. Firstly, the orbital
polaron cannot reproduce the measured ρ T curves of
−
La1−xSrxMnO3 at T < TOO (cf. Fig.3). Polaron hop-
ping model yields ρ = ρ0exp(Ea/kBT), where Ea is the b I
activation energy of polarons, from which the binding
energy(Eb =2Ea)ofapolaroncanbe deduced. Thefit- orb II
ting to experimental data7,12 with hole-polaron hopping a
model gives E 0.06 0.12eV, about an order of mag-
b
∼ −
nitudesmallerthanthetheoreticalvalue(E 0.6eVin
b
∼
Ref.13). Secondly, the observed reentrance of the FMM 2- 2- 2- 2-
O O O O
state at lower temperature is inconsistent with polaron
model since polaron hopping becomes more and more
difficultwhenthetemperatureislowered. Therefore,the
FIG.1: (coloronline)Theorbitalorderinducedquasi-1Dcon-
orbital polaron itself is not sufficient to explain the FMI
finement of the motion of holes in a direction. The dashed
state and the origin of the metal-insulator transitions at
lines denote the weak interchain couplings in b and c direc-
TOO remains intriguing and controversial. tions. ThearrowsneartheO2−ionsindicatethedisplacement
The above difficulties can be removed by including of the oxygen sublattice. The insert shows the orbital order
electron-phonon(e-ph)interactioninthesimpleelectron- inducedeffectivecouplingbetweenadjacentMn3+ andMn4+
orbit coupling model. We argue that the mechanism sitesmediatedbytheoxygen2porbit. ConfigurationIandII
of the FMI state is the e-ph coupling induced Peierls correspondtodifferentoccupationofeg orbitalsontheMn3+
instability16 that opens an energy gap at T < TOO. In site. ∆orb is thesplitting of energy between I and II13.
this paper, we shall show that the Peierls instability can
explain the observed reentrance of FMM state quantita-
tively, and the other experimental features at the quali-
tative level. of configuration II than that of I with an energy dif-
ference ∆ 13; 2) effective Mn3+ Mn4+ coupling with
orb
−
considerable transfer integration (t = 0). As a result,
6
configuration II is stable and favors the motion of holes
II. THEORY
alonga-axis. Inthehole-richplanesshowninFig.1,con-
figuration II periodically repeats itself along a-direction
Our theoretical model is based on the quasi-one- thusformsthequasi-1DMn3+ O2− Mn4+ O2− chain-
dimensional (1D) confinement of the motion of holes in − − −
like pathways of hole transport. Please be noted that
La Sr MnO , which has been demonstrated by fol-
7/8 1/8 3 weak interchain couplings (t⊥) in b and c directions also
lowing experiments: 1) the convergent-beam electron
exist, resulting from the hole transfer between unoccu-
diffraction and selected-area electron diffraction seeing pied and occupied e orbits12. Why the orbitalorder in-
the superstructure (2a 4b 4c ) of the FMI phase6 g
c × c× c ducedquasi-1Dconfinementcanonlybeobservedaround
(anisotropic 3D motion); 2) the resonant X-ray scatter-
x = 1/8? Qualitatively speaking, the orbital disorder-
ing showing an alternation of hole-rich and hole-poor
ordertransitiontakesplaceatlightholedopingprovided
planes in c direction12, which confines holes to move
that the Jahn-Teller phonons and superexchange pro-
in the two-dimensional hole-rich a b planes (2D mo-
− cesses mediate an effective coupling between orbits on
tion); and 3) the resonant X-ray scattering also reveal- neighboring sites13.
ing the formationofOPL12,whichfurther confines holes
to move along the one-dimensional charge stripes in a Now we are ready to present our model Hamilto-
direction (1D motion, see Fig.1 and the following ex- nian to describe the quasi-1D motion of particles (elec-
planations). It is known that the quasi-1D confinement trons/holes). As shown in Fig.1, the particles mov-
originates from the orbital order and its induced effec- ing along Mn3+ O2− Mn4+ O2− chains will simul-
tive coupling between adjacent Mn3+ and Mn4+ sites. taneously couple−to th−e orbits−on the manganese sites
The insert of Fig.1 depicts two possible configurations andlattice displacements (phonons) onthe oxygenones.
of one Mn4+ O2− Mn3+ unit with different e orbital Considering that the quasi-particles of orbital degree of
g
occupations o−n the−Mn3+ site. Configuration II corre- freedom are bosonic orbitons17,18, we can establish an
sponds to e orbit pointing towards the hole along the electron-orbiton-phonon intercoupling model. For sim-
g
axis of oxgen 2p orbit while configuration I corresponds plicity, only Mn sites are included in the model and the
to e orbit pointing towards other directions. Due to or- oxygendegreesoffreedomsareintegratedout,givingrise
g
bital anisotropy, configuration II results in a maximized to the effective Mn-Mn coupling and the phonon modu-
overlapping of wavefunctions of occupied e and 2p or- lation to it [cf Eq.(1)]. Then, the tight-binding model
g
bits. That induces two direct effects: 1) lower energy can be written as (~ = 1 and k = 1 are assumed, and
B
3
they are restored in final results), At T < T , the ferromagnetic t spins of Mn ions
C 2g
exclude the opposite spin to occupied e orbitals due to
g
H = tX(c+j cj+1+h.c.)+Xǫqa+qaq+Xc+j cjQj the Hund’s rules, i.e. only carriers with the majority-
j q j spincontributestothechargetransport. Beforecoupling
+ Xωpb+pbp+X(c+j cj+1Pj +h.c.) tfiorsotrtbeirtmalsinanEdq.p(h1o)n]oinnsm, athjoeriMtyn-s4p+i−nMsunb3s+patcreancsofnerdu[tchees
p j
a half-filled metallic energy band and the bare particle
Qj = (Qj−1+Qj+1) spectrum ξk0 can be written as
= (P P ) (1)
j j+1 j
P − ξ0 =γ0+δ0 (3)
k k k
with
with
Qj = XRqeiqRj(aq+a+−q)
q γ0 = 2tcosk a
k − x
Pj = XGpeipRj(bp+b+−p) (2) δk0 = −2tη(coskyb+coskzc) (4)
p
where the effect of weak interchain coupling (t⊥ = ηt,
where c+ is the creation operator of a particle on site j η 1) has been included in δ0. η is a dimensionless
(R is tjhe atom position), a+ (b+) the creation opera- pa≪rameter denoting relative strkength of the interchain
j q p
tors ofa orbiton(phonon) with momentum q (p), ǫ and coupling to intrachain one.
q
ω are the dispersion spectrum of orbiton and phonon The orbitons and phonons then couple to the tight-
p
respectively. The third term is the e-orb coupling be- binding particles, as described in Eq.(1), and change
tweenaparticleonsitej andtheorbitonsonthenearest abovemetallicbandtoainsulatorone. Thesimultaneous
neighborsites j 1,andthe lastterm describes the e-ph couplings between two bosons to one fermion are techni-
±
coupling due to the phonon modulation of the particle cally difficult to solve, even though the direct orbiton-
hopping between sites j and j+119 (see Fig.1). R and phonon coupling has been ignored in Eq.(1). Thus we
q
G arethee-orbande-phcouplingconstantrespectively, make two approximations for e-orb coupling in follow-
p
∗ ∗
which satisfy G−p = Gp and R−q = Rq to ensure the ing calculations. The first one is the q-independence
Hermitian character of Eq.(1). ǫ (= ǫ) and R (= r), based on the theoretical result
q q
What are the different roles of the e-orb and e-ph that the orbiton is almost dispersionless at strong e-orb
interactions in Eq.(1)? One can see that the orbiton couplings23. The second one is the perturbation theory
couples to the on-site charge density n , which pro- ofsmallpolarons19 atstronge-orb couplings,whichcon-
j
motes the formation of Holstein-like small polarons in duces
the strong-coupling limit20. That is the physical ori-
gin of the formation of orbital polarons12,13. The essen- ξ =ξ0exp( r2/ǫ2) r2 Aξ0 B (5)
tial effect of Holstein-like small polarons is reducing the k k − − ǫ ≡ k−
electron bandwidth (or enlarging the electron effective-
where A denotes the electron bandwidth reduction (or
mass). This interaction predicts a transition from band
effective-mass enhancement) and B the energy shift due
transport to thermal-activated hopping of polarons at
to strong e-orb couplings. The above approximations
high temperature, but it can not open an energy gap
have captured the essential physics of e-orb coupling:
to induce the metal-insulator transition at low tempera-
electroneffective-massenhancement(A)andenergyshift
ture. However, the e-ph interaction in Eq.(1) can take
(B), so that it should produce reasonable results in the
the role of opening the energy gap, since the phonon
limit of strong e-orb interactions. Please be noted that
modulation of the electron transfer predicts the Peierls
above approximations are only valid at finite ǫ to avoid
instability in quasi-1D systems at low temperature16,21.
B unphysically large. After electron coupled to orbital
For La Sr MnO , when the orbital order effectively
7/8 1/8 3 degree of freedom,
confines the particles to move along quasi-1D pathways
(see Fig.1), the strong e-ph interaction distorts the oxy- ξ =γ +δ (6)
gensublattice to make O2− ions displace towardsMn4+, k k k
which enhances the polarization of orbits and helps where
to stabilize the orbital order (see Fig.1). There thus
forms the quasi-1D charge-density-wave (CDW) state γk = Aγk0
in manganese sublattice accompanied with bond-order- δ = Aδ0 B (7)
wave (BOW) state in oxygen sublattice with twice the k k−
period of the original lattices (dimerization). One anal- Let us make some further comments on the e-orb in-
ogous material with similar CDW/BOW ground state is teractions concerned in the present work. Our model
the halogen-bridgedmixed-valence metal complex which Hamiltonian describes electrons coupled to two bosonic
has been well studied with this kind of e-ph interaction fields (orbitons and phonons), which is formally simi-
in the literature22. lar to the model of electrons coupled to two kinds of
4
phonons for cuprates24. The key feature of orbitons dis- V(x)=∆eiKx+∆∗e−iKx. TheanomalousGreen’sfunc-
tinguishingthemfromusualphononsisthestrongspatial tion F can be derived from the Gorkov equations for
anisotropyduetothesymmetryofe electronwavefunc- Matsubara Green’s functions (limit to first order in V)
g
tions,whichhasbeenqualitativelyconsideredinbuilding underthe“nestingcondition”: γk−K =γk−2kF =−γk26,
upourquasi-1DHamiltonian[seeFig.1andEq.(1)]. The
quantitative description of orbitons by means of pseu- G(k,εn) = G0(k,εn)+G0(k,εn)∆F(k,εn)
dospin operators, which may be required for more gen- F(k,ε ) = G (k K,ε )∆∗G(k,ε ), (13)
n 0 n n
eral study13, has been beyond the scope of this paper. −
The parameter characterizing the orbital ordering come which gives the following solutions,
into play due to orbitons is λ r/t. In our calcula-
o ≡ iε δ +γ
tainodnsc,oλnosis∼ten0t.2w−ith0.6li5te,rwathuicrehs1is3.realistic to manganites G(k,εn) = (iεn−nδk−)2k−γk2k−∆2
∗
Particles with new energy spectrum in Eq.(6) then ∆
F(k,ε ) = . (14)
couple to phonon degree of freedom. Now, we can an- n (iε δ )2 γ2 ∆2
n− k − k−
alytically solve the Hamiltonian by transforming it into
momentum space, By replacing iεn with ε, the new energy spectrum is de-
termined by the zero of denominators (pole) of Eq.(14):
H =Xξkc+kck+Xωpb+pbp+Xgpkc+k+pck(bp+b+−p)
k p k,p ε=δk±qγk2+∆2. (15)
(8)
where gpk is the e-ph coupling constant in momentum InsertingEq.(7) into Eq.(15) givesthe energygapEg of
spaceandits dependence onk is tobe neglectedinwhat the system,
follows (g = g∗ M ), as in the literature26. That
p −p ∝ p
Hamiltonian for 1D systems indicates a Peierls super- Eg =2∆ 8Aηt. (16)
−
structure which, described by introduction of the follow-
ing anomalous average25, breaks translationalsymmetry By inserting Eq.(14) into Eq.(12) and then perform-
ing standard calculations, we obtain the self-consistent
of initial lattice:
equation of ∆ (set to be real),
∆=g <b +b+ >=0 (9)
2kF 2kF −2kF 6 g2 sinh√γk2+∆2 1
where angular brackets denote thermodynamic average 1= T . (17)
that can be obtained by performing Gibbs average to 2 Xk cosh√γk2+∆2 +coshδk pγk2+∆2
T T
Matsubaraequationsofmotionforoperatorsb andb+
K −K
(K =2kF for Peierls phase transition)26, where g =gKp2/ωK.
∂
( ω )<b (τ)> = F(k,τ = 0)
−∂τ − K K X − III. DISCUSSION
k
∂
(−∂τ +ωK)<b+−K(τ)> = −XF(k,τ =−0)(10) resSuoltfianrgwfreohmavtehedePrievieedrlsthiensitnasbuillaittyingatsttahteeoartbTita<l oTrC-
k
der transition temperature T . With this mechanism,
OO
where F(kt) = i < Ta (t)a+ (0) > is the anoma- we first quantitatively explain the observed reentrance
− k k−K
lousGreen’sfunctiondescribingtheelementaryUmklapp of FMM state. The key point is that a T-dependent
scattering process k K k. interchain coupling η(T) may induce two critical tem-
− →
After Fourier transformation over Matsubara “time” peratures Tc1 and Tc2 of the metal-insulator transition.
to Eq.(10), we have: The former corresponds to the ordinary Peierls instabil-
ity and the latter to the reentrance of the metallic state.
<b +b+ > = 2gKωKT F(k,ε ) (11) It is called stepped Peierls transition theory, with which
K −K ωm −ω2 +ω2 X n ZhouandGongexplainedtheanomaloustransportprop-
m K k,n erty in NbSe 27. With this theory, we can elucidate the
3
reentranceofFMMstateinLa Sr MnO . Forstrong
The condition for the Peierls phase transition is ωm =0 7/8 1/8 3
e-orb coupling, the self-consistent equation of T [de-
at K =2k , i.e., MI
F
rived from E (T )=0] can be expressed as
g MI
2g2 T
∆=gK <bK+b+−K >ωm=0=− ωK XF(k,εn) (12) ∆(TMI)=4Aη(TMI)t. (18)
K
k,n
In principle, η(T) should increase with the decrease of
IncoordinaterepresentationEq.(9) describesPeierlsde- temperature, in analogy with the role of pressure. Since
formation potential characterizedby the wave vector K: the exact expression of η(T) is hard to determined, we
5
taketheleadinglineartermofitsseriesexpansionatlow
temperature (T <T ),
∆
180
η(T)=η0(1 αT/T∆), (19) TC1
− FMI FMM
150
where T∆ denotes the critical temperature of the charge 0.15 Exp.
oEthrqde.e(Tr1-6[i∆)n]d(Tbeu∆pte)ni=dsea0n]t,liwtptahlericthhoigcfohηienracnitdhdeasαnwTaitchp1hTaetcn1oηamt>eηn0o=.lo0ηg0i[ccaifs.l (K)T19200 (eV)Eg0.10 Theo.
0.05
parameter. Inourcalculations,wefixT =180Kbycon-
∆ 60 TC2
sidering the experimental T = T 150K. Please be 0.00
c1 OO 120 140 160 180 200
∼
noted that at least two parameters in the self-consistent 30 T (K)
FMM
equation [Eq.(17)] dependents on each other after T is
∆ 0
fixed. 0.01 0.02 0.03
We then self-consistently solve Eq.(17)–(19) and il-
lustrate the change of T and T with η in Fig.2.
c1 c2 0
The parameters are chosen as r = 0.2t, g = 1.1√t, FIG. 2: (color online) Two critical temperatures of metal-
ǫ = 0.6t, α = 0.5 and t = 0.4 eV. As shown in Fig.2, insulatortransitions(Tc1 andTc2)asafunctionofinterchain
our calculations can yield T 150K and T 30K couplingstrengthη0. Thelargedotsarethecoincidentpoints
c1 c2
at η 0.028,comparing well w∼ith the experimen∼tal ob- of Tc1 and Tc2. The reentrance of the ferromagnetic metal
0 ∼ stateisshownbythebigarrow. Theinsertshowsthetemper-
servation in Ref. 8 as indicated by the big arrows in the
aturedependenceoftheenergygap. Thelineisthetheoretical
figure. Noreentranceofmetallicstateoccursatsmallin-
resultwhilethedotsareexperimentaldatafrom Ref.30. See
terchaincoupling(η <0.024),characterizedbyT =0.
0 c2 text for details of the parameters.
T decreases slightly with increasing of η in this limit.
c1 0
Nonzero T emerges at about η 0.024. Further in-
c2 0
∼
creasing interchain coupling will induce rapid increas-
ing T and rapid decreasing T meanwhile. When T
c2 c1 c1
and Tc2 coincide into one point at large interchain cou- 6 x=0.12
pling,thePeierlsphasetransitiondisappears. Thisisjust x=0.125
the interchain-coupling-induced delocalization of quasi- x=0.14
4
1Dstates,as occursinconjugatedpolymers28. Since the m x=0.15
valueoftforeg electronsystemisbelievetobe0.3 0.6 c 2
eV13,29,ourtheoryquantitativelyexplainsthereentr∼ance
of the FMM state with consistent parameters in the lit- n 0
l
erature.
-2
In a recent experiment on the (011)-oriented
La Sr MnO films, Chen et al. measured an energy
7/8 1/8 3 -4
gap opening at T 190K and increasing to 0.16 eV
at T = 120K30. Th∼e absent physics mechanis∼m in their 0.08 0.09 0.10 0.11 0.12
1/2 1/2
experiment has been already elucidated in this paper, 1/T (1/K )
that is, the observed energy gap results from the Peierls
FIG. 3: (color online) The fits of the experimental measure-
instability at orbital order transition. To further clarify
this point, we calculate the temperature dependence of mentsofρbyρ=ρ0exp(T0/T)1/2. Theexperimentaldatais
from Ref. 12 (x=0.125) and Ref. 7 (for others).
the energy gap self-consistently, and show the result in
the insert of Fig.2 together with the experimental data.
Some of above parameters are adjusted to fit Chen et
al.’s experiment: T∆ = 200K, r = 0.64t and η0 = 0.02. induced quasi-1D confinement in La7/8Sr1/8MnO3.
As shownin the figure,our calculatedE T curve is in With our theory, we can also explain the other exper-
g
−
good agreement with the experimental data. imental features listed in the introduction at the qual-
We then systematically study the effect of the e-orb itative level. The Peierls instability opens an energy
coupling on the Peierls phase transition, and find that gap[see Eq.(16)] and makes La Sr MnO undergo a
7/8 1/8 3
large r increases T and decreases, in meanwhile, T . metal-to-insulator transition at T . As a consequence,
c1 c2 OO
As a consequence, strong e-orb coupling will enlarge the the charge carriers transport only through the localized
phase area of the FMI state in Fig.2. Sufficient strong gap states at T < T , which will trigger the variable
OO
e-orbcouplingwillannihilatethereentranceoftheFMM range hopping (VRH)31. That picture is confirmed by
state by decreasing T to zero (the figure not shown). thethegoodfitofexperimentalρ T curve7,12withVRH
c2
−
That confirms the orbital order being in favor of the mechanism: ρ=ρ exp( T /T) in Fig.3. The exponent
0 0
p
Peierlsinsulatingphase. PleasebenotedthatthePeierls 1/2resultsfromaparaboladensityofstates(DOS) with
instability can not take place without the orbital order zero-DOS at the Fermi level E (called Coulomb gap).
F
6
As regards the the giant phonon softening of the Mn-O pendents of resistivity and the giant phonon softening,
breathing mode15, we comment that it results from the have been also understood at the qualitative level. Our
celebrated giantKohn anomaly at Peierls instability, i.e. theory supports the belief that the intercouplingof hole-
the suppression of phonon frequency at p 2k 32. orbital-phononis criticalin understanding the electronic
F
∼
properties of doped magnanites.
IV. SUMMARY
Acknowledgments
Insummary,wehavedemonstratedthattheFMIstate
of La1−xSrxMnO3 originates from the electron-phonon
coupling induced Peierls instability when the orbital or- SupportfromtheNationalNaturalScienceFoundation
der confines holes to move along quasi-1D pathways. of China (Grants No. 10604037) and the National Basic
With this picture, the reentrance of the FMM state has ResearchProgramofChina (GrantsNo.2007CB925001)
beenwellexplainedquantitatively. Theotherexperimen- are gratefully acknowledged. XRW is supported by HK
talfeaturesofthe FMI sate,suchasthetemperature de- UGC/GRF grants.
∗
Electronic address: [email protected] Gaudart, B. Bu¨chner, and A. Revcolevschi, Phys. Rev. B
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