Melting of magnetic correlations in charge-orbital ordered La(0.5)Sr(1.5)MnO(4) : competition of ferro and antiferromagnetic states

0.74 MB·English

by  D. Senff

Melting of magnetic correlations in charge-orbital ordered La Sr MnO :
0.5 1.5 4
competition of ferro and antiferromagnetic states
D. Sen(cid:27),1 O. Schumann,1 M. Benomar,1 M. Kriener,1,2 T.
Lorenz,1 Y. Sidis,3 K. Habicht,4 P. Link,5,∗ and M. Braden1,†
1II. Physikalisches Institut, Universit(cid:228)t zu K(cid:246)ln, Z(cid:252)lpicher Str. 77, D-50937 K(cid:246)ln, Germany
2Department of Physics, Kyoto University, Kyoto 606-8502, Japan
3Laboratoire LØon Brillouin, C.E.A./C.N.R.S., F-91191 Gif-sur-Yvette Cedex, France
4Hahn-Meitner-Institut, Glienicker Str. 100, D-14109 Berlin, Germany
5 Forschungsneutronenquelle Heinz Maier-Leibnitz (FRM II),
TU M(cid:252)nchen, Lichtenbergstr. 1, D-85747 Garching, Germany
(Dated: February 4, 2008)
8 The magnetic correlations in the charge- and orbital-ordered manganite La Sr MnO have
0.5 1.5 4
0 beenstudiedbyelasticandinelasticneutronscatteringtechniques. Outofthewell-de(cid:28)nedCE-type
0 magneticstructurewiththecorrespondingmagnonsacompetitionbetweenCE-typeandferromag-
2
netic (cid:29)uctuations develops. Whereas ferromagnetic correlations are fully suppressed by the static

n CE-type order at low temperature, elastic and inelastic CE-type correlations disappear with the
a melting of the charge-orbital order at high temperature. In its charge-orbital disordered phase,
J La Sr MnO exhibitsadispersionofferromagneticcorrelationswhichremarkablyresemblesthe
0.5 1.5 4
1 magnon dispersion in ferromagnetically ordered metallic perovskite manganites.
1
PACSnumbers: 75.25.+z,75.47.Lx,75.30.Kz,75.30.Ds

]
l
e
- I. INTRODUCTION
r
t
s
Charge ordering is one of the key elements to under-
.
t
a standcolossalmagnetoresistivity(CMR)inthemangan-
m iteoxides. Thelargedropoftheelectricresistivityatthe
metal-insulatortransitioncanonlypartiallybeexplained
-
d by the Zener double-exchange mechanism.1 The larger
n part of it seems to arise from the competition between
o
ferromagnetic (FM) metallic and charge-ordered insulat-
c
ing states, and recent experimental and theoretical in-
[
vestigationsfocusonelectronicallysoftphasesandphase

1 separation scenarios.2,3,4,5,6 The metal-insulator transi-
v
tion can be considered as the stabilization of the FM
7
metallic phase over charge-ordered insulating states by
8
7 an external parameter as e.g. temperature or magnetic
1 (cid:28)eld.7,8 FIG.1: (Coloronline)Schematicrepresentationofthecharge,
. At half doping, the insulating, charge-orbital ordered orbitalandspinorderingintheCE-typearrangement,aspro-
1
0 (COO) phase appears most stable, and an ordered state posed by Goodenough.12 The orbital and the magnetic lat-
8 appears as a generic feature in the phase diagrams ticesoftheMn3+-subsystemareindicatedbythedottedand
0 of cubic manganites R A MnO (R=La or a rare dashed lines, respectively. Notice that the zigzag chains run
1−x x 3
: earth, A=Sr, Ba, Ca,...),7 as well as in those of sin- along the [110]-direction.
v
i gle and double-layered systems, as La0.5Sr1.5MnO4 and
X LaSr Mn O .9,10 In spite of its relevance for the CMR
2 2 7
r e(cid:27)ect and in spite of the enormous number of publica- (AFM) coupling between adjacent chains, referred to as
a
tions in this (cid:28)eld, the properties of the charge-ordered CE-type ordering,11 and it explains the observed struc-
state are not fully established till today. Early inves- tural and magnetic superlattice re(cid:29)ections in di(cid:27)raction
tigations on La Ca MnO by Wollan and Koehler11 experiments.13,14 More recently, an alternative model,
0.5 0.5 3
and by Goodenough12 proposed a checkerboard order- consisting of a coherent ordering of magnetic dimers,
ing of charges with sublattices of Mn3+ and Mn4+ called Zener-Polarons, has been proposed,15 which is
sites. Simultaneously, the single e orbitals on the Mn3+ fundamentally di(cid:27)erent. Whereas in the initial model
g
sites order in a stripe-like pattern, giving rise to zigzag charge and orbital ordering is located on the Mn sites,
paths with each e orbital bridging two Mn4+ neigh- the alternative model proposes the ordering of charges
g
bours with 3d3 con(cid:28)guration and an empty e level, to be located on the Mn-O-Mn bonds. The two con-
g
see Fig. 1. This orbital arrangement implies a FM or- cepts remain matter of strong controversy16,17,18,19,20,21
dering along the zigzag chains and an antiferromagnetic with the more recent work favoring the initial site-
2
centered model. In particular for La Sr MnO there observedinthemetallicFMphasesincubicmanganites.
0.5 1.5 4
is strong evidence that the bond-centered model cannot
be applied.20 One should, however, consider the possi-
bility that di(cid:27)erent manganites exhibit di(cid:27)erent types II. EXPERIMENTAL
of charge-orbital order. Furthermore, it is important to
emphasize that the site-centered model of charge and La Sr MnO crystallizesinatetragonalstructureof
0.5 1.5 4
orbital ordering is only schematic. Di(cid:27)erent crystallo- space-groupsymmetryI4/mmmwithroom-temperature
graphic studies10,18,22,23,24,25 (cid:28)nd structural distortions lattice constants a = 3.86¯ and c = 12.42¯.40 For most
in the charge-ordered phase which are far smaller than
of the neutron scattering experiments we used the same
whatisexpectedforafullintegerorderingintoMn3+and crystal as for the analysis of the spin-wave dispersion.20
Mn4+ valencies. Neverthelesswewillusethroughoutthis
Thethermodynamicmeasurementandsomepartsofthe
paper this Mn3+/Mn4+ nomenclature for clarity.
neutron scattering experiments were done with a dif-
Theoriginofthecharge-orderedstateisalsounderde- ferent sample. All crystals were grown using the same
bate,anddi(cid:27)erenttheoreticalstudiesfocusonverydi(cid:27)er- (cid:29)oating-zone technique as described in Ref. 41. Elas-
ent aspects. It has been shown, that the COO state can tic neutron scattering experiments were performed at
bestabilizedprimarilybycooperativeJahn-Tellerdistor- the thermal double-axis di(cid:27)ractometer 3T.1 and at the
tions. In this scenario the magnetic ordering of the CE triple-axis spectrometer G4.3, both installed at the Lab-
type appears as a secondary e(cid:27)ect.26,27,28 On the other oratoire LØon Brillouin (LLB) in Saclay. Selected scans
hand,ithasbeenargued,thatbasedonanisotropicmag- measuredatthehigh-(cid:29)uxinstrument3T.1wererepeated
neticexchangeinteractionstheCOOcanbestabilizedby with the same neutron energy E=14.7meV at the G4.3
purelyelectronice(cid:27)ects.29,30 InthissensetheCOOstate spectrometer with an energy resolution ∆E (cid:46) 0.6meV
isofmagneticorigin,whichnaturallyexplainsitsmelting to estimate the in(cid:29)uence of slow magnetic (cid:29)uctuations.
in magnetic (cid:28)elds.29,31,32 The double-axis spectrometer integrates over a sizeable
Thesingle-layeredmaterialLa Sr MnO isparticu- energy interval, but all data taken on both instruments
0.5 1.5 4
larlywellsuitedfortheexperimentalinvestigationofthe agree quantitatively very well, suggesting that the dif-
propertiesoftheCOOstate. Chargeandorbitalordering fuse magnetic scattering is associated with time scales
occursinthiscompoundbelowT =220Kandhasbeen longer than ∼10−11sec. Data using polarized neutrons
CO
investigated by various techniques.9,33,34,35,36 Magnetic were acquired at the FLEX spectrometer at the Hahn-
ordering of the CE type occurs below T =110K.9 Com- Meitner Institut (HMI) in Berlin. Inelastic neutron data
N
paredtotheperovskitemanganites,theCOOstateisex- were collected on the spectrometers 1T, 2T and 4F, in-
ceptionally stable in La Sr MnO and only very high stalled at the thermal and cold sources at the LLB, and
0.5 1.5 4
(cid:28)elds of the order of 30T can melt the ordered state im- on the cold instrument PANDA at the Forschungsreak-
plyingnegativemagnetoresistancee(cid:27)ects.37 Goodmetal- tor FRM II in Munich. At all instruments the (002)
lic properties are, however, never achieved in the single Bragg re(cid:29)ection of pyrolytic graphite (PG) was used as
layered manganites La Sr MnO , neither by mag- a monochromator and to analyze the energy of the scat-
1−x 1+x 4
netic (cid:28)eld nor by doping.38,39 tered neutrons. The energy on the analyzer side was
always (cid:28)xed to E = 14.7meV at the thermal instru-
In a recent work we have studied the mag- f
ments, and typically to E = 4.66meV on the cold ma-
netic excitation spectrum of the CE-type ordering in f
La Sr MnO at low temperatures.20 The analysis of chines. To suppress spurious contaminations by second
0.5 1.5 4
harmonic neutrons an appropriate (cid:28)lter, either PG or
thespin-wavedispersionisfullyconsistentwiththeclas-
sicalchargeandorbital-ordermodel12 andunderlinesthe cooled Beryllium, was mounted in front of the analyzer.
In most of the measurements, the sample was mounted
dominant character of the FM intrachain interaction:
withthetetragonalcaxisverticaltothescatteringplane,
The magnetic structure has to be regarded as a weak
so that scattering vectors (hk0) were accessible. Some
AFM coupling of stable FM zigzag elements. In this ar-
datawerecollectedinadi(cid:27)erentscatteringplanede(cid:28)ned
ticle we address the thermal evolution of the CE mag-
bythe[110]and[001]directionsofthetetragonalstruc-
netic ground state and report on the development of the
ture.
static and dynamic magnetic correlations as studied in
Speci(cid:28)c-heat measurements were carried out using a
neutron scattering experiments and in macroscopic mea-
home-buildcalorimeterworkingwitha(cid:16)continuousheat-
surements: The magnons of the static CE order trans-
ing(cid:17) method. Magnetizationwasmeasuredinacommer-
form into anisotropic short-range magnetic correlations
remaining clearly observable for T < T < T . Here cialvibratingsamplemagnetometerandelectricresistiv-
N CO
ity by standard four-contact method.
magnetic correlations can be described by a loose AFM
coupling of FM zigzag-chain fragments. These CE-type
(cid:29)uctuations compete with isotropic ferromagnetic corre-
lations between T and T , and they fully disappear III. RESULTS
N CO
upon melting the COO state above T . Instead, in the
CO
charge- and orbital-disordered phase above T we (cid:28)nd Before starting the discussion of our results we illus-
CO
purelyFMcorrelations,whichremarkablyresemblethose trate the di(cid:27)erent structural and magnetic superstruc-
3
tures of the COO state with the aid of Fig. 1. Below
T thecheckerboardarrangementofthenominalMn3+ Q Px Py Pz Imag/Istruc
CO
and Mn4+√sites√doubles the structural unit cell to lattice (0.750.250) SF 14511 1087 14619
spacings 2a× 2awitha∼3.8¯thelatticeconstantof NSF 796 14179 848 1.00/0.00
the original tetragonal cell. The concomitant orbital or- (0.750.750) SF 1625 161 1624
dering reduces the symmetry and the nuclear√lattice be- NSF 208 1659 264 0.94/0.06
comes ortho√rhombic with lattice constants 2 2a along
(1.250.250) SF 3013 475 3194
[110] and 2a along [1-10]. The ordering of charges
NSF 486 3085 498 0.91/0.09
and orbitals is related to superstructure re(cid:29)ections with
k =±(1 10)andk =±(1 10)indi(cid:27)ractionexper- (1.750.250) SF 8550 4475 7508
CO 2 2 OO 4 4
iments, respectively. We emphasize once more that the NSF 72665 76331 72745 0.05/0.95
interpretation of the superstructure in terms of integer
(0.510) SF 12999 1200 13091
chargeandorbitalorderingisonlyqualitative. Theanal-
NSF 797 12653 734 1.00/0.00
ysisoftherealstructuraldistortionrevealsmuchsmaller
e(cid:27)ects than expected for an integer charge ordering and (200) SF 2486 1903 1800
stillneedsquantitativestudiesandanalyzes. Considering NSF 30032 30846 31304 0.00/1.00
the magnetic ordering, the CE-type structure can be di-
videdintotwosublatticesdistinguishingbetweenthetwo
magnetic species. For the Mn3+ ions the m√agnetic√unit TvaAriBoLusEmI:aRgneseutilctsaonfdthsetrluocntguirtauldBinraalgpgoplaorsiiztaiotinosnaatnTaly=sis5fKor.
cell is of the same size as the nuclear one, 2a×2 2a,
For each Q position the observed neutron intensity is shown
but it is rotated by 90◦ with the long axis along [1-10]
and propagation vectors kMn3+ = ±(41−140). There- fPor||Qthe(xd)i,(cid:27)Per⊥enQt cahnodicewsitohfinth(ey)n,euantrdonPq⊥uQantainzdatpioenrpaexnisdiPcuj-,
fore, the Mn3+ spins and the the orbital lattice con- lar to the scattering plane (z), and the spin (cid:29)ipper on (SF)
tribute at di(cid:27)erent Q positions, e.g. there is a magnetic or o(cid:27) (NSF). The last column gives the calculated decompo-
contribution at Q = (0.750.250) ≡ (0.25−0.250), but sition of the observed intensity into magnetic and structural
not at Q = (0.250.250), where the orbital lattice con- components.
tributes. The Mn4+ spins contribute to neither of these
positions, but to positions indexed by k = ±(100)
Mn4+ 2
and ±(010). The full magnetic cell has to be described
2 √
in a pseudocubic lattice with 2 2a along [110] and [1-
10], as shown in Fig. 1. However, the orthorhombic dis-
tortion of the tetragonal symmetry induces a twinning structurere(cid:29)ectionsatT =5KdeterminedattheFLEX
due to the orbital ordering in a sample crystal, as the spectrometer for three di(cid:27)erent choices of the neutron
zigzag chains can either run along [110] (orientation I) quantization axis, P||Q (x), P⊥Q and within the ab
oralong[1-10](orientationII),andthearrangementde- plane (y), and P⊥Q and perpendicular to the ab plane
scribed above is superimposed by the same, but rotated (z). Inaddition tothequarter-indexed re(cid:29)ections, Table
by 90◦. Both twin orientations contribute equally strong I also includes the half-indexed re(cid:29)ection Q = (0.510)
inoursamples,butfortheanalysiswewillalwaysreferto and the integer-indexed re(cid:29)ection Q=(200). These re-
the orientation I depicted in Fig. 1. We emphasize that (cid:29)ections are entirely magnetic, respectively nuclear, and
the twinning due to the COO orthorhombic distortion serveasreferencepositionsfortheanalysisofthequarter-
is the only one occuring in La0.5Sr1.5MnO4, whereas the indexed re(cid:29)ections, providing an estimate of the experi-
octahedrontiltandrotationdistortionsintheperovskite mental accuracy with (cid:29)ipping ratios FR=ISF:INSF of the
manganatesimplyacomplextwinningwithuptotwelve order of 15. Inspecting the distribution of magnetic in-
superposed domain orientations. tensityatQ=(0.510)inthevariousP channelsimme-
j
In a scattering experiment the superposition of both diatelyclari(cid:28)es,thatthemagneticmomentsarecon(cid:28)ned
twin orientations mixes structural and magnetic contri- to the ab planes; a canting of the moments out of the
butionsataquarter-indexedposition. Themagneticcon- planes must be less than ∼5◦, in good agreement with
tribution of orientation I is superimposed by the orbital other estimations.9 Knowing the experimentally deter-
contributionoforientationIIandviceversa. Bothcontri- minedFR’s,thescatteringobservedataquarter-indexed
butions can, however, be well separated using polarized positioncanbedecomposedintomagneticandstructural
neutrons. In the classical polarization analysis spin-(cid:29)ip contributions, see the last column of Table I. With in-
scattering(SF)isalwaysmagnetic,whereasnonspin-(cid:29)ip creasing |Q| the magnetic scattering is suppressed fol-
scattering (NSF) can be either magnetic or structural: lowingthesquareoftheformfactorand,simultaneously,
Magnetic moments aligned perpendicular to both, the the structural component is enhanced. For small |Q|,
scattering vector Q and the neutron’s polarization P, the observed intensity is, however, entirely of magnetic
contributetotheSFchannel, thosealignedparalleltoP origin, and in the following we may associate any scat-
to the NSF channel.42 Table I summarizes the results of teringappearingaroundQ=(0.750.250)withmagnetic
the longitudinal polarization analysis of selected super- correlations.
4
A. Elastic magnetic scattering
The thermal evolution of the static magnetic correla-
tions around Q = (0.750.250) has been determined in
the elastic neutron scattering experiments at the spec-
trometers 3T.1 and G4.3 at the LLB. Within the es-
timated experimental energy resolution "static" refers
to magnetic correlations on a time scale longer than
∼10−11sec. In Fig. 2 we show mappings of the recip-
rocal space around the magnetic CE position Q =
CE
(0.750.250) including the FM position Q = (100)
FM
forfourdi(cid:27)erenttemperatures,aboveT inthecharge-
CO
andorbital-disorderedphaseat250K,intheCOOphase
above T at 200K and at 150K, and below T in the
N N
CE-ordered state at 100K. All four maps exhibit strong
magnetic response, and the comparison of the di(cid:27)erent
temperaturesdirectlyrevealsdrasticchangesinthechar-
acter of the magnetic correlations.
In the charge- and orbital-disordered phase at T = FIG. 2: (Color online) Intensity mappings of the elastic
250K, Fig. 2a, the magnetic scattering appears as a magnetic scattering around the magnetic CE-type position
broad and isotropic feature centered around QFM = Qmag = (0.750.250) and around the two-dimensional FM
(100). In the K NiF type structure corresponding to zone center (100) at various temperatures (a) above the
2 4
space group I4/mmm, (100) is not a three-dimensional charge-orbital ordering at T = 250K, (b,c) below TCO but
Bragg point due to the body-centered stacking of the above the NØel transition at T = 200K, and T = 150K,
and (d) below the AFM transition at T = 100K. All maps
MnO layers. But when neglecting any magnetic inter-
2
were calculated from a grid of 41 × 41 data points with
layer coupling, i.e. analyzing magnetic correlations in a
single layer, any (10q ) is a two-dimensional Bragg po- ∆qh = ∆qk = 0.0125. The two arrows in (c) denote the
l directions of the scans investigated in more detail, scan (1)
sition sensing FM in-plane correlations. From the width
senses the stacking of zigzag fragments in the CE phase and
of the signal in the (hk0) plane a nearly isotropic in-
scan (2) their length.
plane correlation length ξ ≈ 8¯ can be estimated for
iso
ferromagnetic clusters, see below. From the Q depen-
l
dence of the FM signal at (00Q ) studied on a slightly
l
under-doped sample43, we may deduce the fully two- to the chains, i.e. the stacking of the FM zigzag chains
within the MnO planes. In contrast, scan 2 determines
dimensional nature of the FM scattering and that the 2
the correlations parallel to the chains.
moments are aligned predominantly within the planes in
accordance with the anisotropy of the magnetic suscep- Let us start with the discussion of the thermal evolu-
tibility. tion of the magnetic scattering along scan 1, see Fig. 3.
With the transition into the COO phase the magnetic At the highest temperature investigated, T = 250K,
correlations abruptly change. At T = 200K, Fig. 2b, the spectrum consists of a broad, Lorentzian-shaped fea-
the FM signal around QFM has drastically lost intensity, ture centered at QFM = (100), as is already evident
while, simultaneously, magnetic intensity is increased in Fig. 2a. This signal is due to ferromagnetic planar
alongthepath(100)→(0.750.250). Uponfurthercool- correlations of limited correlation length. With decreas-
ing, intensity is transferred from Q to the quarter- ingtemperaturethesignalstaysroughlyuna(cid:27)ected,until
FM
indexed position QCE = (0.750.250) and at T = 150K charge and orbital ordering sets in at TCO ≈ 220K. Be-
two separate features are well distinguished in the map- low TCO the signal at QFM looses spectral weight and
ping, Fig. 2c. The transition into the CE phase at T additional weak and very broad features become appar-
N
(cid:28)nally completely suppresses the FM response and at ent around (1∓ε±ε0). The latter features continuously
100Kallmagneticscatteringiscenteredatthemagnetic sharpen,gaininintensityandshiftoutwarduntilthey(cid:28)-
CE-type Bragg re(cid:29)ection Q , Fig. 2d. nallylockintothecommensurateCE-typepositionswith
CE
To further analyze the competition between FM- and ε=±0.25 close to TN ≈110K. Within the magnetically
CE-type correlations we studied the temperature depen- ordered phase below TN, we do not (cid:28)nd any evidence for
dence along the two lines depicted in Fig. 2c in more FM correlations anymore and the AFM CE-type re(cid:29)ec-
detail. Scan 1 runs along [1-10] and connects Q and tionsbecomesharpandresolutionlimitedatlowtemper-
FM
Q , while scan 2 is oriented perpendicular along [110] ature, Fig. 3b.
CE
andcrossesscan1atQ . AsaroundQ onlythemag- The thermal evolution along scan 2, i.e. along [110]
CE CE
netic scattering of the twin orientation with the zigzag and parallel to the zigzag chains, is shown in Fig. 4. At
chains running along [110] contributes (orientation I), T = 250K no signal is observable at Q . However,
CE
scan 1 probes the magnetic correlations perpendicular below the COO transition a magnetic signal emerges,
5
So far we have only discussed the magnetic correla-
tions within the MnO layers. In Fig. 5 we show raw-
2
data scans along Q = (0.250.25q ) for various temper-
l
atures below T aiming at the magnetic correlations
CO
along [001]. In contrast to the in-plane correlations, the
scansalong[001]arenotstructuredabove T . TheCE-
N
type magnetic correlations are entirely two-dimensional
for T > T . Below the magnetic phase transition at T
N N
a well de(cid:28)ned structure develops along q , and two dis-
l
tinctsetsofre(cid:29)ectionscenteredaroundhalf-andinteger-
indexed q values are detected. Both types of re(cid:29)ections
l
can be associated with a di(cid:27)erent stacking along the c
axis, and the observed distribution of intensity with the
half-indexed q values dominating agrees well with for-
l
mer observations.9,39 Along [001] the pro(cid:28)le of the re-
(cid:29)ections is always signi(cid:28)cantly broader than the exper-
imental resolution, indicating a (cid:28)nite correlation length
perpendicular to the layers of about 50¯ even at lowest
temperatures.
Foraquantitativeanalysisofthedi(cid:27)usemagneticscat-
teringwemodeledallspectraassumingLorentzianor,at
lower temperatures, Gaussian line shapes for the di(cid:27)er-
ent contributions. The integrated intensity of the re(cid:29)ec-
tion then directly determines the square of the magnetic
order parameter, and the width, corrected for resolution
e(cid:27)ects,isproportionaltotheinverseofthemagneticcor-
relation length. The results of this analysis are summa-
rized in Fig. 6. Structural superlattice re(cid:29)ections prob-
ing the order parameter of the orbital and the charge
ordering, which set the frame for the discussion of the
magnetic correlations, appear below T = 221(1)K, in
CO
good agreement with the literature.33,35,36 The temper-
FIG.3: (Coloronline)Temperaturedependenceoftheelastic ature dependencies of the intensity of the FM scatter-
magnetic intensity along scan 1, perpendicular to the zigzag
chains. (a) Contour plot derived from a grid of data with
∆T =10Kand∆qk =0.0052aπ. (b)Representativeraw-data
scans underlying the contour plot. For clarity, the data are
successively shifted vertically by 300counts. The inset gives
the pro(cid:28)le of the magnetic Bragg re(cid:29)ection at low tempera-
tures, T=2.5K. Lines correspond to (cid:28)ts as described in the
text. In all data a minor contamination by second harmonic
neutrons centered at Q=(100) is subtracted. The di(cid:27)erent
scattering of the two CE-type re(cid:29)ections arises from the Mn
form-factor and geometry conditions.
which is easily separated from the background level al-
ready at 220K, i.e. more than 100K above T . Note,
N
that there is no structural component in the scattering
at these |Q| values, see above. The magnetic signal at
Q rapidly sharpens and increases in intensity, re(cid:29)ect-
CE
ing the transfer of spectral weight from Q along the
FM FIG.4: (Coloronline)Temperaturedependenceoftheelastic
path (100)→(0.750.250) to Q . The magnetic phase
CE magneticintensityalongscan2,paralleltothezigzagchains,
transition at T is evidenced by the change of the line
N at selected temperatures (a) above and (b) below the NØel
shape,below110Kthepro(cid:28)lechangesfromaLorentzian transition at T = 110K. Note that for the scans at 150K
N
into a Gaussian with the width determined by the ex- and 130K the scale on the ordinate is the same in both pan-
perimental resolution. The intensity of the re(cid:29)ection in- els. In all data a common background is subtracted. Lines
creases monotonically down to the lowest temperature correspondto(cid:28)tswitheitherLorentziansorGaussiansasdis-
investigated, T =3K. cussed in the text.
6
FIG. 5: (a) (Color online) Raw-data scans along the line
(0.250.25ql) for various temperatures below TCO. Gray-
shaded areas mark spurious contributions by the scattering
from Aluminium. (b) Raw-data scans along [001] centered
around ql = 2.5 for various temperatures close to TN. Lines
denote (cid:28)ts with Lorentzians.
ing at Q = (100) and that of the CE-type re(cid:29)ection
FM
Q = (0.750.250) as determined from the scans pre-
CE
FIG. 6: Summary of the results of the analysis of the elastic
sentedinFig.3andFig.4areshowninFig.6a(cid:21)c. With
magnetic scattering showing the temperature dependence of
the transition into the COO phase at T the intensity
CO (a)theintensityobservedattheFMpositionQ=(100),and
of the FM correlations decreases and vanishes close to
(b,c) at the AFM position Q=(0.750.250) on a linear, and
TN. The in-plane correlation length of the FM signal is logarithmic scale, (d) of the determined correlation length ξ
isotropic and temperature independent, ξiso ≈ 8¯. Be- in a direction parallel to the chains, ξ||, perpendicular to the
low TN no FM signal can be detected anymore in our chains,andwithintheabplane,ξ⊥,andalongthetetragonal
neutron scattering experiments. In contrast, the AFM axis, ξc, and (e) of the position of the AFM-signal along the
correlations of the CE type emerge with the transition line Q=(1∓ε±ε0).
into the COO phase and compete with the FM phases
between T and T . Even in this pure half-doped ma-
CO N
terial the transition between the high-temperature FM
exhibitapronouncedanisotropyandtemperaturedepen-
correlations and the CE-type ordered state seems to oc- dence. Both in-plane correlation lengths, ξ parallel and
cur via a microscopic phase separation.5,6 We may not ξ perpendicular to the zigzag chains, rap||idly increase
⊥
fully exclude that the coexistence of CE-type and FM
and (cid:28)nally diverge as the temperature decreases towards
scattering is caused by a canting or a rotation of the T ≈110K. For T >T ξ is always larger than ξ , in-
N N || ⊥
spins within a single magnetic cluster, but the di(cid:27)erent
dicating that the intrachain correlations are much better
Qshapeofthescatteringaswellasthedi(cid:27)erenttemper- de(cid:28)ned than the interchain correlations. Close to T the
N
ature dependencies of the associated correlation lengths ratio between ξ and ξ is most pronounced attaining
|| ⊥
render such an explanation unlikely. a factor of ∼4, and ξ diverges at slightly higher tem-
||
The observed peak-height of the magnetic scattering peratures than ξ . The magnetic transition at T has
⊥ N
at the CE-type Bragg re(cid:29)ection does not exhibit a clear to be interpreted as the coherent AFM ordering of pre-
anomaly at T and the thermal evolution appears con- formed FM zigzag chains. The ratio of ξ /ξ perfectly
N || ⊥
tinuous in the entire temperature regime below 220K, re(cid:29)ects the ratio of the magnetic interaction parameters
although the major intensity increase is found below in the CE phase at low temperature, where the interac-
T . The temperature dependence of the magnetic re- tion along the chain is by far dominating20. The out-of-
N
(cid:29)ections, for example (0.5,1,0), sensing the magnetic or- plane correlation length for the CE ordering, ξ , is also
c
der of the Mn4+ sites perfectly scales with that of the included in Fig. 6d. In contrast to the in-plane correla-
quarter-indexed ones sensing the Mn3+ order con(cid:28)rming tions,ξ remains(cid:28)niteatlowesttemperatures,ξ ≈50¯,
c c
the close coupling of the two magnetic sublattices form- and the inter-layer correlation rapidly disappears above
ing the complex CE-type magnetic ordering. A clear in- T . Finally, Fig. 6e displays the evolution of the AFM
N
dication for the magnetic phase transition at T is, how- peak position along the line (1∓ε±ε0). The incommen-
N
ever, seen in the behavior of the magnetic correlation surability ε directly re(cid:29)ects the AFM coupling between
lengths, Fig. 6d. The AFM correlations of the CE type adjacentormoredistantzigzagchains. Withtheonsetof
7
themagneticcorrelationsnearT ,εincreasesmonoton- for H⊥ab and H||ab. This behavior may be ascribed
CO
icallyandlocksslightlyaboveT intothecommensurate to the FM preordered zigzag chain fragments with con-
N
value ε = 0.25. Hence, the modulation wavelength per- siderable AFM coupling already above T . At the NØel
N
pendicular to the zigzag chains decreases upon cooling transitiononlythestackingofthezigzagchainsbecomes
until at T adjacent chains couple antiferromagnetically. better de(cid:28)ned. In this sense the AFM transition may
N
The asymmetric shape of the CE-type di(cid:27)use scattering be considered as an order disorder one.32 The ratio be-
close to T , see e.g. Fig. 3b, has to be ascribed to the tween M and M agrees with the expectations for an
N ⊥ ||
asymmetric distribution of ε ≤ 0.25: The stacking of AFM order of moments aligned within the ab planes
the zigzag chains cannot occur with a repetition√scheme due to an easy-plane anisotropy. Below T ≈ 135K M⊥
shorterthannearest-neighborchains, whichis2 2acor- is larger than M , whereas the opposite is observed in
||
responding to ε=0.25. the paramagnetic phase. At low temperatures, below
Weemphasizethatthewellde(cid:28)ned,three-dimensional T ≈ 50K, both magnetization components M⊥ and M||
magnetic CE-type order together with the full suppres- exhibit a pronounced Curie-like upturn. Usually, a low
sionoftheFMresponseisreminiscentofthehighquality temperature upturn in the magnetization is associated
of our crystal. An earlier sample of La Sr MnO 43 as with sample-dependent impurities, but in the case of
0.5 1.5 4
well as the crystal used in Ref. 9 exhibit signi(cid:28)cantly re- La Sr MnO it might be a generic feature as it is ob-
0.5 1.5 4
duced CE-type correlation lengths. The high quality of servedinvariousstudiesusingdi(cid:27)erentsamplecrystals.38
thesampleisfurtherdocumentedbyaclearspeci(cid:28)c-heat
anomaly observed at T , see below. Themostprominentfeatureconcernsthesuddenmag-
CO
netization drop at the COO transition. As pointed out
by Moritomo et al., the singular behavior at T can
CO
be attributed to the quenching of the double-exchange
B. Thermodynamic properties
interaction with the localization of the e electrons into
g
the charge-ordered state,38 which is supported by ESR
Theunusualevolutionofthemagneticstatewithstatic measurements.44 The neutron analysis, however, clearly
short-range correlations appearing 100K above T also
N shows, that the FM correlations are not just reduced at
a(cid:27)ects the thermodynamic quantities. In Fig. 7 we show
T , but they become replaced by the AFM CE-type
CO
the temperature dependence of the electric resistivity
(cid:29)uctuations even well above the NØel transition. Due to
ρ (T) along the planes, the speci(cid:28)c heat c (T), and the
ab p the distinct magnetic symmetries, the magnetic transi-
macroscopic dc magnetization M (T) and M (T) for a
⊥ || tion from a FM state to the AFM CE-type order must
(cid:28)eld H = 1T applied perpendicular and parallel to the
be of (cid:28)rst order allowing for phase coexistence.
MnO layers, respectively. All three quantities show a
2
well-de(cid:28)ned anomaly at T , but none around T . The
CO N
electricresistivityρ exhibitsinsulatingbehaviorwitha
ab
signi(cid:28)cant jump-like increase at T re(cid:29)ecting the real-
CO
space ordering of the charge carriers.38 Note, that we
(cid:28)nd no hysteresis in the temperature dependence of the
resistivity at T . The speci(cid:28)c heat displays a pro-
CO
nounced anomaly at the same temperature document-
ing the well-de(cid:28)ned character of the COO transition in
our La Sr MnO crystal. Below T , however, the
0.5 1.5 4 CO
speci(cid:28)cheatseemstobedeterminedbyphononiccontri-
butions, and it is di(cid:30)cult to detect a clear signature for
an additional release of entropy around the magnetic or-
dering, which, however, is consistent with the formation
of short-range magnetic correlations well above T .
N
The macroscopic magnetization M(T), Fig. 7c, is di-
rectly correlated with the neutron scattering results pre-
sented above. For T > T , M(T) increases linearly
CO
upon cooling and M is always smaller than M , as
⊥ ||
there is an easy plane anisotropy parallel to the MnO
2
layers. The magnetization reaches a maximum slightly
above T , at ≈ 240K, and it is strongly suppressed
CO
at the transition into the COO phase. Upon further
cooling M(T) continues to decrease down to T = 90K FIG. 7: (a) Temperature dependence of the in-plane electric
and it roughly scales with the temperature dependence resistivity ρab, (b) the speci(cid:28)c heat cp, and (c) the macro-
of the magnetic neutron intensity observed at Q . Re- scopic magnetization for a (cid:28)eld H =1T applied parallel and
FM
markably, there is no well de(cid:28)ned signature of the NØel perpendicular to the ab planes. Vertical grey lines mark TCO
transition, as M(T) varies continuously across T , both andTN asdeterminedintheneutronscatteringexperiments.
N
8
C. Dynamic magnetic correlations
Sofarwehaveonlyconsideredthethermalevolutionof
thestaticmagneticcorrelations. Theanisotropiccharac-
ter of the AFM correlation and the competition between
AFM and FM interactions should, however, also signif-
icantly in(cid:29)uence the dynamic magnetic properties. The
developmentofthemagneticcorrelationsat(cid:28)niteenergy
transferhasbeenstudiedintheexperimentsatthespec-
trometers 4F, 1T, 2T, and PANDA.
In our previous work20 we established the low-energy
part of the magnetic excitations in the CE-type ordered
statewhichcanbewelldescribedbyspin-wavetheory. At
low temperatures, the magnon dispersion is anisotropic
FIG. 8: (Color online) (a) Energy scan at the AFM zone
with a steep dispersion along the zigzag chains, re(cid:29)ect-
center Q = (0.750.750) at T = [4]K, and (b) at di(cid:27)erent
ing the dominant FM interaction along this direction.20 positions perpendicular to the propagation of the chains at
The pronounced magnon anisotropy can be taken as a Q = (0.75+qh0.75-qh0). (c) ql dependence of the magnon
strongindicationagainstthebond-centereddimermodel, signaltakenwithadi(cid:27)erentexperimentalsetup. Linesdenote
whereas it is naturally described within the CE-type or- (cid:28)ts to the data. See text for details.
bital and magnetic model.
In the CE-ordered phase at T = 5K the spin-wave
spectrum is gaped at the antiferromagnetic zone center, cal. To take the di(cid:27)erent experimental conditions into
q =0,seeFig.8a,andtwodistinctmagnoncontributions account and to resolve the two di(cid:27)erent magnon contri-
canberesolved. ThedegeneracyofthetwoAFMmagnon butions in all scans, we convoluted the four-dimensional
branches seems to be removed due to anisotropy terms. resolutionfunctionwiththedispersionsurfaceasderived
As already seen in the high-temperature behaviour of inRef.20usingtheResLib-code.46 Ina(cid:28)rststepweeval-
M(T), La Sr MnO exhibits an easy-plane single-ion uated the data taken with [001] vertical and re(cid:28)ned the
0.5 1.5 4
anisotropy above the COO transition. Due to the or- magnonenergiesatq =0yieldingω1 =0.97(2)meVand
thorhombic symmetry in the COO phase, the easy-plane ω2 = 1.97(4)meV, respectively. Using these values as a
anisotropy45 musttransformintoaneasy-axissymmetry, starting point we modeled the data taken in the second
whichishiddenbythetwinninginthemacroscopicmea- setup. As a (cid:28)rst result, all data with di(cid:27)erent ql values
surements. The magnetic anisotropy, however, is visible can simultaneously be described using the same magnon
intheexcitationspectraintheformoftheobservedzone- frequencies. Thereisnomeasurablespin-wavedispersion
center gap and splitting. At the antiferromagnetic zone vertical to the MnO layers. As a second (cid:28)t parameter
2
center we (cid:28)nd two magnon excitations around 1.0meV we modeled the intensity distribution at the various ql
and2.0meV,Fig.8a. Thesplittingofthemodesis,how- positions. With increasing |Q|, the signal ω1 follows the
ever, restricted to the zone center, and for (cid:28)nite momen- square of the magnetic formfactor, while the signal ω2
tum |q| both modes merge rapidly into a single excita- is additionally suppressed. Assuming the mode ω2 to be
tion, Fig. 8b. entirelypolarizedalongc,we(cid:28)ndagoodagreementwith
Toprobethecharacterofthetwozone-centermodeswe thedata,andthesplittingofthemagnonfrequenciescan
studiedtheirq dependence, Fig.8c. Asonlythecompo- befullyascribedtodi(cid:27)erentmagneticanisotropies: Fluc-
l
nentofthemagnetizationperpendiculartothescattering tuationswithintheMnO2 layersaremorefavorablethan
vectorcontributesinneutronscattering,increasingq will those along the c axis as it is expected. The sizeable gap
l
suppress a (cid:29)uctuation polarized along the c axis while a associated with the in-plane anisotropy, ω1=0.97meV is
mode (cid:29)uctuating perpendicular to c will remain less af- remarkable as it documents that magnetic moments are
fected or even increase in intensity. For this purpose we also pinned through the orbital anisotropy of the zigzag
usedascatteringplanede(cid:28)nedby[110]/[001],wherethe chains.
steep[1-10]branchofthedispersionpointsalongthever- Todeterminethetemperaturedependenceofthemag-
tical axis. As the vertical Q resolution is low on a focus- netic (cid:29)uctuations we scanned the excitations around
ingtriple-axisspectrometer,thiscon(cid:28)gurationintegrates Q = (0.75−0.750) and Q = (100) in di(cid:27)erent di-
CE FM
overasizeablepartoftheverticaldispersionstronglyaf- rections at a constant energy of E = 2.75meV. These
fecting the shape of the measured signal. In the scans scans were performed at 10K and 100K in the CE or-
taken using this con(cid:28)guration, Fig. 8c, the two magnon dered phase, in the COO phase above T at [130]K and
N
contributionsappearonlyasaratherbroadfeaturewhile at200K,andinthedisorderedphaseat250K,seeFig.9.
theycanbeeasilyseparatedwiththeusualcon(cid:28)guration First, we discuss the thermal evolution around Q . At
CE
with c vertical to the scattering plane. Due to the weak T = 10K and along [110], i.e. parallel to the zigzag
interlayercouplingthedispersionalongcisnegligibleand chains, the spectrum can be decomposed into the two
hence the integration is very e(cid:30)cient with [001] verti- magnoncontributionscenteredatQ +q andQ −q,
CE CE
9
sity is fully smeared out, and at T = 200K we do not
(cid:28)nd any correlations which can be associated with the
inter-zigzagcoupling, whereas, inthedirectionalongthe
chains the inelastic intensity is still well centered around
Q . The inelastic CE-type magnetic correlations are
CE
thus turning one-dimensional in character between T
N
and T : Only the magnetic coupling within a zigzag
CO
fragment remains (cid:28)nite close to T . Above the charge-
CO
orbital ordering the magnetic (cid:29)uctuations reminiscent of
the CE-type magnetic order are completely suppressed.
AroundtheFMQpointwe(cid:28)ndafundamentallydi(cid:27)er-
entbehaviorofthemagnetic(cid:29)uctuations. Q =(100)
FM
is also a Bragg position of the CE-type magnetic struc-
ture, and therefore inelastic neutron scattering may de-
tect the CE-type spin-wave modes also around (100)
but with a strongly reduced structure factor, see Fig. 3
in Ref. 20. However, the scattering around (100) does
not evolve like the CE-order parameter and the associ-
ated(cid:29)uctuationsdescribedabove. Theinelasticintensity
close to (100) remains well-de(cid:28)ned over the entire tem-
perature range up to highest temperatures, see Fig. 9c.
AtT =250Kthedi(cid:27)erencesbetweenthespectraaround
the di(cid:27)erent Q positions are most evident: Around Q
CE
no inelastic signal can be detected anymore, whereas the
dynamiccorrelationsaroundQ areclearlystructured.
FM
These(cid:29)uctuationsareentirelyFMincharacter(cid:21)thereis
FIG. 9: (Color online) (upper panel) Q scans at a (cid:28)nite en-
ergy E = 2.75meV for di(cid:27)erent temperatures across the CE no evidence for CE-type correlations left at this temper-
position(0.75−0.750)inadirection(a)paralleltothezigzag ature(cid:21)andtheyhavetobeassociatedwiththeisotropic
chains, [110], and (b) perpendicular to the chains along [1- FM clusters revealed in the di(cid:27)use magnetic scattering.
10]. (lower panel) Raw-data scans tracking (c) the tempera- AsaroundQFM bothtypesofmagneticcorrelationsmay
turedependenceofthemagnetic(cid:29)uctuationsaroundtheFM contribute,CE-typeaswellasFMones,thethermalpro-
position QFM = (100) with E = 2.75meV, and (d) the q gressionofthedynamicsaroundthisposition,Fig.9,doc-
dependence of the FM (cid:29)uctuations for T = 250K. All scans uments how the isotropic FM correlations compete with
are corrected for the di(cid:27)erent Bose contributions after the
and (cid:28)nally are replaced by the CE-type ordering (upon
substraction of a linear background. For clarity, subsequent
cooling), as it is fully consistent with the coexistence of
scansareshiftedbyaconstantamountontheabscissa. Lines
di(cid:27)erent magnetic phases in the elastic scattering.
correspond to (cid:28)ts with Gaussians.
At T=250K, i.e. above any magnetic and charge or-
dering, we followed the q dependence of the FM (cid:29)uctua-
tions up to a maximal energy of 35meV along the main
see Fig. 9a. However, as the dispersion in this direction
symmetrydirectionsintheMnO layers,seeFig.9d. The
2
is steep, both signals strongly overlap in agreement with
inelasticresponseisalwaysratherbroadinQspace, and
our previous study.20 With increasing temperature, the
above 12.5meV two di(cid:27)erent features overlap strongly,
magnon signal is suppressed following roughly the mag-
which are, however, centered at equivalent q positions in
neticorderparameterandshiftsoutwardduetotheover-
neighboringFMBrillouinzones,(100)and(110). With
all softening of the magnetic dispersion. In consequence,
increasing energy both signals disperse towards the FM
themagnoncontributionsarefullyresolvedatT =100K,
zone boundary, which they (cid:28)nally reach close to 30meV
which is corroborated by further scans at 4meV exhibit-
at (10.50). In the diagonal direction along [110] the
ing a similar behavior (data not shown). Upon heating
energies of the FM (cid:29)uctuation extend to even higher en-
across T the inelastic response broadens, but we do not
N ergies(rawdatanotshown),andtheresultingdispersion
observe a signi(cid:28)cant change in the magnon frequencies.
oftheFM(cid:29)uctuationsinthedisorderedphaseabovethe
At200Kthespectrumcanbedescribedbytwocontribu-
COO transition is summarized in Fig. 10.
tions centered at the same positions as at 100K, indica-
On a square lattice, the spin-wave dispersion for a
tive of the stable FM interaction within the zigzag chain
Heisenberg ferromagnet with isotropic exchange J be-
iso
fragments. In the perpendicular direction, Fig. 9b, the
tween nearest neighbors is given by:
twomagnoncontributionsareseparatedalreadyat10K,
as in this direction the spin-wave velocity is signi(cid:28)cantly (cid:126)ω(q)=4J S(2−cos(2πq )−cos(2πq )). (1)
iso h k
reduced.20 Upon heating, the signal shifts outward, too,
but this shift is more pronounced than that parallel to The observed q dependence of the magnetic correla-
the chains. Furthermore, for T >T the inelastic inten- tions is reasonably well described by this simple Hamil-
N
10
tonian with only a single nearest-neighbor interaction, IV. COMPARATIVE DISCUSSION OF THE
underlining the isotropic character of the FM correla- TEMPERATURE DEPENDENCIES OF THE
tions above T . The slight overestimation of the fre- MAGNETIC CORRELATIONS
CO
quencies at the low-|q| limit may arise from the (cid:28)nite
size of the FM clusters. We do not (cid:28)nd evidence for The combination of the macroscopic and of the neu-
an excitation gap, and the best (cid:28)t to the data yields tron scattering studies results in a comprehensive de-
an exchange energy 2JisoS = 7.5(5)meV. The strength scription of the evolution of the magnetic correlations
of the ferromagnetic exchange in the disordered phase in La Sr MnO upon heating across the magnetic
0.5 1.5 4
is signi(cid:28)cantly reduced compared to the FM interac- and the charge/orbital transition temperatures. The
tion in the CE structure, 2JFMS ≈ 18meV along the untwinned nature of the La Sr MnO -sample crystal
zigzagchains,20butstillpointstoasizablehoppingmedi- (cid:21) besides the twinning dire0c.t5ly 1in.5troduc4ed through the
atedthroughtheZenerdoubleexchangeeventhoughthe COO order (cid:21) is of great advantage, as we may easily in-
single-layer compound remains insulating. Furthermore, terpret the distinct signals. Real-space sketches of the
2Jiso is well comparable with the magnetic exchange in- magnetic correlations for di(cid:27)erent temperatures are pre-
teraction in the FM metallic phases of perovskite man- sented in Fig. 11 to illustrate the di(cid:27)erent stages of the
ganites: Thespin-wavedispersionintheFMphaseofthe magnetic ordering between the short-range FM clusters
CMR-compound La0.7Pb0.3MnO3 is included in Fig. 10, at high temperature and the well-de(cid:28)ned CE-type mag-
which is also described by a single nearest-neighbor ex- netic order at low temperature. In the following we will
changeinteraction.47 Thedispersionofmagneticcorrela- discuss the evolution of the magnetic order with increas-
tions in paramagnetic La0.5Sr1.5MnO4 and the magnon ing temperature. Although the details of the magnetic
dispersion in FM La0.7Pb0.3MnO3 are remarkably sim- ordering might depend on the precise composition of the
ilar. Therefore, the strength of the Zener exchange in half-doped manganite,49 and in particular on its single-
the disordered phase above the COO transition in the layer, double-layer or perovskite structure, the general
insulating compound La0.5Sr1.5MnO4 must be of similar aspects, how magnetic correlations evolve with temper-
magnitude as that in the metallic state of the perovskite ature, should be qualitatively the same, as previous less
CMR compounds.48 The fact that the dispersion is per- comprehensive studies indicate.50,51,52,53,54,55
fectly isotropic parallel to the planes fully excludes the
At low temperature, La Sr MnO exhibits the well
interpretation that the FM clusters are formed by the established CE-type magn0.e5tic1.o5rder94with no trace of
coupling of FM zigzag chain fragments.
another coexisting magnetic phase, see Fig. 11a. More-
over, the magnon excitations in this phase can be well
described within spin-wave theory and perfectly agree
with the site-centered charge-orbital ordering model.
In La Sr MnO the spin-wave velocity is highly
0.5 1.5 4
anisotropicas the magnetic interactions alongthe zigzag
chains are by far the strongest.20 The localized elec-
tron on the Mn3+ site seems to yield a strong mag-
netic bridging within the zigzag chains, as discussed by
Solovyev.31,32
The magnetic transition at T is uncommon, as
N
one does not (cid:28)nd any signature of it in the
temperature dependence of the magnetization in
La Sr MnO aswellasinmanyhalf-dopedperovskite
0.5 1.5 4
manganites.50,51,52,53,54,55 The smooth variation of the
susceptibility across T relates to the temperature de-
N
pendence of the magnetic di(cid:27)use scattering. Short-range
magnetic correlations of the CE type persist above T =
N
110K and can be observed up to T = 220K. These
CO
correlations are purely two dimensional and restricted
to single MnO layers. Moreover, the rod-like structure
2
of the magnetic scattering within the a∗b∗ planes doc-
uments the strong anisotropy of these two-dimensional
correlations: The coupling parallel to the chains is con-
FIG.10: (Coloronline)q dependenceoftheFM(cid:29)uctuations siderably better de(cid:28)ned than that in the perpendicular
in the disordered phase at T=250K for q =(qh00) and q = directioninperfectagreementwiththemagneticinterac-
(qhqh0). Solidlinesdenotea(cid:28)ttothedatausinganisotropic tionparametersdeducedfromthespin-wavedipersion20.
dispersion relation according to Eq. 1, dotted lines give the For T < T < T zigzag fragments are formed as iso-
N CO
magnondispersionintheFMmetallicstate(T=[10]K)ofthe lated objects, see Fig. 11b and c. With the reduction
perovskite La Pb MnO taken from Ref. 47.
0.7 0.3 3 of temperature down towards TN, the typical length ξ||