Confined spin waves reveal an assembly of nanosize domains in ferromagnetic La(1-x)CaxMnO3 (x=0.17,0.2)

0.22 MB·English

by  M. Hennion

Confined spin-waves reveal an assembly of nanosize domains in ferromagnetic
La1−xCaxMnO3 (x=0.17, 0.2)
M. Hennion1, F. Moussa1, P. Lehouelleur1, F. Wang1,2, A. Ivanov3, Y. M. Mukovskii4 and D. Shulyatev4
1 Laboratoire L´eon Brillouin, CEA-CNRS, CE-Saclay, 91191 Gif sur Yvette, France.
2 Institute of Physics Chinese Academy of Sciences, 100080 Beijing, China
3 Institut Laue-Langevin, 156 X, 38042 Grenoble Cedex 9, France
4 Moscow State Steel and Alloys Institute, Moscow 119991 Russia
5
0
0 We report a study of spin-waves in ferromagnetic La1−xCaxMnO3, at concentrations x=0.17
2 and x=0.2 very close to the metallic transition (x=0.225). Below TC, in the quasi-metallic state
(T=150K),nearlyq-independentenergylevelsareobserved. Theyarecharacteristicofstandingspin
n
waves confined into finite-size ferromagnetic domains, defined only in (a, b) plane for x=0.17, and
a
inalldirectionsforx=0.2. Theyallowanestimationofthedomain’ssize,afewlatticespacings,and
J
of the magnetic coupling constants inside thedomains. These constants, anisotropic, are typical of
1
an orbital-ordered state, allowing to characterize the domains as ”hole-poor”. The precursor state
1
of theCMR metallic phase appears, therefore, as an assembly of small orbital-ordered domains.

]
l PACSnumbers: PACSnumbers: 74.25.Ha74.72.Bk,25.40.Fq
e
-
r
st In metallic La1−xCaxMnO3, for x≈0.3, the origin of Inelastic neutron experiments have been carried out
. the colossal magneto-resistance (CMR) which occurs at at the reactor Orph´ee (Laboratoire L´eon Brillouin) and
t
a the metal-insulator transition is still a challenge for the- at the Institut Laue-Langevin, on triple axis spectrom-
m
ories. The role played by an inhomogeneous ground eters, using fixed final wave vector of neutrons varying
- state has been outlined by several theoretical[1] and ex- from 1.05 to 4.1˚A−1, and appropriate filters. The T
d C
perimental works[2, 3]. In the semi-conducting parent values are 175K and 180K for x=0.17 and x=0.2 respec-
n
o LaMnO3, the magnetic coupling is of super-exchange tively. Both samples have been characterized by resis-
c (SE)type,ferromagnetic(F)inthe(a,b)plane(J >0) tivity measurements. In La Ca MnO , the high-
a,b 0.83 0.17 3
[ and antiferromagnetic (AF) along c (J <0), consistent temperature pseudo-cubic structure, with lattice param-
c
2 withtheorbitalorderingwhichoccursattheJahn-Teller eter a0=3.89˚A, becomes orthorhombic at TJT=240K,
v transition T . Doping with holes induces a canted whereas such an orthorhombicity is unobservable for
JT
1 AF state (CAF). There, neutron diffuse scattering in- La Ca MnO . All Q values (Q=q+τ and q=ζ) are
0.8 0.2 3
1
dicates the existence of magnetic inhomogeneities at- given in reduced lattice units with pseudo-cubic indexa-
6
tributed to hole-rich clusters embedded in a hole-poor tion. Thetwosinglecrystalsaretwinned,sothateachdi-
8
0 matrix[4], andanew spin-wavebranchappearsatsmall- rection is superimposed on related symmetry directions.
4 q around F Bragg peaks. This new branch coexists with Dataarefitted bya lorentzianshape weightedby aBose
0 the spin-wave branch close to that of LaMnO (SE type factor. ThisanalysisyieldstheenergyE(q),thedamping
3
/
t ofcoupling),attributedtothehole-poormatrix[5],which Γ(q) with Γ(q)/E(q)≈1/5 and the intensity.
a
disappears at x=0.125 (F state). The ferromagnetic
m We first consider La Ca MnO . The spin wave
state which occurs in the range 0.125≤x<0.225 shows 0.83 0.17 3
- modes obtained at T=150K, 100K and 10K along
d a quasi-metallic behavior below TC and an insulating [001]+[010]+[001] directions are reported in Fig. 1, left
n one at lower temperature[6]. There, several works have
panel. At 150K and 100K, one may distinguish two dis-
o also proposed an inhomogeneous picture using NMR[7],
persive modes labelled (1) and (3). They are very close
c
Mossbauer[8] or magnetization measurements[9].
: to previous measurements at x=0.125 reported in or-
v
In the present paper, we report a determination of thorhombic indexation[5]. This comparison allows us to
i
X spin-waves in ferromagnets La1−xCaxMnO3 at x=0.17 assign the curve (1), dispersing up to ≈18 meV, to [100]
r and0.2veryclosetothe”true”metallicstate(x≥0.225). or [010] directions, which have been shown to be equiv-
a
BelowT ,in the quasi-metallicstate,q-independent en- alent, and the curve (3), with a down-turn at q=0.25,
C
ergy levels of magnetic origin are observed in the large to the [001] or c direction. We mention that this down-
q-range. Theq-dependenceoftheirintensity,theirevolu- turn, also observed at x=0.125 and in the CAF state, is
tionwithtemperatureandmagneticappliedfieldsuggest surprisingfora F coupling. It denotes anunderlying AF
thatthey canbe ascribedto standingspinwavescharac- coupling reminiscent of the orbital ordering of LaMnO .
3
teristic of a confinement into small domains. The shape Theverynewfeatureisthegap-openinginthedispersive
and the size (a few lattice spacings) of the domains can curve (1). Within this gap lies a nearly q-independent
be estimated as well as the magnetic coupling inside the energy level, (2), at a mean value of 4.5 meV at 150K.
domains. All the observations are consistent with a pic- With decreasing temperature, all the energies increase.
ture of hole-poor and orbital-ordereddomains. At100Kandbelow, asingledispersioncurveis observed
2
x=0.17 x=0.2 x=0.2, [100]+[010]+[001]
[100] T=150K T=100K T=150K ζ=0.275 300 ζ=0.5
20 [001] (1) 20 E[100] (1) 300 1T5=02K10K T=150K
B ph
(1) 250
Energy (meV) 1105 (2) 1105 E[B00,1]½E[1B00] (2) Counts/120s 125000 ph utron counts/120s 200 (1) ph
5 (2) (3) 5 ½EB[001] (3) 100 (2) Ne 100
(3) 50 (3) (3) (2)
(0) (1)
0 0
0.00 0.25 0.05.0000.00 0.25 0.50 0.0 0.1 0.2 0.3 0.4 0.5 0 00 4 8 12 16 20 24 28
0 4 8 12 16 20 24 28
20 T=10K (1) 20 T=17K (1) Energy (meV) Energy (meV)
T=50K
T=50K
FIG. 2: Examples of energy spectra along [100]+[010]+[001]
V) 15 15 (2) at H=0, after application of a magnetic field H=2T. Left
me (2) panel: ζ=0.275 at T=150K (circles) and 210K (triangles,
y ( shifted by 100 neutron counts). Right panel: ζ=0.5. The
g
ner 10 10 modes (1), (2) and (3) correspond to spin-wave branches in-
E
dicated in Fig. 1, and ”ph” is a phonon mode.
5 5
(3)
(0) x=0.2 compound, the ratio, ≈1/4, between the energies
0 0 of the level (2) and of the zone boundary, determines a
0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5
[1+ζ,0,0]+related symmetry [1+ζ,0,0]+related symmetry size of 4 lattice spacings (16˚A) along [100] (or [010]). In
the insulating state and specially below 100K, this pic-
FIG. 1: Magnetic excitations measured along tureisnolongervalid. Wemayexplaintheoriginofgaps
[100]+[010]+[001] for x=0.17 (left panel) and x=0.2 and the modulation of the level (2) by assuming an un-
(right panel) at several temperatures. Full (empty) circles derlyingperiodicityof4a inthe(a,b)plane. Atthenew
0
correspond to modes with main (weak) intensity. In left
zoneboundariesofthesuper-cell,thedispersionisfolded
panel, the solid and broken lines are guides to the eyes,
andnewgapsoccur. Thisdescriptionofthespindynam-
and the vertical lines locate 1/8, 1/4 and 3/8 q values. In
right-upper panel, the dashed line indicates the spin-wave ics is likely related to observations in La7/8Sr1/8MnO3,
dispersion of a virtual large-size domain (see the text). where static superstructures are observed[11].
The study of La Ca MnO reveals a very interest-
0.8 0.2 3
ing evolution with x. This sample has been first stud-
forq<0.125,largergapsopenatq=1/8,1/4and3/8and ied in zero field. Preliminary observations at 17K along
the level labelled (2) appears modulated with a maxi- [001]+[010]+[001]havebeen reported[5]. Results arede-
mum close to 3/8. Measurements of spin waves along scribed with decreasing temperature. At 150K, unlike
[110]and[111]at150Kalsorevealq-independent energy the x=0.17case, a single dispersionbranch, labelled (0),
levels lying at nearly the same values in the two direc- is observed in the small q range up to q≈0.3, indicat-
tions. ing that the [100](a and b) and [001]( c) directions are
These observations call for the following comments. now equivalent and the dispersion isotropic (see Fig 1-
A q-independent energy level indicates localized excita- right upper panel). For q≥ 0.3, the magnetic intensity
tions. The existence of a gap-opening in the branch (1) issharedbetweenseveralnearlyq-independentlevelsde-
points out its interaction with level (2). This implies fined by their mean values: a broad energy level, (1),
that level (2) belongs to the same macroscopic domain, at18±1meV, likelycoupled to the loweropticalphonon
namely to the (a, b) plane, but not to the c direction. mode,alevel(2)at9±0.5meVandanoverdampedlevel,
Thelocalizedexcitationsorstandingspinwavesarecon- quasielastic. A magnetic field (H=2T) applied at 150K,
fined within these planes, exhibiting a two-dimensionnal suppresses the quasi-elastic intensity attributed to spin
(2D) character. This is consistent with observations fluctuations,andreducestheenergylinewidthofthe dis-
along [110] and [111], as indicated below. Since the dis- persionless magnetic levels. When removing the field at
persionless level appears above q ≈0.2, an approximate 150K,thespinfluctuationsremainconsiderablyreduced,
cr
size ξ=a /q ≈ 20˚A may be providedfor the domain. A andthelevelskeepthecharacteristicsobservedinapplied
0 cr
more quantitative determination of the size can be done field. A low-energy mode (3) is now defined at a mean
by considering the energy value of the q-independent value 4.5meV(see Fig 1)andthe mode (1)appearssep-
level. Following the arguments developped below for the arated from the phonon mode (24 meV), not reported
3
in Fig 1. Corresponding energy spectra are displayed in Ca 20% Ca 20%
50 50
Finicgr.ea2s,esshforwomingq=th0e.2q7-5d,etpoe0n.d5,enthceeionftethnesitiyntoefntshitey.mAodseqs 40 mmgg (PN) T=150K (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)2E(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)[B(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)10(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)0+](cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)E(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)[B00(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)1](cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)T=1(510)K 40
(2) and (3) is transferred towards the energy mode (1)
(18meV), so thatthe intensity followsthe q-dependence eV) (cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(1(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1))(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)
m
opaftera2s1iFs0tKdaibsinopveFersiTgio.Cn2(c,1ul8re0vftKe.p).aVTneehrlyi,swiinshtesehrreeoswtainnsglbilgyyh,tththdeeesscpereemcatsoreudmeosf Energy ( 2300 (cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)((cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)3(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1))(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)EB(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1) [ 1 (cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)0 0+(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)]1(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)/2E[B001] (2) 2300
the two energy levels (2) and (3) is observed whereas a (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(2(cid:0)(cid:0)(cid:1)(cid:1))(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)
quasielastic intensity (spin fluctuations) increases above 10 (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)((cid:0)(cid:0)(cid:1)(cid:1)4(cid:0)(cid:0)(cid:1)(cid:1))(cid:0)(cid:0)(cid:1)(cid:1) 10
T . Incontrast,the small-qdispersivebranch(0)renor-
C (0) (0)
malizes to zero at T . By lowering temperature in zero
C 0 0
field, the lower-energy mode (3) nearly disappears and 0.0 0.1 0.2 0.3 0.4 0.50.0 0.1 0.2 0.3 0.4 0.5
level (2) becomes more dispersed, which reduces the en- [1+ζ,ζ,0]+related symmetry [1+ζ,ζ,ζ]+related symmetry
ergy gaps (Fig. 1, lower-rightpanel).
FIG. 3: Magnetic (mg) excitations for q along
Spin wave measurements along [110]+[101]+[011]and
[110]+[101]+[011] (left panel) and [111] (right panel) at
[111] directions are reported in Fig 3 at T=150K. At
T=150K, measured with unpolarised (circles) and half-
small q, the quadratic dispersion ω=Dq2, (0), defines polarized (triangles) neutrons. Full (empty) symbols refer
an isotropic stiffness constant (D=30±1meV˚A2 becom- to modes with main (weak) intensity. The hatched area
ing 48meV˚A2 at 10K). At larger q values, the magnetic correspond to calculated levels (see the text). Dashed lines
intensity is transferred to nearly q-independent energy are guide to the eyes for phonon branches measured at the
same temperature.
levels. Along [111], a level (2) is determined at 23±1
meVandaslightlydispersiveone(1)around46±2meV.
Fig4displaysthebalanceinintensitybetweenthemodes x=0.2 [111]
(0) and (2) as q varies. Along [110]+[101]+[011],the en- ζ=0.135
tanglement between magnon and phonon branches (see 30s 600 ζζ==00..11575 T=150K
dashed lines in Fig. 3-left panel), led us to use polar- nts/ 500 ζζ==00..225
u
o
ized neutrons(PN) which allowto identify magnons and c 400
n
phonons. Several levels have been determined, more or utro 300
less dispersive. Dispersion could have been induced by Ne (2)
200
the applied magnetic field (H=2T) which aligns macro-
100
scopic domains. Excitations at energy larger than 35 (0)
meVcouldnotbeendetectedbecauseofatooweakinten- 0
0 5 10 15 20 25 30
sity. By lowering temperature, the energy levels slightly Energy (meV)
increase.
FIG. 4: Energy spectra for several ζ along [111] at 150K,
These overall observations can be explained as it fol-
showing a dispersive mode(0) and a q-independentone (2).
lows. Unlike La Ca MnO where the confined spin
0.83 0.17 3
waves have been assigned to the (a, b) plane only (2D
character), for x=0.2, the isotropy of the small-q disper-
E , for which the nearest neighbour spins fluctuate
sionsuggeststhatalldirectionsareconcerned. Thelevels B
in phase opposition, a half-period corresponds to one
are attributed to standing spin-wavesinside 3D clusters.
lattice spacing. Therefore, one expects that E is a
Let us use the energy of the propagating wave for a 3D B
multiple of E . The number of lattice spacings defining
Heisenberg model (see dotted line in Fig. 1 upper-right L
the size may be provided by the ratio E /E . For a
panel): B L
size of two lattice spacings along [100], one expects 2
E(q ,q ,q )=8S{J [1-0.5(cos(2πq )+cos(2πq ))]+
x y z a,b x y levels, with values at E =E /2 and E , corresponding
L B B
J /2[1-cos(2πq )]}, where q , q , q are related to
c z x y z to confined half-wave and full-wave respectively. Along
a, b, c directions. This expression yields relations
the other directions, if the cluster is isotropic or nearly
between J , J and the zone boundary energies
a,b c cubic, one expects the same number of levels with the
EB: E[B100]=E[B010]=8SJa,b, E[B001]=8SJc, E[B110]=2E[B100], same ratiobetweenthe energies,the energyvalues being
E[101]=E[011]=E[100]+E[001] and E[111]=2E[100]+E[001] deducedfromtheaboverelations. Weshownowthatthe
B B B B B B B
These latter relations are also valid for finite-size clus- observations support this assumption. In Fig. 1, right
ters. According to predictions[10], the cluster’s size ξ is panel,level(1),E[100]≈18meV,whichdefinestheenergy
B
related to the level with the lowest-energy value E . In ofthefirstneighborcouplingalong[100],andlevel(2)at
L
thecaseofsmallclusters,itcorrespondstoa”half-wave” half this value, are assigned respectively to the full-wave
orahalf-periodofwave. Fortheconfinedwaveofenergy and half-wave, standing along [100] (or [010] equivalent)
4
J(meV) −−0011210.......0505005 CAFJaJ,b(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)c(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)F (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)FM vJltiaoenhatfavgue,tbeJiraoslaeaspnn,nbaieds(ndrffxaeuew)Jtncrcaletad,ovpnow(deo1dpeerb2etrtr%eJdedarcdnomc(iowxpcnihm)inintteophighdsf.oetSuamhI1Ennte0od1FKJtns5yio[v-g05p1ta.K]oe5l.un50oBfeoKbrusueospsosermpibardaevntetrcaeghsrdipeenoa)aise,qnnssd-tmetihtalnh,ahetdetle1lehvl0ptoaeCeKwervmAinaafddFprtloueioe/onpemrFnts--
0.00 0.05 0.10 0.15 0.20 0.25
boundary (J =0 at x=0.125),showing a tendency to be-
x(Cxa(C)a) c
ξ∼8 Α come isotropic at x=0.225 (metallic state). This varia-
(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)bc(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)0(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1).ξ0(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)∼5<2(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)ξ0x(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)∼ <Α3(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)00.(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) 1Α(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)25(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)a(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)bcξ(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)∼(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)16(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) 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taoTitnirnrohiddbnLiesuarCitevMmeAdadpnrFsilOtaitoeats3siit”odeoahnerwosc,iilsionetom-hcfptlhmooSaeosEoerrnCo”ttuAyooogprFrhtieghwl,syietnicotalhhritfnaeooetre,ruiaactttcrahhthlieeesoffrplicSeersosecEtudtircpiecoclogotfifiuniootpgahnnlnession.[n1odgT2rotb]ihph.sieitenarAagetFls---.
fore, the cluster could consist of one Mn3+ with its first
FIG. 5: Upper panel: Variation of the magnetic coupling Mn3+ neighbourgs, the mobiles holes being confined at
values Ja,b (full symbols) and Jc (empty symbols) with x at their boundaries. The small-q dispersion (0), which de-
10K (circles) and 150K (squares). Lower panel: Schematic termines T , could be attributed to a coupling induced
C
drawing showing hole-rich (empty) and hole-poor (hatched)
by mobile-holes through the clusters. These clusters dif-
media. Increasingxfromlefttoright,itshows2DFhole-rich
fer from those found in the CAF state where the ”hole-
spin clusters, 2D F hole-poor spin clusters and isotropic 3D
poor” regioncorrespondsto the matrix andthe clusters,
hole-poor spin clusters. A half (dashed line) and a full (solid
line) standing waves are shown inside a cluster. described as ”hole-rich” platelets[4]. The general evolu-
tionwith xindirectspaceis schematicallyshowninFig.
5. Finally, a comparison with other techniques[7, 8] al-
confined in a cluster with 2 lattice spacings (ξ=8˚A). In lowstoestimatethelifetimeτ oftheseclustersforx=0.2,
10−6s<τ <10−9s, very large for the neutron probe.
the same way, level (2) at ≈9 meV and level (3) at half
this value (≈4.5 meV) are respectively assigned to the Inconclusion,thisstudyreportsaquantitativedescrip-
fullandhalfwavealongcor[001]. Level(2)corresponds tion of the precursor state of the metallic phase which
therefore to 1/2E[100] and E[001] values, superimposed occursforx≥0.225. Anevolutionoftheshapeandofthe
B B size of clusters with x is proposed, thanks to the exis-
because of twinning. From the E[100] and E[001] values,
B B tence of confined spin waves which are observed for the
J (1.12±0.1 meV) and J (0.56±0.05 meV) are
a,b c first time in small F clusters. Very interestingly, these
determined. Within the assumption of isotropic or
magnetic clustershavefeatures (size, isotropy)verysim-
nearly-cubic shape, two levels at E and E /2 are also
B B ilar to those observed at larger x in CMR compounds
determinedalongthe othersymmetrydirections. Due to
around T [2]. The present observations could be there-
C
theexperimentaluncertainty,theyareshownbyhatched
forecrucialfortheunderstandingoftheCMRproperties.
area instead of narrow lines in Fig 3. In left panel, the
TheauthorsareveryindebtedtoL.P.RegnaultandJ.
sets (1), (2) and (3), (4), belong respectively to [110]
Kuldafortheirhelpforexperimentswithfieldandpolar-
and [101]+[011] directions, unequivalent, weighted by
ized neutrons, and N. Shannon, T. Ziman, D. Khomskii
1/3 and 2/3. The agreement with experimental values
and A. M. Ole´s for helpful discussions.
is good. It supports the proposed assignation of the
levels and the assumption of isotropic shape for the
clusters. In the same way, for x=0.17, J may be
a,b
determined from E[100] (or E[110]=2E[100]) and J , from
B B B c
the difference between E[111] and E[110]. These values [1] A. Moreo et al. Science 283, 2034 (1999)
B B [2] J. W. Lynnet al. Phys. Rev.Lett. 76, 4046 (1996)
are reported in Fig. 5, upper panel, with those obtained
[3] J. M. De Teresa et al. Nature 386, 256 (1997)
at x=0.2. The small value of J is consistent with the
c [4] M. Hennion et al. Phys. Rev. Lett. 81, 1957 (1998) and
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