Incommensurate magnetic structure, Fe/Cu chemical disorder and magnetic interactions in the high-temperature multiferroic YBaCuFeO5

2.2 MB·English

by  M. Morin

Incommensurate magnetic structure, Fe/Cu chemical disorder and magnetic
interactions in the high-temperature multiferroic YBaCuFeO
5
M. Morin,1 A. Scaramucci,1,2 M. Bartkowiak,1 E. Pomjakushina,1 G. Deng,1,3 D. Sheptyakov,4
L. Keller,4 J. Rodriguez-Carvajal,5 N.A. Spaldin,2 M. Kenzelmann,1 K. Conder,1 and M. Medarde1,∗
1Laboratory for Developments and Methods, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland
2Materials Theory, ETH Zu¨rich, 8093 Zu¨rich, Switzerland
3Bragg Institute, Australia Nuclear Science and Technology Organization,
New Illawarra Road, Lucas Height, New South Wales 2233, Australia
4Laboratory for Neutron Scattering and Imaging,
5 Paul Scherrer Institut, 5232 Villigen PSI, Switzerland
1 5Institut Laue Langevin, BP 156, 6, rue Jules Horowitz, 38042 Grenoble Cedex 9, France
0 (Dated: January 9, 2015)
2
Motivatedbytherecentobservationsofincommensuratemagneticorderandelectricpolarization

n in YBaCuFeO5 up to temperatures TN2 as high as 230K1,2 we report here for the first time a
a model for the incommensurate magnetic structure of this material that we complement with ab-
J
initiocalculations ofthemagneticexchangeparameters. Usingneutronpowderdiffraction weshow

8 that the appearance of polarization below TN2 is accompanied by the replacement of the high
temperaturecollinearmagneticorderbyacircularinclinedspiralwithpropagationvectorki=(1/2,
] 1/2, 1/2 q). Moreover, we find that the polarization approximately scales with the modulus of
l ±
e the magnetic modulation vector q down to the lowest temperature investigated (3 K). Further,
r- we observe occupational Fe/Cu disorder in the FeO5-CuO5 bipyramids, although∼a preferential
t occupationofsuchunitsbyFe-Cupairsissupportedbytheobservedmagneticorderandbydensity
s
functional calculations. Wecalculate exchangecoupling constants for different Fe/Cu distributions
.
t and show that, for those containing Fe-Cu dimers, the resulting magnetic order is compatible with
a
m the experimentally observed collinear magnetic structure (kc=(1/2, 1/2, 1/2), TN2 > T > TN1 =
440K). Based on these results we discuss possible origins for the incommensurate modulation and
-
its coupling with ferroelectricity.
d
n
o PACSnumbers: 71.27.+a,71.30.+h,71.45.Lr,61.05.fm
c
[
I. INTRODUCTION at unexpectedly high temperatures (T < TN2 230K)1
1 and in a temperature range more than 10 tim∼es larger
v
than CuO. The reported P values are also fairly large,
5 The discoveryofmaterialswithstronglycoupledmag- reaching 0.4 µC/cm2 in powder samples.1 In contrast to
3 netic and ferroelectric orders has raised a great deal of
9 CuO, the ICM magnetism observed in the ferroelectric
interest in view of their possible use in magnetoelectic
1 phaseofYBCFOissomewhatsurprisingasthehighsym-
device applications. In many such materials the sponta-
0 metry tetragonal perovskite structure of this material is
. neousappearanceofelectricpolarization(P)is linkedto a priori not prone to magnetic frustration. A further
1 the onset of incommensurate (ICM) magnetic order.3–7
0 unanswered question is the nature of the ICM magnetic
This is often the signature of competing magnetic in-
5 order,whichtoourbestknowledgehasnotbeenreported
1 teractions 8 and hence is characterized by low ordering although its existence has been known since 1995.14 To
: temperatures. As a result, their promising technological understand its origin and the consequent multiferroism,
v
multifunctionalities such as the control of magnetism by
i a detailed knowledge of the magnetic structure and ex-
X applied electric fields usually occur at temperatures too
change interactions is clearly required.
low for most practical applications.
r
a
To date there are only two knownexamples of switch- Here we report novel neutron diffraction results that
able, magnetism-driven ferroelectricity at zero field and enable us for the first time to propose a model for the
temperatures above 200K. One is cupric oxide CuO,9,10 ICMmagneticstructureofYBaCuFeO . Wealsopresent
5
where the lowmonoclinic symmetry promotesfrustrated experimental evidence suggesting the existence of a par-
magnetic interactions. A spiral magnetic multiferroic ticular kind of Cu/Fe chemicaldisorder characterizedby
phase results in the limited temperature range of 213 theexistenceofCu-Febipyramidaldimers. Densityfunc-
to 230K.9 The secondexample, whichhas receivedmuch tional theory (DFT) calculations carried out for vari-
less attention due to its unavailability as a single crystal ous Fe/Cu distributions provide additional support for
or thin film, is the layeredperovskite YBaCuFeO . This this scenario. We also calculate the magnetic exchange
5
material was first synthesized in 1988,11 one year after coupling parameters between next and (selected) next-
the discovery of high-temperature superconductivity in nearestneighboursinordertogaininsightintotheorigin
YBa Cu O .12 Although it is not superconducting,13 ofthemagneticorderandthemagneticfrustrationinthis
2 3 6+x
YBaCuFeO displays magnetism-driven ferroelectricity material. To conclude, we discuss the polarizationdirec-
5
2
tion and the possible origins of the multiferroicity based III. CRYSTAL STRUCTURE AND FE/CU
in the symmetry of the ICM magnetic structure and in DISTRIBUTION
the similar temperature dependences of the polarization
and the magnetic modulation parameters. The crystal structure of YBaCuFeO is displayed in
5
Fig.1. Thetetragonalunitcellcanbedescribedasanor-
deredarrayof layerscontaining the large Ba2+ ions plus
two corner-sharing square pyramids separated by Y3+
sheets. Equal amounts of Fe3+ and Cu2+ sit inside the
pyramids, though at different distances from the basal
II. EXPERIMENTAL DETAILS plane.14Ifthetwoionsareequallydistributedamongthe
pyramids as shown in Figs. 1a and b, the average struc-
tureiscentrosymmetricwithspacegroup(SG)P4/mmm.
TheYBaCuFeO5ceramicsampleusedinthisworkwas IftheFe/CudistributionisasymmetricasinFigs.1cand
preparedbysolidstatesynthesis. Stochiometricamounts d, the mirror plane containing the Y3+ ions is lost and
ofY2O3 (previouslypre-annealedat950◦Cfor10hours), the structure is non-centrosymmetric (SG P4mm). Per-
BaCO ,CuOandFe O werethoroughlymixedandfired fect Fe/Cu order along the c axis is a particular case of
3 2 3
at 1050◦C in air for 50h. The resulting black powder this scenario (see Fig. 1d).
wasgroundandpressedintopelletswhichwereannealed DuetotherelativelysmalldifferencebetweentheFe3+
again under the same conditions. The phase purity was and Cu2+ ionic radii (0.07˚A18), the occupation of the
checked by laboratory x-ray powder diffraction (Brucker twositesisinfactstronglydependentonthepreparation
D8 Advance, Cu K ), which indicated the absence of method andthe two spacegroupshavebeen reportedby
α
foreign phases as well as an excellent crystallinity. The different authors in the past.11,14,19–21 This has an im-
cationic distribution in the sample, as determined by x- pact on the magnetic interactions and on the value of
ray fluorescence spectroscopy, was found to be homoge- T , which displays an important dispersion in the lit-
N2
neous within a 30µm scale with Y/Ba/Fe/Cu ratios in erature(180to240K).1,2,11,14,20–22 Apropercomprehen-
excellent agreement with the nominal composition. The sionof the magnetismin YBaCuFeO thus requiresthus
5
oxygen content, as determined from thermogravimetric information about the Cu/Fe distribution within the 2
analysis, was 4.95(2). available square-pyramidalsites.
The results obtained for the refinement of the high
DCmagneticsusceptibilitymeasurementswerecarried
resolution NPD data measured on HRPT (λ = 1.1546
out ona commercialPhysicalProperties MeasuringSys- ˚A) at roomtemperature (RT) are summarizedin Tab.I.
tem (Quantum Design). A cylinder-shaped YBaCuFeO
5 WeusedtwodifferentFe/Cudistributionmodelsforeach
pellet (D = 5mm, H = 7mm) from the same batch as
SG.ForP4/mmm wecomparedasinglesiteoccupiedby
thesampleusedfortheneutrondiffractionmeasurements
50% Fe and 50% Cu with a model with split Fe and Cu
wascooledinzerofielddownto1.8K.Themagnetization
sites, each of them also with half occupation. As shown
of the sample was then measured in a magnetic field of
in Table I, the fit obtained using split sites results in
1T while heating at a constant rate of 2K/min.
significantly better reliability factors.
Theelectricpolarizationwasdeterminedfrompyrocur- A similar conclusion was derived from the fits using
rent measurements which were carried out using a Kei- P4mm,which,incontrasttocentrosymmetricP4/mmm,
thely 6517B electrometer. A thin pellet (D = 11mm, allows us to refine the Fe/Cu occupation. For this space
H = 1mm) was sputtered with gold on both faces and group we compared a model with full Fe/Cu order with
mounted on the stick of a He cryostat. The sample was another with split Fe/Cu sites. The agreement between
cooled from RT down to 3K with an electric field of the observed and the calculated patterns was again sig-
300V applied between the gold-coveredfaces. At 3K th±e nificantlybetter forthe secondcase,whichdisplayedthe
fieldwasremovedandthestraycharges(ifany)recorded bestreliabilityfactorsofthefourmodelspresentedinTa-
during 600s. The pyrocurrent was then measured by bleI (seealsoFig.2). Theoccupationofthe splitFe/Cu
heating the sample at 20K/min. sitesobtainedwiththislastmodelisslightlyasymmetric
with approximately1/3Fe + 2/3Cu (z 0.25)and 2/3
Neutronpowderdiffraction(NPD)measurementswere Fe+1/3Cu(z 0.75). Thisindicatesth∼atthematerial
carried out at the Swiss Neutron Source SINQ of the isnon-centrosym∼metriconaveragewithapolaraxispar-
Paul Scherrer Institut in Villigen. Several patterns were allelto the 4-foldaxis along c. As we willshow later,no
recorded between 1.5 and 500K at the powder diffrac- permanent polarization is observed above T = 200K,
N2
tometers HRPT (λ=1.1546˚A)15 and DMC (λ=2.45˚A).16 probably because the Fe/Cu disorder prevents the exis-
The two series of experiments were carried out consec- tence of coherence between the Fe/Cu displacements.
utively using the same cryofurnace, whose contribution The existence of disorder is also supported by the
tothebackgroundwasminimizedusingoscillatingradial Fourier difference maps calculated for the four models,
collimators. All data were analyzed using the Rietveld whicharedisplayedinFig.1. WeusedtheFullProfSuite
package FullProf Suite.17 programFourier17 and structure factors corresponding
3
MODEL 1 MODEL 2 MODEL 3 MODEL 4
T = 300K P4/mmm P4/mmm P4mm P4mm
(1 single Fe/Cu site) (Fe/Cu sites split) (Fe/Cu fully ordered) (Fe/Cu split, partial order)
a(˚A) 3.87323(1) 3.87326(1) 3.87325(1) 3.87325(1)
c(˚A) 7.6651(3) 7.6655(3) 7.6651(3) 7.6655(3)
Ba 1a (0 0 0) 1a (0 0 0) 1a (0 0 z) 1a (0 0 z)
z 0 0
U11(˚A2) 0.0042(4) 0.0043(3) 0.0024(4) 0.0035(3)
U33(˚A2) 0.0189(12) 0.0231(12) 0.014(2) 0.024(2)
Y 1b (0 0 1/2) 1b (0 0 1/2) 1a (0 0 z) 1a (0 0 z)
z 0.4931(10) 0.5053(16)
Uiso(˚A2) 0.00263(17) 0.00250(14) 0.00281(19) 0.00249(18)
Cu 2h (1/2 1/2 z) 2h (1/2 1/2 z) 1b (1/2 1/2 z) 1b (1/2 1/2 z)
Occ 0.5 0.5 1 0.703(2)
z 0.26729(13) 0.2833(3) 0.7155(10) 0.2856(7)
Uiso(˚A2) 0.00435(11) 0.00156(12) 0.00402(12) 0.00149(13)
Fe 2h (1/2 1/2 z) 2h (1/2 1/2 z) 1b (1/2 1/2 z) 1b (1/2 1/2 z)
Occ 0.5 0.5 1 0.297(2)
z 0.26729(13) 0.2544(2) 0.2511(10) 0.2516(8)
Uiso(˚A2) 0.00435(11) 0.00156(12) 0.00402(12) 0.00149(13)
O1 1c (1/2 1/2 0) 1c (1/2 1/2 0) 1b (1/2 1/2 z) 1b (1/2 1/2 z)
z -0.0096(14) 0.0179(15)
U11(˚A2) 0.0074(4) 0.0067(4) 0.0084(5) 0.0067(4)
U33(˚A2) 0.0136(9) 0.0145(8) 0.0157(11) 0.0090(17)
O2 4i (0 1/2 z) 4i (0 1/2 z) 2c (1/2 0 z) 2c (1/2 0 z)
z 0.31603(12) 0.31601(10) 0.3077(12) 0.3265(15)
U11(˚A2) 0.0050(3) 0.0043(3) 0.0052(3) 0.0043(3)
U22(˚A2) 0.0022(3) 0.0024(2) 0.0024(3) 0.0023(2)
U33(˚A2) 0.0113(4) 0.0090(3) 0.0112(10) 0.0086(4)
O2’ 2c (1/2 0 z) 2c (1/2 0 z)
z 0.6758(12) 0.6947(15)
U11(˚A2) 0.0052(3) 0.0043(3)
U22(˚A2) 0.0024(3) 0.0023(2)
U33(˚A2) 0.0112(10)) 0.0086(4)
Chi2 2.64 2.01 2.46 1.98
Rp 4.52 3.90 4.33 3.86
Rwp 5.74 5.01 5.54 4.96
RBragg 5.34 4.05 4.98 3.81
TABLE I: Atomic coordinates, thermal parameters and Fe/Cu mag-
netic moments of YBaCuFeO5 at 300K, as refined in the space groups
P4/mmm andP4mm (bothwithZ=1)usingtheneutronpowderdiffrac-
tion data recorded on HRPT (λ = 1.1546 ˚A). The reliability factors of
the different models are also provided.
to reciprocal space vectors H with modulus smaller Fouriertransformsofthedifferencebetweentheobserved
than10.7˚A−1. The contourplots in Fig.1representthe andthecalculatedneutronscatteringdensityatRT.The
4
a) P4/mmm (Model 1) c) P4mm (Model 3)
Ba
Cu +Fe Cu
0.5 0.5
Y
0.19 Cu +Fe Fe
0.16 0.5 0.5
0.13
0.10
0.06
0.03
0.00
-0.03
-0.06 b) P4/mmm (Model 2) d) P4mm (Model 4)
-0.10
-0.13
Fermi/Å3
Fe Fe
0.5 0.7
Cu Cu
0.5 0.3
c Cu Cu
0.5 0.7
Fe Fe
0.5 0.3
a
FIG.1. (Coloronline) ModelsforthecrystalstructureofYBaCuFeO5 usedfortheRietveldfitsoftheRTNPDdatarecorded
onHRPT(seealsoTable I).(a)Centrosymmetric(P4/mmm)withasingleFe/Cusite. (b)Centrosymmetric(P4/mmm)with
Fe/Cusitessplit. (c)Non-centrosymmetric(P4mm)withperfectFe/Cuorderalongc. (d)Non-centrosymmetric(P4mm)with
partial Fe/Cu order. The contour plots are Fourier difference maps of the (x, 1/2, z) plane showing the neutron scattering
density not reproduced byeach of themodels.
results obtained for the two ordered models (1 and 3 in IV. MAGNETIC TRANSITIONS
Table I) show the existence of scattering density (bright
yellow spots) not reproducedby these models above and
Fig. 3a shows the temperature dependence of the low-
below the refined Cu/Fe positions (black circles). These
angleregionoftheNPDpatternsrecordedonDMC.Two
spots are absent for the disorderedmodels 2 and 4, with
phase transitionsinvolvingthe appearanceofnew Bragg
resultsslightlybetter forthe secondone. Themodelsin-
reflectionsareclearlyobservableatT 440KandT
N1 N2
volvingCu/Fedisorder(thatweassumetoberandomin ∼
200K.ThenewpeaksappearingbelowT correspond
N1
our fits) provide thus a better description of the experi- ∼
tothepropagationvectork =(1/2,1/2,1/2),indicating
c
mentaldata,evenif the presenceofcorrelationsbetween
that the magnetic structure is commensurate(CM) with
theFeandCusiteoccupationscannotbecompletelydis-
the crystallographic unit cell between 440 and 200K in
regarded. In particular, it has been suggested that the agreement with previous reports.1,2,14,20–22
bipyramidal units linked by the apical oxygen O1 could
BelowT twosatellitesappeararoundeachCMmag-
N2
always host Cu-Fe pairs, which would be randomly ar-
netic reflection. They can be indexed with the propaga-
ranged in the structure.14 Since the Fe-O1 and Cu-O1
tionvectork =(1/2,1/2,1/2 q),whichinvolvesanICM
i
apicaldistancesare slightlydifferent, sucha distribution ±
modulation of the magnetic moments along the c axis.
isexpectedtogiverisetolowermicrostrainsalongcthan
Themodulationparameterqincreasescontinuouslywith
one with coexistingCu-Cu(long), Fe-Fe (short)and Cu-
decreasingtemperature andremains ICM down to 1.5K,
Fe (intermediate) pairs. We show later that both the
seeFig.4. TheonsetoftheICMmagneticordercoincides
proposed magnetic structures and the DFT calculations
with a sharpanomaly in the magnetic susceptibility and
favor such a scenario.
with the appearance of electric polarization P (Fig. 4),
indicatingadirectrelationshipbetweenthetwophenom-
ena. Below 50K P reaches 0.64µC/cm2, close to the
∼
5
a) DMC, (cid:79) = 2.45 Å
nits) P4mm, model 4 YH BRaPCTu, F λe O= 51 ,. 1R5T46 310.50KK
u
y 1.5K
ar AF incommensurate
y (arbitr e (K) TN2 = 200K (1/2 1/2 1/2 +q)
sit ur (1/2 1/2 1/2-q) (1/2 1/2 3/2-q)
nten erat (1/2 1/2 1/2) (1/2 1/2 3/2+q)
I p
m T = 430K AF commensurate (1/2 1/2 3/2)
e N1
T
paramagnetic
500K
20 40 60 80 100 120 140 160 24 28 32 36 2(cid:84) (degrees)
2Theta (degrees)
c)
FIG. 2. (Color online) NPD pattern measured on HRPT at
RT. Red crosses: observed data. Black lines: Rietveld fit
obtained using the model 4 of Table I. The vertical ticks
indicate the positions of the Bragg reflections for the crystal
(upperrow) andthecommensurateAFMmagneticstructure
with kc = (1/2, 1/2, 1/2) (lower row, see also Fig. 5a).
value reported by Kundys1 ( 0.4µC/cm2) and about
10 times larger than the one∼reported by Kawamura2
(0.04µC/cm2). ThetemperaturedependenceofP closely
follows that ofq, a behaviorthat we will addresslater in
the text.
Fig.3bshowstheevolutionoftheintegratedintensities
of the first magnetic peak and its satellites. Below T
N2
FIG.3. (Coloronline)a)2Dcontourplotshowingthetemper-
themainCMreflection(1/2,1/2,1/2)startstodecrease.
Atthesametimetheintensitiesofthetwosatellitesstart aturedependenceoftheNPDpatternsforYBaCuFeO5. The
patternsat1.5Kand300Kareshownseparately. b)Temper-
growing. At 1.5K the CM peak is still visible, but its
aturedependenceoftheintegratedintensityofthe(1/2, 1/2,
intensityismuchlowerthanthatoftheICMsatellites. A
1/2)magneticreflectionanditsincommensuratesatellites. c)
similar behaviour is observed for all CM/ICM reflection PortionoftheNPDpatternsshowingthesereflectionsforour
sets, see Figs. 3a and 6. Such behavior contrasts with sample(230K and1.5K) andasamplepreparedaccording to
previous reports, where the ICM satellites were either ref.14 (1.5K).d)TemperaturedependencetheFe3+ magnetic
absent21 or much less intense than the CM reflections moment. Inset: angleθ betweenthemagneticmomentdirec-
at all temperatures.2,14,22 This is illustrated in Fig. 3c, tion(TN1<T<TN2)andthespiralplane(T<TN2)withthec
where the region around the first CM reflection (1/2, axis.
1/2, 1/2) measured at 1.5K for our sample (black) and
AandBforbothP4/mmm andP4mm andthetwoprop-
a sample preparedaccording to the method described in
agation vectors k and k together with tables with the
ref.14 (blue) are displayed. The improved quality of the c i
symmetry-allowed basis functions associated with each
ICM magnetic reflection set obtained with our synthesis
irrep. Such tables indicate that, if only one irrep be-
procedure,togetherwiththelargernumberofreflections
comes active below each of the magnetic transitions, the
measured compared with previous works,2,14,22 enables
direction of the moments is restricted to either the ab
us for the first time to propose a model for the ICM
plane or along the c axis. We find instead that, at all
magnetic structure of YBaCuFeO .
5 temperatures, the best fits to the data correspond to in-
clinedarrangementsneedingthe combinationof2irreps,
see the Appendix A and B for details.
V. MAGNETIC STRUCTURES Two collinear models and a commensurate helix are
compatible with our observations and they give rise to
We used representation analysis to find the possible the same neutron powder diffraction patterns if Cu and
magneticmomentarrangementscompatiblewiththe the Fe are located exactly at z = 1/4 and z = 3/4. For
space groups P4/mmm and P4mm. The characters of the refined Fe and Cu positions, which have z coordi-
theirreduciblerepresentations(irreps)ofthelittlegroup nates rather close, but not identical to these values (see
Gk,formedbytheoperationsofthespacegroupGwhich Table I) the three models give rise to slightly different
leave the k-vector invariant, are shown in the Appendix intensities. As shown in the Fig. 10, the best agreement
6
T
N2 a) 230 K b) 1.5 K
2 ] 0.10 -6
0. 8.4x10
1
P / P / max or q (rlu)0.05 qPP χ ((D+-3C30 000VV)) 88..20 χ
ation [ n vect0.00 7.8 DC (e
z o m
d polari Modulati-0.05 7.6 u/g)
e
z 7.4
ali
m
or -0.10 7.2
N
0 100 200 300
Temperature (K)
c
c c
b b a
FIG.4. Reddots: DCmagneticsusceptibilityofYBaCuFeO5 a a b
measured at 1T by heating after cooling in zero field. Black
open squares: Incommensurate modulation vector q (in re- kc = (½ ½ ½) ki = (½ ½ ½ ± q)
ciprocal lattice c∗ units). Blue dotted/continuouslines: nor-
malizedelectricpolarizationmeasuredbyapplyinganelectric
field of± 300V.In ordertousethesameaxis asqthepolar- FIG.5. (Coloronline)MagneticstructuresofYBaCuFeO5. a)
ization valueshavebeennormalized totheirsaturation value Colinearmagneticorderat230K.b)Twoviewsofthecircular
( 0.64µC/cm2) and further divided by a constant value of spiral order at 1.5 K. For clarity, only one crystal cell within
∼
10.2 . theab plane is shown.
∼
correspondstothecollinearmagneticstructuredisplayed ment involves the preservation of the AFM coupling be-
in Fig. 5a. Spins in the ab plane are antiferromagneti- tween the 3d metal sites without connecting oxygen ob-
cally (AFM) coupled whereas the alignment along c al- served in the commensurate phase, see Fig. 5a. It also
ternates: it is AFM across the O-free Y planes and fer- implies the loss of the FM coupling within the bipyra-
romagnetic (FM) inside of the bipyramidal blocks. Note mids, suggesting that this magnetic coupling is more af-
thattheorientationofthespinstheab planeisarbitrary fected by the thermal evolution of the structure than is
because their direction in the plane perpendicular to the the one across the O-free Y layers.
4-fold axis cannot be determined from NPD. The angle Our results indicate that the plane of the helix forms
θ between magnetic moments and c axis decreases con- an angle θ with the c axis which decreases continuously
tinuously from 75◦ (at 400K)to 65◦ (at 200K), see inset withtemperature(θ 65◦ at200K,θ 45◦ at1.5K,the
of Fig. 3d. anomalously low valu∼e at 150K is pro∼bably due to the
Below TN2 two propagation vectors kc and ki are strong superposition of the 2 incommensurate satellites
presentdowntothe lowesttemperatureinvestigated,see at this temperature). The ICM magnetic order evolves
Fig. 3b and Fig. 6. The magnetic intensities can be de- thus from an inclined helix towards a cycloid with de-
scribed as arising from either a multi-k arrangement or creasing temperature. The reasons for this behaviour
from two distinct magnetic phases; our NPD data alone are unclear, but it could be related to different Cu2+
cannot distinguish between the two possibilities. How- and Fe3+ magnetic anisotropies and their effect on the
ever, the fact that the intensities of both reflection sets temperature dependence of the magnetic moment orien-
have opposite temperature dependencies below TN2 fa- tations.
vors the second one. UsingthepreviouslydescribedmodelsfortheCMand
As in the CM case, two different models give rise to ICM magnetic structures we determined their fractions
very similar magnetic intensities. However,the excellent inthesamplebelowT . Byrestrictingthemodulusand
N2
statisticsoftheDMCdataandthefactthatFeandCuz the θ angle of the Cu2+ and Fe3+ magnetic moments in
coordinatesdiffer significantlyfromz = 0.25and0.75at bothphasestobeidenticalandtheirratiotobethesame
alltemperaturesallowus todistinguishthem, seeFig.6, as for their spin-only values (1 to 5) we obtain 8% (CM)
Fig. 11 and further details in the Appendix B. The best and 92 % (ICM). This contrasts with previous studies,
agreementwiththeexperimentaldatacorrespondstothe where most of the sample displayed CM magnetic order
circular helix displayed in Fig. 5b. Such a spin arrange- belowT andonlyasmallfractionwasable toundergo
N2
7
the CM ICM phase transition. As we discuss in the and negligibly small for two Cu ions). This agrees with
→
next sections, differences in the Fe/Cu distribution are the observation of an ICM modulation only along this
the most probable origin of these differences. direction and suggests that the appearance of magnetic
The evolution of the Fe3+ magnetic moment is shown frustration below T could be due to a temperature-
N2
in Fig. 3d. Its value at 1.5 K is 3.74(2) (0.748(4)µ driven imbalance of the magnetic couplings along the c
B
for Cu2+), about 1/3 reduced with respect to those ex- axis. Such a scenario is consistent with the continuous
pected for the free-ion, spin-only moments. Such reduc- evolutionofthemodulationparameterq withdecreasing
tion may, among other reasons,also be related to Fe/Cu temperature (Fig. 4). Note also that, within the GKA
disorder. The diparoundT is notanartifactfromthe frameworkandfortheCMphase,theexperimentallyob-
N2
fits since the same dip is observed in the total (central servedFM coupling within the bipyramids is only possi-
peak + satellites) integrated intensity as a function of ble if they are occupied by a Cu-Fe pair.
temperature (Caignaert and co-workers found a similar
behaviour, see14). This suggests that the incommensu-
rate domains are large enough to produce a mesurable VII. AB INITIO CALCULATIONS
contribution to satellites only a few degrees below T .
N2
Further insight requires detailed quantitative calcula-
YBaCuFeO5 , 1.5 K tionsoftheexchangeinteractionsthatweobtainusingab
DMC, λ = 2.458 Å initio calculations with the Local Spin Density Approx-
y units) 2-q) 1/2 3/2-q) itumiloaanttaioilontnhpepaolcurkysaaHgseuibm(VbpaAlreSdmPeU)n.2t(4eL,d2S5iDnFAtohr+eUtVh)ei2es3nentcoaaaldcbeun-liasnititityoionfsusinmwce--
ensity (arbitrar (1/2 1/2 1/2-q)(1/2 1/2 1/2+q) (1/2 1/2 3/1/2 1/2 3/2+q) (3/2 1/2 1/2-q)(3/2 1/2 1/2+q) (3/2 (3/2 1/2 3/2+q) (1/2 1/2 7/2-q) (1/2 1/2 7/2+q) (3/2 3/2 1/2-q) (3/2 3/2 1/2+q) uoTstiersvhtbeeedittHovapaulUrslonuFtdjeere’sec=satoctof5oerduoeapnVaul-sgisanmivtngaeedslneewUntffeecCedrecuetwsJi=tvaaHevt8eeC=sepVofo1outrwleeoVbnhmtoiliabteahnltisdnFhwtJeeeHiaortahnncd-=3tsidiCot0enaufneoiwffdoreenF3rcspee-.
nt ( Fe Cu
I and Cu, respectively. For all the calculations, except for
those relative to some of the next-nearest-neighbormag-
netic couplings along c (see Appendix C), we considered
20 40 60 80 a supercell with a = √2 a and c = 2c (a and c are
c c c c
2Theta (degrees)
thecrystallographicunitcellparameters)containingfour
formulaunits, asdepictedinFig.7, aΓ-centeredk-point
FIG. 6. (Color online) NPD pattern measured on DMC at gridofsize8 8 4andanenergycut-offE =600eV.
cut
1.5K. Red crosses: observed data. Black lines: Calculated Relaxationso×fth×ereducedionicpositionsintheunitcell
intensities. The vertical ticks indicate the positions of the wereperformeduntilallatomicforceswerebelow2 10−5
Bragg reflections for the crystal (upper row), the CM mag- eV/˚A and using the experimental lattice paramete·rs at
netic structure with kc = (1/2, 1/2, 1/2) (intermediate row) 1.5K (a=b=5.462 ˚A, c=15.258 ˚A for the supercell.).
andtheICMmagneticstructurewithkc=(1/2,1/2,1/2 q)
∓
(lower row).
A. Cu/Fe distribution
VI. MAGNETIC COUPLINGS FROM
GOODENOUGH-KANAMORI-ANDERSON First,weinvestigatedthestabilityofthecrystalstruc-
RULES ture of YBaCuFeO under different Fe3+/Cu2+ distri-
5
butions. The fractional coordinates of all atoms were
To understand the origin of the magnetic structures relaxed starting from different arrangements for the two
we first consider the Goodenough-Kanamori-Anderson transitionmetalions,keepingthe commensurateantifer-
(GKA) rules of superexchange. For Fe3+ (3d5) and romagneticorderofFig.5a,fixingthelatticeparameters
Cu2+ (3d9) in the square-pyramidal arrangement of the tothe experimentallyobservedvaluesat1.5Kandinab-
YBaCuFeO structure, these rules predict strong AFM senceofthespin-orbitcoupling. Fig.7showsthedifferent
5
nearest-neighbour (NN) couplings within the ab plane configurationsforthe Fe/Cudistributionandthe energy
in agreement with our observations. Interestingly, the of the relaxed structures compared with the lowest en-
sign of the couplings is independent of the Cu/Fe distri- ergy one. We see that there are two energy hierarchies
bution. Along the c axis the situation is more complex. depending on which ions are present in the bipyramids.
On one side, superexchange between NN is not possible Low energy configurations (up to 0.214 eV 2500 K),
across the Y layers due to the absence of the apical O. panels(a)to(e)withintheblueframe,contai≈nboth Fe3+
Onthe other,the signof the coupling within the bipyra- and Cu2+ in all bipyramids, while those containing two
mids is expected to be strongly dependent on the Fe/Cu Cu2+ and/ortwo Fe3+ ions in atleastone ofthe bipyra-
distribution (AFM for two Fe ions, FM for a Fe-Cu pair mids have higher energy (from 0.996 eV 11600 K),
≈
8
panels (f) to (j) within the red frame . in the absence of spin-orbit coupling to extract the ex-
change couplings as described in Appendix C. We note
that in this minimal model we assume the presence of
only nearest-neighbour (NN) Heisenberg exchanges and
do not consider higher order terms such as biquadratic
and ring exchange which have been found to play a role
in cuprates26,27 and, more recently, in manganites.28
Results for the exchange coupling constants are listed
inTab.II.Remarkably,foranypairofNN,thesignofthe
magnetic interactions is the same for all five configura-
tions. The exchange constant, J , between neighboring
⊥
spins in the same tetragonal plane is AFM and is by far
the strongest coupling for all of configurations. J and
kO
J , which correspondto the exchange couplings between
k
ions in neighboring planes separated by an oxygen layer
or not are, respectively, FM and AFM and, generally,
take values smaller than J . This confirms the c axis as
⊥
thedirectionwiththeweakestcouplings,whichisthedi-
rectionwhereanincommensuratewavevectorisobserved
below T . Interestingly, the only FM exchange con-
N2
stant is J , which corresponds to the coupling within
kO
the bipyramids occupied by a Cu-Fe pair.
We note that the signs of all couplings in configura-
tions (a) to (e) are in agreement with the Goodenough-
Kanamori-Anderson rules as well as with the observed
CM magnetic structure (T < T < T ), see Fig. 5a.
N1 N2
This is not the case for the higher energy configurations
(f) to (j), where the sign of J for bipyramids occu-
kO
pied by an Fe-Fe pair is AFM and hence not compatible
with the observed magnetic order.29 To summarize, the
FIG. 7. (Color online) Three-dimensional view of the su-
configurations containing exclusively Cu-Fe pairs in the
percell with a = √2 ac and c = 2cc used in the ab-initio
bipyramidsaremorestable,andthecouplingwithinsuch
calculations (left upper panel) and its projection on the ab
plane (right upperpanel) for one of theFe2+/Cu3+ distribu- dimersistheonlyFMoneamongNNinteractions. Since,
tionsconsidered. Notethattheaandbaxesarerotatedby π as shown in Fig. 10, the magnetic structure which gives
4
withrespecttothoseinFig.1. Panelsfrom(a)to(j)showthe the best reliability indexes involvesFM couplings within
projection on the ac plane of the considered supercells with thebipyramids,theonlypossibilityisthatsuchunitsare
differentorderingsofFe2+ ions(goldensquarepyramids)and occupied by Cu-Fe pairs. This result strongly supports
Cu3+ (blue square pyramids) and their energies relative to the existence of Cu-Fe “dimers” as necessary condition
that of structure (a). For clarity Ba2+ and Y3+ ions are not to stabilize the observed CM magnetic structure. More-
shown. The blue and red frames surround respectively the
over,tobeconsistentwiththeresultsdisplayedinFig.1,
low-energy and high-energy sets mentioned in section VII.A.
these dimers should be randomly distributed.
B. Nearest-neighbour magnetic couplings and CM C. Next-nearest-neighbour magnetic couplings and
magnetic order ICM magnetic order
Next,weevaluatedtheexchangecouplingconstantsfor We will focus now on the ICM magnetic structure ob-
the obtained relaxedstructures of the low energyconfig- servedbelowT . To obtainfurther insightonits origin
N2
urations (a) to (e), i.e., those where the bipyramids are we considered the effect of next-nearest-neighbor J
NNN
always occupied by a Fe-Cu pair. We assumed that the magneticcouplingsalongthe cdirection. The valuesob-
magnetic interactions are described by the Heisenberg tained by ab initio calculations are summarized in the
Hamiltonian fourth column of Tab. II. For each of the configurations
(a),(b),(d)and(f)inFig.7thereareonlytwoinequiva-
1
H = XJijSi Sj, (1) lentJNNN’s. Forconfiguration(c)their numberismuch
2 ·
larger (eigth). Therefore for this configuration we ex-
i,j
tract only J , J , J and J and assume that
3,7 1,5 2,6 2+c,6
where, S =5/2, S =1/2 and i,j label the magnetic J J , J J , J J andJ J .
Fe Cu 3+c,7 3,7 1+c,5 1,5 4,8 2+c,6 4+c,8 2,6
≈ ≈ ≈ ≈
sites,andperformedcollinearspinpolarizedcalculations To estimate the size of J necessary to give rise to
NNN
9
J⊥ (meV) Jk (meV) JkO (meV) JNNN (meV)
(a) J1,2 = 134.5 J1,3 = 10.6 J5,3 = -1.6 J1,5 = -0.05
J7,8 = 8.7 J5,7 = 2.8 J1+c,5 = -0.01
(b) J1,2 = 129.9 J1,3 = 1.4 J3,5 = -1.6 J1,5 = 0.07
J3,4 = 8.9 J3,7 = 0.19
(c) J3,4 = 28.6 J5,7 = 1.1 J2,8 = -1.5 J3,7 = 0.20
J1,2 = 133.0 J2,4 = 8.9 J1,7 = -1.5 J1,5 = 0.09
J7,8 = 8.7 J1,3 = 1.7 J3,5 = -1.7 J2,6 = - 0.07
J5,6 = 28.2 J6,8 = 3.0 J6,4 = - 1.7 J2+c,6 = -0.01
(d) J1,2 = 28.3 J1,3 = 3.1 J3,5 = -1.6 J1,5 = -0.04
J7,5 = 7.5 J1+c,5=-0.01
(e) J1,2 = 28.3 J1,3 = 1.3 J3,5 = -1.6 J1,5 = 0.12
J2,6 = 0.20
TABLE II. (Color online) Calculated exchange coupling
constants for the different configurations in Fig. 7. Posi-
tive/negative signs correspond to AFM/FM interactions, re-
spectively. J⊥ , JkO, Jk and JNNN are defined in the main
text. To avoid ambiguities the exchange coupling constants
Ji,j are also labeled by the position i,j of the magnetic ions
asinFig.7. NotethataccordingtoEq. 5theenergyscalefor
FIG. 8. (Color online) Phase diagrams obtained using the
e2a5cfhorcoFuep3+li-nFge3is+ocbotuapinlinedg(bbyromwunl)t,ip5lyfionrgFiet3+by-CSui2S+j,cothuaptlinisg: spiral ansatz Eq. 2 for configurations (a), (b), (d) and (e).
4 4 Thebluecolorindicatesthecommensuratecollinearstructure
(black) and 1 for Cu2+-Cu2+ coupling (blue).
4 shown in the left pannel of Fig. 3. The red color and the
yellow color indicate, respectively, an incommensurate spiral
stateandacommensuratenon-collinearstate. Thegreendot
amagneticspiralstatewecalculatedthe phasediagrams indicates the valuesof theNNNin Tab. 1.
for the minimal energy state of Eq. 5 by tuning the in-
the ab-initio calculations of exchange couplings, we can-
equivalent J ’s of each configuration between -1 and
NNN
notcompletelyexcludeNNNcouplingastheoriginofthe
1meVandundertheassumptionthatthemagneticorder
incommensurate state.
is of spiral type. Calculations for configuration (c) were
not considered due to the large number of inequivalent
next-nearest-neighborcouplings along c. We assume the
VIII. POSSIBLE ORIGIN OF ELECTRIC
magnetic structure to be described by a spiral ansatz of
POLARIZATION
the form
Tofinish,webrieflyaddressthequestionsofthe direc-
Sµ(Ri)=cos(φµ+q Ri)v1+sin(φµ+q Ri)v2, (2) tion of the electric polarization in the incommensurate
· ·
phaseandtheoriginofthemagnetoelectriccoupling. Al-
where v and v are two orthogonal unit vectors, µ= thoughtheycannotbeproperlyansweredduetothelack
1 2
1,...,8labelsthe magneticionsinthe unitcellsofFig.7, of single crystals,it is possible to make some predictions
qisthewavevector,φ istheangleoftheµ-thspininside using the symmetry properties of the refined ICM mag-
µ
the unit cell and R is the position of the i-th unit cell. netic structure and the various mechanisms proposed in
i
InsertingEq. 2inEq. 1,consideringthe exchangeofthe the literature.
firstthreecolumnsofTab.IIandminimizingnumerically Looking at Fig. 5b, we see that the only symmetry
theobtainedenergywithrespecttoqandφ weobtained element of the depicted inclined spiral is a binary axis
i
the states depicted in the phase diagrams Fig. 8 as a along the b direction. Its point group is thus .2., which
function of inequivalent J . iscompatiblewiththeexistenceofP onlyalongb. Inter-
NNN
As shown in Fig 8, incommensurate states are stable estingly, the ionic, non-switchable polarization expected
onlyifatleastoneoftheNNNcouplingsisferromagnetic in the case of a perfect Cu/Fe order would appear along
(i.e., if it frustrates the collinear commensurate order). c.
According to Tab. II, the only ferromagnetic NNN cou- This prediction agrees with those of the Landau The-
plings are those between a Cu2+ and a Fe3+ which are ory formalisms proposed in Ref. 6 as well as in Ref. 30,
present in configuration a) and d). However, the calcu- wherethe magnetoelectriccoupling is describedby a tri-
latedstrengthofthesecouplings(greendots)istoosmall linear interaction term. According to the formalism in
to stabilize a spiralstate. Therefore,the phase diagrams Ref. 30, P transforms as the product of the two irreps
in Fig. 8 obtained with the ansatz Eq. 2 indicate that describing the magnetic structure. Looking at Tables V
the next-nearest-neighbor couplings obtained in Tab. II and VII, it is easy to see that P is not allowed for k
c
are either too weak or of the wrong sign to stabilize a but it may exist in the ICM phase only within the ab
spiral state. However, due to the uncertainty present in plane.
10
Similar conclusions can be derived from the
Dzyaloshinskii-Moriya (DM) and/or spin-current
models for magnetoelectric coupling. According to these 0.6
mechanisms, the polarization direction is expected to
be given either by e S S or q S S , 0.5
were eij is the vectorijco×nneciti×ng thje i and×j siite×s anjd 2 m)0.4
c
q = (0, 0, kz) is the magnetic modulation vector. In C/ 80
the incommensurate phase q e , so the two models (cid:82)0.3
make identical predictions. Frokm Fijig. 5b, we see that in P ( eg.)6700
both cases the polarization is expected to be along b, in 0.2 (d50
(cid:86)
40
agreement with the conclusions derived from symmetry 0.1
0 100 200 300 400
arguments. T (K)
0
0 50 100 150 200
We alsospeculatethatthe similartemperaturedepen- T (K)
dence of P and q shown in Fig. 4 might indicate that
Dzyaloshinskii-Moriya (DM) and/or spin-current mech-
anisms could be responsible for the ferroelectricity. This
maylooksurprisinginviewofthelargevalueofthepolar- FIG. 9. (Color online) Temperature dependence of the elec-
ization in YBaCuFeO (0.64 µC/cm2). It is however tricpolarization (bluedots)andestimations usingθ andq as
5
∼ described in thetext (red diamonds and black open dots).
not unreasonable since TbMnO , where multiferroicity
3
is believed to originate from these mechanisms, displays
IX. SUMMARY AND CONCLUSIONS
a polarization which is only 6 times smaller ( 0.09
µC/cm2). ∼
As mentioned in the introduction, YBaCuFeO is
5
Fromtheabovementionedmechanisms,onewouldex- together with CuO the only known material to dis-
pectP c Si Sj, whereiandj arenearest-neighbor play switchable, magnetism-driven ferroelectricity above
∝ × ×
magnetic sites along c. As shown in Fig. 3d, the size of 200K.Aprerequisitetounderstandthe existenceofmul-
magneticmomentsbelowTN2isapproximatelyconstant. tiferroicity at such high temperatures in YBaCuFeO5 is
Therefore, one can assume the magnetic spiral state de- the knowledge of its ICM magnetic structure. However,
scribed by Eq. 2, where µ = 1,2 labels the magnetic it was never reported evenif its existence is knownsince
sites in Fig. 1, v1 =sin(θ)aˆ+cos(θ)ˆc, v2 =sin(θ)bˆ and 1995. In this study we have successfully synthesized
the spin value is constant. Moreover, as the magnetic YBaCuFeO ceramic samples of unprecedented quality
5
moments of neighboring magnetic ions along z not sepa- and we have conducted new, high-resolution and high-
ratedbyoxygenareantiparallel(seeFig.5bandTableII intensity neutron diffraction measurements that enabled
),onecanassumeφ2 =φ1+π. Undertheseassumptions us for the first time to solve the incommensurate mag-
theelectricpolarizationgivenbyDMand/orspin-current neticstructureofYBaCuFeO . Ourresultsareconsistent
5
coupling is Pb = Ccos(θ)sin(2π(21 − q)) where C is a with the replacement of the collinear magnetic order ex-
temperature-independent constant. isting between T and T = 340K by a circular spiral
N2 N1
withtemperaturedependentinclinationdescribedbythe
Fig.9showsthecomparisonbetweenthemeasuredval-
propagationvector k =(1/2, 1/2, 1/2 q).
ues of P (blue dots) and those obtained from the previ- i ±
The origin of the ferroelectricity observed below T
ous expression setting C in such a way that at the lower N2
and its coupling with the incommensurate magnetic or-
temperature the calculated polarization coincides with
der can not be fully explained from our results alone,
theobservedvalue. Thepointsrepresentedbyblackdots
in particular because our ceramic samples do not allow
wereobtainedusingthemeasuredvaluesofq andθ while
to determine the direction of the polarization. However,
for the points representedby red diamonds the values of
the symmetry of the observed magnetic spiral suggest
the linear interpolation of θ below 190 K were used (see
that P should be within the ab plane. Also, the very
inset of Fig. 9). Taking into account that the only free
similar temperature dependence of the magnetic modu-
parameter is the proportionality constant C, the agree-
lationparameterq andthepolarizationindicatethatthe
ment between the observed and calculated temperature
Dzyaloshinskii-Moriya and/or spin-current mechanisms
dependence of P is reasonably satisfactory.
could be at the origin of the magnetoelectric coupling.
According to the scenario described above, the ap- Furtherexperimentalwork,preferablyonsinglecrystals,
proximate proportionality of P and q originates from will be necessary to get additional insight about the va-
the relatively small changes in q (which implies P lidity of this scenario.
b
∝
2πCqcos(θ)) and the fact that θ does not change dra- Wehavealsoinvestigatedthecrystalstructure,inpar-
matically below T . We also note that this behavior ticular the Fe/Cu distribution between the two available
N2
would not hold if the size of magnetic moment would square-pyramidalsites,andwefindclearevidenceforthe
strongly depend on temperature below T , e.g., if the existence of occupational disorder. The observed CM
N2
magnetic spiral phase would appear close to T . magnetic structure suggests however that the bipyrami-
N1