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Solid State Sciences 5 (2003) 59–71www.elsevier.com/locate/sssc

(3+ 1)D superspace structural determination of two new modulatecomposite phases: Sr1+x(CuxMn1−x)O3; x = 3/11 andx = 0.3244

Ahmed El Abeda,b, Etienne Gaudina, Hans-Conrad zur Loyec, Jacques Darrieta,∗

a Institut de chimie de la matière condensée de Bordeaux (ICMCB-CNRS), 87, av. du docteur A. Schweitzer, 33608 Pessac cedex, Francb Laboratoire de physique du solide, faculté des sciences, Université Mohamed Ier, Oujda, Maroc

c Department of Chemistry and Biochemistry, University of South Carolina, Columbia, SC 29208, USA

Received 11 March 2002; accepted 16 May 2002

Dedicated to Sten Andersson for his scientific contribution to Solid State and Structural Chemistry

Abstract

We report the structure determination of two new phases belonging to the A1+x(A′xB1−x)O3 family of oxides with A= Sr, A′ = Cu,

and B= Mn, wherex = 3/11 andx = 0.3244, corresponding to a commensurate and incommensurate composite structure, respThese two compounds are the first examples of oxides belonging to the Sr1+x(CuxMn1−x )O3 family. Their structures were solved in th(3 + 1) dimensional superspace formalism as modulated composite structures with two subsystems [(Cu,Mn)O3] and [Sr]. The superspacgroup used to solve the structures isR3̄m(00γ )0s. The first phase(x = 3/11), corresponding to the chemical formula Sr14Cu3Mn8O33,was obtained as a single crystal with unit cell parameters ofa = 9.6025(3) Å and c1 = 2.5660(8) Å (q = 7/11c∗

1, Z = 3), wherec1 is thelattice parameter corresponding to thec-axis of the trigonal subsystem [(Cu,Mn)O3]. The second phase (x = 0.3244(1)), is a polycrystallinesample with unit cell parameters ofa = 9.5933(7) andc1 = 2.5933(3) (q = 0.6622c∗

1, Z = 3). In both structures, one dimensional charun along thec-axis which contain octahedra and trigonal prisms occupied by manganese and copper atoms, respectively. The rresults show that in both cases copper occupies the rectangular faces of the trigonal prism while manganese occupies the octaThe magnetic measurements of the polycrystalline phase (Sr1+x(CuxMn1−x )O3, x = 0.3244(2)) and the Curie constant obtained from thigh temperature susceptibility are in agreement with a spin state configuration ofS = 3/2 for Mn4+ andS = 1/2 for Cu2+. 2003 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.

Keywords:Perovskite; Composite structure; Modulation; Magnetic properties; Spin exchange interaction

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1. Introduction

Compounds structurally closely related to the 2-H hexonal perovskite and belonging to the A3n+3mA ′

nB3m+nO9m+6nfamily of oxides (A= alkaline earth, A′, B = alkali, alkalineearth and transition d-elements) have received a greatof attention in the recent literature. This interest has bmotivated by both structural investigations as well as byinteresting physical properties exhibited by oxides beloing to this family [1–19]. The main characteristic of thecompounds is that their structures can be described assisting of one dimensional chains made up of BIV O6 octahe-dra and A′II O6 trigonal prisms sharing faces along thec-axis.These chains are separated by columns of A cations. Aported by Darriet and Subramanian [1], the structures

* Corresponding author.

E-mail address:darriet@icmcb.u-bordeaux.fr (J. Darriet).

1293-2558/03/$ – see front matter 2003 Éditions scientifiques et médicalesdoi:10.1016/S1293-2558(02)00081-X

l

-

-

be described as resulting from the stacking ofn(A3A ′O6)andm(A3O9) layers, where the generated octahedral sare occupied by the B cations. Alternatively, the compotion of the whole family can be expressed by the genformula A1+x (A ′

x ,B1−x)O3 wherex = n/(3m+ 2n). By thelatter formalism, the structures are best described as bcomposite systems resulting from the combination of twodependent crystallographic substructures [8,20,21]. Theone consists of [(A′,B)O3] chains withc-lattice parameterc1

and the second one is formed by the A cations with a pmeterc2 (c2 ≈ cperov≈ 2c1, cperov is thec-parameter of 2Hhexagonal perovskite). The two subsystems interact stroand create a modulation along thez-direction. A unifying de-scription of these phases as a modulated composite struusing the superspace formalism is by now well establis[8,13,15,20,21].The composition of a given phase belongto the A1+x (A ′

x ,B1−x )O3 family is directly related to theγ∗ ∗

component of the modulation vector,γ = c1/c2 = c2/c1 =

Elsevier SAS. All rights reserved.

60 A. El Abed et al. / Solid State Sciences 5 (2003) 59–71

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(1 + x)/2, where the [(A′,B)O3] system is used as the reerence. Theγ value can vary between 0.5 and 0.75 corsponding tox values of 0� x � 0.5. Depending on the fractional value ofγ (irrational or rational) the composite systecan be considered as an incommensurate or a commensstructure, respectively. In the latter case,γ can be expresseas a fractionγ = p/q (p andq integers) where the supestructure cell parametercs is given bycs ≈ c1q ≈ c2p.

In this family of oxides, the existence of order and dorder within octahedral and trigonal prismatic sites remaan important issue, as it directly impacts our ability to uderstand the physical properties of these materials. Msingle crystal structure determinations using the supersformalism have established the tendency of the A′ cationsin their trigonal prismatic sites to move out of the centerthe site toward/into the faces of the trigonal prism [8,11,115,18,19]. Other oxide phases, whose structures havesolved on X-ray powder data using the classic 3D formaliexhibit disorder or similar displacements of cations towathe rectangular faces of trigonal prisms [3,6,7,10,12]. Hever such polycrystalline commensurate composite cpounds are very difficult to obtain, and one must pay clattention to the accurate control of the chemical composiof the phase. As demonstrated recently [18,19] a slightference in composition of two oxides Sr1+x (NixMn1−x)O3

(x = 1/3 andx = 0.3244) results in significant differencein the observed magnetic properties.

In this paper, we present the full structural invesgation of the first modulated composite members ofSr1+x (CuxMn1−x)O3 family with values ofx = 3/11 andx = 0.3244(2). The first compound (x = 3/11, i.e.,Sr14Cu3Mn8O33) is a commensurate composite structand was obtained in single crystal form. Its compositcorresponds to that of then = 9 andm = 5 member ofthe A3n+3mA ′

nB3m+nO9m+6n series, where to date, very feisostructural compounds have been described in the liture. We are aware of only two isostructural oxides that hbeen reported, namely (i) Sr14Co11O3 [11], where a singlecrystal structure determination showed that the cobalt aoccupies both the octahedral and trigonal prism sites, ana polycrystalline and a single crystal structure determinaof Ba14Cu3Ir8O33 [7] and [14], where the rectangular facof the trigonal prisms are partially [7] or totally [14] occpied by the copper atoms. In fact, for most other comptions, results obtained from powder X-ray diffraction daindicate that copper always occupies the trigonal prismsite and in several cases is displaced from the three foldtoward the rectangular faces: Sr4CuIr2O9 [6], Ba6CuIr4O15

[3], Ba5CuIr3O12, Ba9Cu2Ir5O21 and Ba16Cu3Ir10O39 [7],Ba6Mn4CuO15 [12], Sr3CuIrO6 [22] and Sr3CuPtO6 [23].

The structure of the second, polycrystalline phaSr1.3244(Cu0.3244,Mn0.6756)O3 (x = 0.3244(2)) was shownto be an incommensurate composite structure. Determithe structure of this polycrystalline incommensurate co

′

posite material belonging to the A1+x (Ax ,B1−x )O3 family

te

n

of oxides, represents the first time that this has been achiusing the(3+ 1)D superspace formalism.

For the structure determination of theses two phasesrefinements were carried out using the(3 + 1) dimensionalsuperspace formalism in the centrosymmetric supersgroupR3̄m(00γ )0s. The structure description was achievusing a saw tooth function to model both the occupatioand the displacive modulations of the atoms [8,20].

2. Experimental

2.1. Single crystal: Sr14Cu3Mn8O33

2.1.1. SynthesisSingle crystals of Sr14Cu3Mn8O33 were grown by flux

synthesis. A ground mixture of SrCO3 (Aldrich 99.9%),Mn2O3 (Aldrich 99.999%) and CuO (Aldrich 99.99%) waplaced into an alumina crucible and covered by ab20 g of K2CO3. The sample was heated in air from 251200◦C at 60◦C/h, kept at this temperature for 48 hours asubsequently cooled to 880◦C at 6◦C/h. At this temperaturethe furnace was turned off and allowed to cool to rotemperature. The single crystalline product was recovfrom the melt by washing with distilled water.

2.1.2. Data collectionSeveral single crystals were tested and their quality

sessed on the basis of the size and the sharpness of thfraction spots. First, a rapid scan on an Enraf-Nonius KpaCCD diffractometer using MoKα radiation gave a hexagonal cell with parametersa = 9.6025 Å andc = 28.2260 Å.The measurements indicated the existence of the misfit cacter of the structure and the contribution of the two ssystems [Sr] and [(Cu,Mn)O3] was clearly distinguished bthe miller indices (hkL). Three kinds of reflections were observed: (i) intensehkL reflections withL = 7 · m (m inte-ger) identified as being reflections due to the [Sr] substem, (ii) less intensehkL reflections withL = 11 · l (l in-teger) assigned to the second subsystem [(Cu,Mn)O3], (iii)weak reflectionshkL whereL can be expressed as a comnationL = 11 · l + 7 · m (l andm = 0), identified as satellite reflections due to the strong interaction between thesubsystems. As is known for these composite systemsexplained in references [8,11,20] this interaction genera modulation vectorq along thec-axis. If the subsystem[(Cu,Mn)O3] is chosen as the reference system, the molation vector componentγ is given byγ = c1/c2 (= c∗

2/c∗1),

wherec1 and c2 are thec-axis parameters of the [Sr] an[(Cu,Mn)O3] subsystems, respectively. In order to calculthe value ofγ exactly, measurements were carried outa CAD4 diffractometer and data were collected for esubsystem. 25 reflections were centered and the refineled to the following parameters:c1 = 2.5660(8) Å for the[(Cu,Mn)O3] subsystem,c2 = 4.0322(3) Å for the [Sr] sub-

system, and ana-parameter (a = 9.6025(3) Å) common to

A. El Abed et al. / Solid State Sciences 5 (2003) 59–71 61

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Table 1Crystallographic data for Sr14Mn8Cu3O33

Physical, crystallographic, and analytical dataFormula Sr1.2727Mn0.7273Cu0.2727O3Crystal color blackMW (g mole−1) 216.8Crystal system TrigonalSuperspace group R3̄m(00γ )0sNo. of reflections used for 17761cell parameters determinationParameters a = 9.6025(3) Å, c1 = 2.5660(8) Å,

q = 0.6363(3)c∗1V (Å3) 204.91(6)Z 3Density calc. (g·cm−3) 5.27Crystal description hexagonal blocCrystal size (mm) 0.056× 0.06× 0.094

Data collectionTemperature (K) 293Diffractometer Enraf-Nonius KappaCCDMonochromator Oriented graphiteRadiation MoKα (λ= 0.71069 Å)Scan mode CCD scanh k l range −11< h< 14,−14< k < 13,

−41< l < 42θmax 32.00◦

Data reductionLinear absorption coeff. (mm−1) 30.00Absorption correction GaussianTmin/Tmax 0.1643/0.2678No of reflections 2139Rint 0.0678No of independent reflections 5128Criterion for observed reflections I > 3.0σ(I )Number of observed reflections 1376

Refinement resultsRefinement F2

F(000) 295Twin matrix (78%) 1̄00/01̄0/001R factors R(F)= 4.68%,wR(F2)= 11.05%Main reflections (384) R(F)= 3.21%,wR(F2)= 8.10%First order (610) R(F)= 5.23%,wR(F2)= 10.33%Second order (312) R(F)= 8.01%,wR(F2)= 15.85%Third order (70) R(F)= 15.55%,wR(F2)= 41.61%No. of refined parameters 52Weighting scheme w = 1/(σ2(I )+ 0.0004I2)

Diff. Fourier residues (e/Å3) [−3.0,+2.6]

both subsystems. The modulation component (γ = c1/c2)therefore equalsγ = 0.6363(2), which is close to the fraction γ = 7/11. This value demonstrates that this phasea commensurate, modulated composite structure. If we cosider the reduced formula Sr1+x (Cux ,Mn1−x)O3, the valueof x can be derived from the relationship:γ = (1 + x)/2,wherex = 3/11.

The final data collection was carried out on the KapaCCD diffractometer. Intensity data were collected insupercell approach usingγ = 7/11 (a = 9.6025(3) Å and

c ≈ 7 · c2 ≈ 11· c1 ≈ 28.2260(8) Å).

Data processing, transformation of the 3D indices(3 + 1)D (hklm) values and the refinement were performusing the Jana2000 program package [24]. A Gaussianabsorption correction was applied, where the shape ocrystal was determined using the video microscope ofKappaCCD instrument (Table 1).

2.2. Polycrystalline sample: (Sr1+xCuxMn1−xO3,x = 0.3244)

2.2.1. SynthesisA powder sample was prepared in an alumina cruc

using the standard solid state synthesis method. A mixof SrCO3, Mn2O3 and CuO, corresponding to the overcomposition ofx = 1/3, was thoroughly ground using aagate mortar, heated at 900◦C for 24 h to decompose thcarbonate, and subsequently pelletized, and heated prosively at temperatures up to 1250◦C with intermittent grind-ing. The progress of the reaction was carefully followedX-ray diffraction and the reaction was deemed to be coplete when no further changes were observed in the difftion pattern. The structural model described in referencefor applying the(3+ 1)D superspace formalism to compoite compounds belonging to the A1+x (A ′

x ,B1−x )O3 familyillustrates that the evolution of the structure based onanalysis of X-ray powder diffraction data is very useful aallows the determination of an accuratex-value. Thus theformula unit was formally identified as Sr1+xCuxMn1−xO3,with x = 0.3244(2) (vide infra).

2.2.2. Data collectionX-ray powder diffraction data of the final produc

Sr1+xCuxMn1−xO3, x = 0.3244, was collected at roomtemperature over the angular range 5◦ � 2θ � 110◦ with astep size of∆(2θ)= (0.02)◦ using a Phillips X-pert diffrac-tometer operating with CuKα radiation.

The X-ray diffraction data was refined by a profile anasis using the Jana2000 program package. The backgrwas estimated by a Chebyshev function and the peak shwere described by a pseudo-Voigt function varying six pfile coefficients [25]. The refinement of peaks asymmewas performed using four parameters [26].

2.2.3. Magnetic measurements of Sr1+xCuxMn1−xO3

(x = 0.3244)Magnetic measurements were carried out using a Q

tum Design SQUID magnetometer. The susceptibility wmeasured in the range 5 to 390 K in an applied field of 10where the magnetisation is linear with applied field overwhole temperature range. Identical data were obtainedboth zero field cooled (ZFC) and field cooled (FC) measu

ments.

62 A. El Abed et al. / Solid State Sciences 5 (2003) 59–71

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3. Results

3.1. Refinements

The structure refinements for both the single cry(Sr14Cu3Mn8O33) and the polycrystalline samp(Sr1+xCuxMn1−xO3, x = 0.3244) used the(3 + 1)D su-perspace formalism approach, in the centrosymmetricperspace groupR3̄m(00γ )0s. As proposed by Perez-Matet al. [20] a sawtooth function, defined by its centre(x̂4),its width (∆) [27,28] and its maximum amplitude for thdisplacivez-component (δ), was used for the description othe atomic positions of Mn, Cu and O (the first subsyst[(Cu,Mn)O3] was used as the reference). For the [Sr] ssystem the superspace group isP 3̄c1(001/γ ). No saw toothfunction was used for the strontium atom. Only one inpendent position of the Sr atom(1/3,0,1/4), with full oc-cupancy and the corresponding atomic modulation func(AMFs) described by a Fourier series, was needed toscribe the two types of Sr atoms belonging to the Sr3O9 andSr3CuO6 layers.

3.1.1. Single crystalThe compound Sr14Cu3Mn8O33 (or Sr1+xCuxMn1−xO3,

with x = 3/11) has a modulated composite structure wtwo subsystems, [(Cu,Mn)O3] and [Sr], having the sama-parameter and differentc-parameters,c1 andc2, respec-tively. The observation of the Bragg reflectionH = ha∗ +kb∗ + lc∗

1 + mc∗2 = (h, k, l,m) shows the contributions o

the two subsystems where one can distinguished betwthe main reflections(h, k, l,0) and (h, k,0,m) (with l = 0and m = 0) generated by the two subsystems. The mulations of the two subsystems create true satelliteflections (h, k, l,m) with l andm = 0. The observed extinction conditions—h + k + l = 3n for (h, k, l,m) andm = 2n for (h,0, l,m) are consistent with the superspagroupsR3m(00γ )0s and the corresponding centrosymmric R3̄m(00γ )0s.

The use of the superspace formalism approach toscribe the structures of compounds belonging to the fily A 1+x (A ′

x ,B1−x)O3, deriving from the 2H hexagonal peovskite, is now well documented [8,11,13–15,20]. In tcase, thez-modulation component of theq vector isγ =

7/11. Consequently, the structure was treated as acom-

mensuratemodulated composite structure. The(3 + 1) di-mensional centrosymmetric superspace groupR3̄m(00γ )0sgives rise to three possible 3D space groups (P 3̄, P32 andP3) depending of thet-phase section (t = 0, t = 1/4 andtarbitrary, respectively) [8,20]. Each possible section wtested using the same number of refinable parametersTheP3 andP 3̄ three dimensional space groups gave silar residualR-factors(R(F ) ≈ 0.0522). The space grouP32 gave a lower residualR-factor (R(F ) = 0.0468) and,thus, by comparison, appeared to be the better choice.sequently, the sectiont = 1/4 was chosen for the structurefinement and the discussion of the corresponding commsurate model will be limited to thet = 1/4 section.

The refinement was started by considering theplacive z-component(δ) as the only refinable parametfor the [(Cu,Mn)O3] subsystem, where manganese and cper atoms occupy the center of the octahedra and trnal prisms, respectively. Subsequently, first and secondder displacive modulations for Sr were added. The reual R factor converged toR(F) = 0.552 (wR(F 2) =0.771). The application of the common obverse/revetwinning law leads to a reduction in theR-factor toR(F) =0.148 (wR(F 2) = 0.355). At this stage of the refinementhe isotropic atomic displacement of the Cu atom exhiba large thermal parameter,Uiso = 0.1225 Å2. The analysisof the Fourier difference map att = 0.25 revealed a verylarge maximum in the electron density located towardcenter of the rectangular faces of the trigonal prism atposition(x, x,0) with x ≈ 0.05 (Fig. 1). Taking this obser

Fig. 1. x1x2 section atx3 = 0 and x4 = 1/4 of the difference Fouriecontour maps around Cu. Contour lines in intervals of 2.0 (e/Å3).

Table 2Average atomic positions for Sr14Mn8Cu3O33

Atoms x0 y0 z0 x̂4 ∆ U∗eq (Å2)

Subsystem [(Mn,Cu)O3]: R3̄m(00γ )0sMn 0 0 0 0 0.3637 0.0094(2)Cu 0.0519(3) 0.0519(3) 0 1/4 0.1363 0.0153(8)O 0.1559(3) 0.1559(3) 1/2 1/4 0.5 0.0189(9)

Subsystem [Sr]:P 3̄c1(001/γ )Sr 1/3 0 1/4 0.0118(2)

Ueq= 1/3∑

i

∑j Uij a

∗ia∗j

ai · aj.

A. El Abed et al. / Solid State Sciences 5 (2003) 59–71 63

Table 3Anisotropic displacement parametersUij (Å)2 for Sr14Mn8Cu3O33

U11 U22 U33 U12 U13 U23

Mn 0.0088(3) = U11 0.0108(4) = 1/2 ·U11 0 0Cu 0.0162(9) = U11 0.0211(11) 0.0138(9) 0.0016(6) = −U13O 0.0154(10) = U11 0.0219(13) 0.0046(11) 0.0002(5) = −U13Sr 0.0110(2) = U11 0.0133(3) = 1/2 ·U22 0 0

The anisotropic displacement factor exponent takes the form:−2π2 ∑i

∑j Uij a

∗ia∗j

hi · hj.

Table 4Atomic positional and Debye–Waller factors modulation coefficients for Sr14Mn8Cu3O33 (only coefficients= 0 are given)

Mn UMnz,1 = −0.0049(4) UMn

z,3 = 0.0067(6)

UMnz,5 = −0.0056(9)

Amplitude= −0.01982= δMn/c1 x̂4 = 0 ∆ = 0.3636

UMnU11,2 = UCo1

U22,2 = 2UCo1U12,2 = −0.0027(3)

UCo1U33,2 = 0.0009(6)

Cu UCux,1 = UCu

y,1 = −0.0006(3) UCuz,1 = 0.0069(12)

UCux,2 = UCu

y,2 = −0.0007(9)

Amplitude= −0.0178= δCu/c1 x̂4 = 1/4 ∆ = 0.1364

O UOz,2 = 0.0027(10)

UOx,3 = −UO

y,3 = −0.0047(2) UOz,3 = 0.0007(8)

UOx,4 = −UO

y,4 = −0.0024(3)

Amplitude= −0.1456= −δO/c1 x̂4 = 1/4 ∆ = 12

UOU11,1 = UO

U22,1 = −0.013(1) UOU33,1 = −0.0097(15)

UOU12,1 = −0.0072(13) UO

U13,1 = −UOU23,1 = −0.0003(5)

UOU11,2 = −UO

U22,2 = −0.0024(11) UOU13,2 =UO

U23,2 = 0.008(1)

UOU11,3 = −UO

U22,3 = 0.0025(10) UOU13,3 =UO

U23,3 = −0.0025(10)

UOU11,4 = UO

U22,4 = −0.0022(10) UOU33,4 = −0.0007(14)

UOU12,4 = −0.0018(11) UO

U13,4 = −UOU23,4 = −0.0007(7)

Sr USrx,S1 = 0.5USr

y,S1 = −0.00928(3) USrx,C1 = 0.01608(5)

USrx,S2 = 0.5USr

y,S2 = 0.00402(2) USrx,C2 = 0.00696(4)

USrz,S3 = 0.0023(2)

USrx,S4 = 0.5USr

y,S4 = −0.00128(10) USrx,C4 = 0.0022(2)

USrx,S5 = 0.5USr

y,S5 = −0.00025(12) USrx,C5 = 0.0004(2)

USrz,S6 = 0.0039(25)

USrU11,S1 = USr

U12,S1 = 0.0028(1) USrU13,S1 = −0.0051(1)

USrU11,C1 = −0.5USr

U22,C1 = −USrU12,C1 = 0.00161(8)

USrU13,C1 = 0.5USr

U23,C1 = −0.00294(7)

USrU11,S2 = USr

U12,S2 = −0.00028(2) USrU13,S2 = −0.00274(16)

USrU11,C2 = −0.5USr

U22,C2 = −USrU12,C2 = 0.00016(10)

USrU13,C2 = 0.5USr

U23,C2 = −0.00158(9)

Modulation functions for a parameterλ of an atom ν defined in restricted interval (case of Mn, Cu and O) are given by:Uνλ (x4) =

∑kn=0U

νλ,n Orthoνn(x4), where the orthogonalized functions, obtained through a Schmidt orthogonalization routine, are given by: Orthoν

i (x4) =Bν

0 + ∑kn=1A

νn sin(2πnx4) + ∑k

n=1Bνn cos(2πnx4). For Sr atom, the modulation functions are classically expressed as:Uν

λ (x4) = Uνλ,0 +

∑kn=1U

ν sin(2πnx4)+ ∑kn=1U

ν cos(2πnx4).

λ,Sn λ,Cn

omcy-thesity

d to

therieror

vation into account, a split model, displacing the Cu atfrom the three fold axis, was used. A few refinementcles clearly indicated that the Cu atom is only located infaces of the trigonal prism, as no residual electron denwas observed in the center of the trigonal prism. TheR fac-

2

tor converges rapidly toR(F) = 0.102 (wR(F ) = 0.257)

and the isotropic atomic displacement (ADP) decreaseUiso = 0.0148 Å2.

To account for the remaining electron density inFourier difference maps, higher order displacive Fouamplitude waves (4 for Mn, 2 for Cu, 3 for O and 6 f

Sr), anisotropic displacement factors for all atoms and higher

64 A. El Abed et al. / Solid State Sciences 5 (2003) 59–71

Table 5Coefficients of the orthogonalized functions for Sr14Mn8Cu3O33

Orthoνi Bν0 Aν

1 Bν2 Aν

3 Bν4 Aν

5 Bν6

ν = Mn

OrthoMn0 1

OrthoMn1 0 1.729

OrthoMn2 −0.623 0 1.882

OrthoMn3 0 −1.681 0 2.055

OrthoMn4 1.216 0 −2.203 0 2.249

OrthoMn5 0 3.394 0 −2.819 0 2.464

OrthoMn6 −2.504 0 4.607 0 −3.542 0 2.702

ν = O Bν0 Aν

1 Bν1 Aν

2 Aν3

OrthoO0 1

OrthoO1 −2.069 3.249

OrthoO2 0 0 1.414

OrthoO3 0 0 −2.271 2.675

OrthoO4 −2.187 2.785 0 0 1.953

ν = Cu Bν0 Bν

1 Bν4

OrthoCu0 1

OrthoCu1 0 4.118

OrthoCu2 −1.632 0 2.826

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illerdmg totemgthe

n

order Debye–Waller factor (DWF) modulation waves (1Mn, 2 for O and 2 for Sr), were progressively introducBecause the atomic modulation functions (AMFs) wnot completely defined along the internal coordinatex4,the higher order displacive AMFs were introducedapplying an orthogonalization procedure to the Fouseries coefficients to reduce correlation’s [27]. The firesidual factor converged toR(F) = 0.0468 (wR(F 2) =0.1105) for a total of 52 variables (Table 1). The final resuare given in Tables 2–5.

3.1.2. Polycrystalline sample: Sr1+xCuxMn1−xO3

(x = 0.3244(2))3.1.2.1. Structural analysis.Before describing the refinement process it is instructive to discuss, in general, the Xdiffraction analysis and the identification of the phase.was expected, the compound is a composite system coning two subsystems [(Cu,Mn)O3] and [Sr]. The synthesis othe powder sample as a commensurate phase remainsdifficult and one must take great care controlling the preration conditions and heat treatments. The transition frocommensurate to an incommensurate system can occura narrow temperature range and heating time [6,12]. Sutransition is in general not reversible by an additional thmal treatment. Initially the synthesis targeted the commsurate phase withγ = 2/3 (γ = (1 + x)/2), however, aftertrying several different synthetic strategies, the final prodalways corresponded to a composition with a slightly smavalue ofγ (γ < 2/3). Analysis of the X-ray diffraction patterns, indicated successive appearance of different inc

mensurate phases. The thermal treatment was stopped whe

-

y

r

the X-ray pattern stopped changing, both with respect toappearance/disappearance of peaks and the peak posit

The first attempt to identify the incommensurate phwas done by indexing the Bragg peaks using two subcThe first subcell, [(Cu, Mn)O3], was indexed in spacgroupR3̄m with a = 9.5917(7) Å and c1 = 2.5946(2) Å;the second subcell [Sr] was indexed in space groupP 3̄c1with a = 9.5927(4) Å and c2 = 3.9161(2) Å. The c1/c2

ratio (γ = 0.6625) clearly indicated that the phase is ncommensurate. As shown in Fig. 2, Bragg peaks belonto either the first subsystem or to the second subsystemwell indexed in this approach. However we can seethere remain some peaks that are not indexed (see arin Fig. 2). For the second attempt, we used the supersformalism approach with the(3 + 1)D superspace grouR3̄m(00γ )0s (γ = c1/c2 = (1+x)/2) [8,20] to index all theBragg peaks of the incommensurate phase using four mindices (h, k, l,m). The Bragg peaks were fully indexewith four (h, k, l,m) indices (Fig. 3). The first subsysteis characterised by weak peak intensities correspondin(h, k, l,0) in comparison with those of the second subsys[Sr] corresponding to(h, k,0,m) reflections. The remaininpeaks are true satellites and are fit by reflections oftype (h, k, l,m, with l andm = 0), which result from theinteraction between the two subsystems. Thed-spacing ofthe (h, k, l,m) reflections is given by(1/d2) = (4/3a2)(h2+k2 + l2)+ (l + mc1/c2)

2/c21. The final compound has bee

identified as having the compositionx = 0.3244(2) withlattice parameters ofa = 9.5933(7) Å, c1 = 2.5933(3) Åand γ = 0.6622(1) (q = 0.6622(1)c∗

1), where the [(Cu,

nMn)O3] subsystem is being used as the reference system.

A. El Abed et al. / Solid State Sciences 5 (2003) 59–71 65

Fig. 2. Observed (∗), calculated (—) and difference X-ray diffraction patterns from Sr1+xCuxMn1−xO3 (x = 0.3244). Profile obtained with two independentsubcells with 3D space groups. The insert (a) shows a part of non indexed satellite reflections.

Fig. 3. Observed (∗), calculated (—) and difference X-ray diffraction patterns from Sr1+xCuxMn1−xO3 (x = 0.3244). Profile obtained usingR3̄m(00γ )0s(3+ 1)D superspace group.

66 A. El Abed et al. / Solid State Sciences 5 (2003) 59–71

of

o-ions

.lliteec-

dingrre-

elyy us

llite2x-

ever

ide,-

len-tahefirstthe

r

ce--c-dle

c-out.

lo-op-ces

la-ererge,

n

ic

turenyZeroverag-lot0 K

de-

Fig. 4. Comparison of profile analysis of XRD patternSr1+xCuxMn1−xO3 (x = 0.3244) obtained for two closeγ -values(a) γ = 0.6630 and (b)γ = 0.6622.

It is important to notice that during this identification prcedure, we were able to distinguish between compositthat are very close to one another, for examplex = 0.3244(γ = 0.6622) andx = 0.3260 (γ = 0.6630) (see Fig. 4)This was possible because of the presence of true satethat are very sensitive to the variation of the modulation vtor and therefore of the composition(x). In particular, this isobserved for the first order satellite reflections corresponto (2,0, 1̄,2) and also for the second order satellites cosponding to(1,0, 2̄,4 and 1,0, 2̄,2). The difficulty in find-ing the correct lattice parameters for compositionally closrelated composite compounds, as pointed out earlier b[18] and Battle [6,12], is that the change of the 2θ peak po-sitions is not unidirectional. In other words, some satereflections move to higher and some to lower values ofθ

whenc1 and/orγ is varied. Consequently, matching the eact positioning of these peaks remains a challenge, howwhen it is achieved, the solution is unique forc1 andγ .

Structure refinement of the incommensurate oxSr1.3244Cu0.3244Mn0.6756O3, using the collected XRD powder data, was successfully carried out in the(3 + 1)D cen-trosymmetric superspace groupR3̄m(00γ )0s. The refine-ment was started by consideringδ (the maximum ampli-tude for the displacivez-component) as the only refinabparameter for the [(Cu,Mn)O3] subsystem, where the maganese and copper atoms occupy the center of the ocdra and trigonal prisms, respectively. Subsequently, aorder displacive modulation was introduced to model

strontium atom. The residualR factor converged toR =

s

,

-

Fig. 5. x1x2 section atx3 = 0 and x4 = 1/4 of the difference Fouriecontour maps around Cu. Contour lines in intervals of 0.3 (e/Å3).

0.0823 (Rp = 0.0426,Rwp = 0.0587 andχ2 = 10.39). Atthis step copper exhibits a large isotropic atomic displament (Uiso = 0.1513 Å2). An analysis of the Fourier difference map atx4 = 0.25 revealed a very large residual eletron density near the Cu position, located near the midof the rectangular faces of the trigonal prism at(x, x,0),x ≈ 0.05 (Fig. 5). Allowing the copper atoms to also ocupy these sites, several refinement cycles were carriedAt this point it became clear that there is no coppercated at the center of the trigonal prism and that the cper atoms occupy only the positions in the rectangular faof the trigonal prisms with full occupancy. TheR factorconverged toR = 0.0771 (Rp = 0.0375,Rwp = 0.0528 andχ2 = 8.41). Subsequently, higher order displacive modution waves (order 2 for Mn, and O and order 6 for Sr) wintroduced. This caused the refinement to quickly convereducing the residualR factor toR = 0.0419 (Rp = 0.0293,Rwp = 0.0383 andχ2 = 4.44). The final results are listed iTables 6–8.

3.1.2.2. Magnetic properties.The inverse molar magnetsusceptibility for the incommensurate Sr1.3244Cu0.3244-Mn0.6756O3 phase, measured as a function of temperaat 1 kG, is shown in Fig. 6. The data did not reveal afield dependence for measurements carried out underField Cooled (ZFC) and Field Cooled (FC) conditions othe temperature range of 2–350 K. Up to 50 kG the mnetisation is linear with the applied magnetic field. The pshows a pseudo-plateau of the susceptibility between 6and 140 K. Above 200 K,(χ−1) follows a Curie–Weiss lawwith C = 1.46 emu·K·mol−1.

4. Discussion

In modulated structures, the atomic positions arescribed by their average position (x0, y0, z0) plus an atomicmodulation function (AMF)Ur(x4) = (Ux(x4), Uy(x4),Uz(x4)). Fig. 7 is a plot of the variation of thez-coordinates

of the atomic positions of Sr14Mn8Cu3O33 versust (t =

A. El Abed et al. / Solid State Sciences 5 (2003) 59–71 67

Table 6Average atomic positions and crenel functions for Sr1.3244Mn0.6756Cu0.3244O3

Atoms x0 y0 z0 x̂4 ∆ U∗eq (Å2)

Subsystem [(Mn,Cu)O3]: R3̄m(00γ )0sMn 0 0 0 0 0.3378 0.012(2)Cu 0.0555(11) 0.0555(11) 0 1/4 0.1622 0.023(5)O 0.1563(6) 0.1563(6) 1/2 1/4 0.5 0.010(2)

Subsystem [Sr]:P 3̄c1(001/γ )Sr 1/3 0 1/4 0.0066(12)

Ueq= 1/3∑

i

∑j Uij a

∗i a

∗j ai · aj.

Table 7Atomic positional modulation coefficients for Sr1.3244Mn0.6756Cu0.3244O3 (only coefficients= 0 are given)

Mn UMnz,1 = 0.022(2)

Amplitude= −0.05246= δMn/c1 x̂4 = 0 ∆= 0.3378

Cu Amplitude= −0.0384= δCu/c1 x̂4 = 1/4 ∆= 0.1622

O UOz,2 = 0.0075(23)

UOx,2 = −UO

y,2 = −0.0031(5)

Amplitude= −0.1426= −δO/c1 x̂4 = 1/4 ∆ = 0.5

Sr USrx,S1 = 0.5USr

y,S1 = −0.01001(9) USrx,C1 = 0.0173(2)

USrx,S2 = 0.5USr

y,S2 = 0.0049(2) USrx,C2 = 0.0085(3)

USrz,S3 = 0.0033(26)

USrx,S4 = 0.5USr

y,S4 = −0.0015(8) USrx,C4 = −0.0025(13)

UMnz,3 = 0.5x̂ = −0.0040(9) USr

x,C5 = −0.0070(16)

USrz,S6 = 0.0305(34)

Modulation functions for a parameterλ of an atom ν defined in restricted interval (case of Mn, Cu and O) are given by:Uνλ (x4) =

∑kn=0U

νλ,n Orthoνn(x4), where the orthogonalized functions, obtained through a Schmidt orthogonalization routine, are given by: Orthoν

i(x4) =

Bν0 + ∑k

n=1Aνn sin(2πnx4) + ∑k

n=1Bνn cos(2πnx4). For Sr atom, the modulation functions are classically expressed as:Uν

λ (x4) = Uνλ,0 +

∑kn=1U

νλ,Snsin(2πnx4)+ ∑k

n=1Uνλ,Cncos(2πnx4).

tibility

ms.uratfethe

ionely

ed

tingod-

Fig. 6. Temperature dependence the inverse molar magnetic suscepof Sr1+xCuxMn1−xO3 (x = 0.3244).

x4 − q · r) for the oxygen, manganese and copper atoThe squares and circles correspond to the commenscase(t = 1/4) and represent thez-atomic coordinates othe chain located atx ≈ 0 andy ≈ 0. As can be seen, thsaw-tooth function effectively models the modulation of

oxygen and copper positions. Only for manganese does one

e

Table 8Coefficients of the orthogonalized functions for Sr1.3244Mn0.6756-Cu0.3244O3

Orthoνi Bν0 Aν

1 Bν2

ν = Mn

OrthoMn0 1

OrthoMn1 0 1.827

OrthoMn2 −0.829 0 2.067

ν = O Bν0 Aν

1 Bν1

OrthoO0 1

OrthoO1 −2.069 3.249

OrthoO2 0 0 1.414

observe slight deviations from the ideal saw-tooth functrequiring additional, higher order, modulations to effectivdescribe the manganese positions.

In most modulated compounds belonging to the A1+x (A ′x ,

B1−x )O3 family, the chemical formula can be predictdirectly from the cell parametersc1 and c2 and thus, inturn, the stoichiometry can be determined before stara structure refinement. Moreover, for commensurate m

ulated structures, the knowledge of the composition (x),

68 A. El Abed et al. / Solid State Sciences 5 (2003) 59–71

et

m-c-l

se-face

as

ismonal

the

f

se-

uc-ce-

fromnidthev-gen

Thee,e.

in

odic-to

d at

re-

for

ore:

Fig. 7. Variation of the fractionalz coordinate of [(Cu,Mn)O3] subsystemversust (t = x4 − q · rav). The points correspond to the commensuratz

atomic coordinates into the chain atx = y = 0 (circles) and the chain ax = 1/3, y = 2/3 (squares).

which is directly related to the modulation vector coponentγ = (1 + x)/2 [20], provides the sequence of otahedra (Oct) occupied by(1 − x) B atoms and trigonaprisms (TP) occupied byx A ′ atoms along thec-axis. Inour case, theγ value is 0.6363= 7/11 (x = 0.2727= 3/11)and the ratio (TP)/(Oct)= x/(1 − x) = 3/8 implies thatthe [(Cu, Mn)O3] subsystem chains consist of repeatingquences of 3 face-sharing trigonal prisms (TP) and 8sharing octahedra (Oct). The formula can be writtenSr14/11(Cu3/11Mn8/11)O3 or Sr14Cu3Mn8O33.

The repeat sequence of the octahedra and trigonal prcan be deduced from the Farey tree [29], where the fractivalue ofx is expressed asx = r/s, wherer and (s − r) rep-resent the number of the trigonal prisms and octahedra insingle repeat sequence,r = 3 and(s − r) = 8, respectively.Furthermore,x = 3/11 can be written as a “combination” otwo fractions(r1/s1) = 1/3 and(r2/s2) = 1/4, specificallyx = 3/11= (r1 + 2r2)/(s1 + 2s2) = (1 + 2∗1)/(3 + 2∗4).Consequently, the sequence of polyhedra along thec-axiscan be described as the juxtaposition of the following twoquences: two times (1TP+ 3Oct)+ one time (1TP+ 2Oct).The projection of this composite structure along thec-axis isshown in Fig. 8, where the two subsystem [(Cu,Mn)O3] and[Sr] chains are clearly identified. A view of the superstrture is given in Fig. 9 showing the repeat sequence of fasharing octahedra and trigonal-prisms as determinedthe structure refinement (sectiont = 1/4). This sequence cabe obtained alternatively by considering the domains w(∆) occupied by each Mn and Cu atom. As described in seral papers [8,11,14,15,17,20], the positions of the oxyatoms can be split into two groups, Oa and Ob, consisting ofthree oxygen atoms forming an equilateral triangle each.succession of Oa–Ob (or Ob–Oa) creates an octahedral sitwhereas Oa–Oa (or Ob–Ob) creates a trigonal prismatic sitThe domains width(∆) of the octahedra (Octa–b or Octb–a)

and that of trigonal prisms (TPa–a or TPb–b) depend on the

s

Fig. 8. Approximate [001] projection of the Sr14Cu3Mn8O33 structure.

Fig. 9. [110] view of the Sr14Cu3Mn8O33 superstructure (a) and the chaat x = 0, y = 0 (b).

compositionx, containing(1 − x)/2 Mn atoms and(x/2)Cu atoms, respectively. Each domain represents a periity of 1/2 alongx4 and should be symmetric with respectx̂4 = 0 andx̂4 = 1/2 (Fig. 10). In our case, sincex = 3/11,the crenel function for the manganese is centred atx̂4 = 0(and x̂4 = 1/2) by symmetry with(∆)Mn = (1 − x)/2 =4/11. The crenel function for the copper atom is centrex̂4 = 1/4 (andx̂4 = 3/4) with (∆)Cu = (x/2) = 3/22. Thesequence of octahedra and trigonal prisms along thec-axisis now completely determined by thex4 positions deducedfrom the translations of thez-componentγ of the modu-lation vector and the initial phaseΦ, i.e., from the valuesof the occupational AMF of the Mn and Cu atoms, corsponding tox4 = (7/11)n + Φ (0 � n � 10 andΦ = 1/4in this case). In Fig. 10, we can follow this procedure:Φ = 1/4 the origin is on a trigonal prism TPa–a (n = 0),the next polyhedra corresponds to Octb–a (n = 1, x4 =7/11+ 1/4) and so on. The whole sequence is therefTPa–a

–Octb–a–Octa–b

–Octb–a–TPb–b

–Octa–b–Octb–a

–TPb–b–

– –

Octa–b Octb–a Octa–b.

A. El Abed et al. / Solid State Sciences 5 (2003) 59–71 69

Fig. 10. Schematic representation of the sequence of octahedra and trigonal prisms forx = 3/11 visualised along the internal coordinatex4 for a column of[(Cu,Mn)O ].

3

nc--

ein ainseoc5].us-

luesery-ang-elyeris

nter-en

Å toeenbe-n–ox-

into

m-.

O,4)rvedt

ge

Fig. 11. Mn–O and Cu–O distances in Sr14Cu3Mn8O33 as function of theinternal coordinatet . Chain atx = y = 0 (circles) and chain atx = 1/3,y = 2/3 (squares).

The Mn–O and Cu–O distances are plotted as a fution of the internalt-coordinate in Fig. 11, where the commensurate case(t = 1/4) is identified by the location of thcircles and squares. The circles correspond to the chax ≈ 0 andy ≈ 0, while the squares correspond to the chaat (1/3,2/3, z) or (2/3,1/3, z). The Mn–O distances arin good agreement with distances for manganese in antahedral environment found in the literature [12,18,30–3A calculation of the bond valence sums for manganeseing bond valence parameters given in [36] leads to varanging between 3.98 v.v. and 4.15 v.v. which agree vwell with an oxidation state of+IV for manganese. For copper, two sets of Cu–O distances are observed: four ring between 2.031 Å and 2.064 Å and two approximatat 2.545 Å. These Cu–O bond distances are characttic of Cu2+, which is a Jahn Teller ion (3d9). The inter-atomic metal–metal distances are plotted versus the inal t-coordinate in Fig. 12. The Mn–Mn distances betwetwo adjacent face-sharing octahedra range from 2.4612.535 Å, and are shorter than the Mn–Cu distances betwadjacent octahedra and trigonal prisms, which rangetween 2.630 Å and 2.701 Å. The observed values of the MMn distances are in good agreement with those of otherides where the manganese ions (MnIV ) occupy face-sharingoctahedra [18,32–35]. The strontium atoms are grouped

two types belonging to layers of (Sr3O9) and (Sr3CuO6), re-

t

-

-

Fig. 12. Mn–Mn and Cu–Mn distances in Sr14Cu3Mn8O33 as function ofthe internal coordinatet . Chain atx = y = 0 (circles) and chain atx = 1/3,y = 2/3 (squares).

Fig. 13. Mn–O and Cu–O distances in Sr1+xCuxMn1−xO3 (x = 0.3244)as function of the internalt-coordinate.

spectively. Their coordination environments are more coplex, and the shortest Sr–O distances are close to 2.39 Å

In the case of the polycrystalline Sr1.3244Cu0.3244-Mn0.6756O3, both the metal–oxygen, Mn–O and Cu–(Fig. 13) and metal–metal, Mn–Mn and Mn–Cu, (Fig. 1bond lengths are in good agreement with those obsefor Sr14Cu3Mn8O33. Thex value of 0.3244 is close to, budifferent from x = 1/3, which corresponds to the avera

composition Sr4Mn2CuO9 having the repeat sequence of

70 A. El Abed et al. / Solid State Sciences 5 (2003) 59–71

r

he-etionr-ationl-

Oct)

-tal

ratio-uen

ns

se-

um-be

ep-t

in-

entntal

n-

a-an-ter-sys-n ofstemnd

an-

er-

d by

of

of

a

ric

Fig. 14. Mn–Mn and Cu–Mn distance in Sr1+xCuxMn1−xO3 (x = 0.3244)as function of the internalt-coordinate.

(1TP+ 2Oct) along the [(Cu,Mn)O3] subsystem chains. Fox = 0.3244, the ratio (TP)/(Oct)= 0.4801 is smaller than1/2, indicating that there is a small percentage of octadra trimeric units (1TP+ 3Oct) within the chains. The valuof x = 0.3244 can be represented by the rational fracx = 12/37 (= 0.32434). Thus, an approximation of the coresponding commensurate structure leads to a modulvector componentγ = (1 + x)/2 ≈ 49/74 with a supercelc-parametercs ≈ 74c1 ≈ 49c2 ≈ 191.92 Å. The chains consist of a combination of two times (12TP+ 25Oct). Thearrangement (or the sequence) of the 12 (TP) and 25 (can be deduced from the Farey tree by writingx as a com-bination of eleven repeats of (1TP+ 2Oct) plus one repeat of (1TP+ 3Oct). As in the case of the single crysSr14Cu3Mn8O33 (x = 3/8), the fractional valuex ≈ 12/37of the polycrystalline sample, can be expressed as ax = r/s wherer and (s − r) represent the number of trigonal prisms and octahedra, respectively, in the single seqtial unit (r = 12 and(s − r) = 25). Thus,x = 12/37 canbe written on the basis of a “combination” of two fractio(r1/s1) = 1/3 and(r2/s2) = 1/4 as follows:x = 12/37=(11r1 + r2)/(11s1 + s2)= (11∗1+ 1∗1)/(11∗3+ 1∗4). Con-sequently, the repeat sequence of polyhedra along thec-axiscan be described as the juxtaposition of the followingquences: two times [1(1TP+ 3Oct)+ 11(1TP+ 2Oct)]. Thedoubling of the sequence is required by the fact that the nber of layers in the hexagonally stacked unit-cell musteven.

The experimental Curie constant of Sr1.3244Cu0.3244-Mn0.6756O3, calculated from the high temperature susctibility data, is C = 1.46 emu·K·mol−1. Considering thaonly Cu2+ (3d9, S = 1/2) and Mn4+ (3d3, S = 3/2) ionscontribute to the total susceptibility, the calculated sponly Curie constant for Sr1+xCuxMn1−xO3 (x = 0.3244)is C = 1.39 emu·K·mol−1 for g = 2. It is well known thattheg-factor for Cu2+ in a pseudo square planar environmis greater than 2, which can explain why the experime

Curie constant is greater than the calculated spin-only value.

-

For Cu2+ (3d9) in a square planar environment, the ucoupled electron is located in the 2e level while the threeunpaired electrons of Mn4+ occupy the 1a and 1e levelsconstituting thet2g-block levels [37]. By comparison withSr4Mn2NiO9 [19], one can consider in a first approximtion that the exchange interaction between copper and mganese is weak compared to the Mn–Mn exchange inaction between face-sharing octahedra. The magnetictem can therefore be approximated as the combinatiotwo independent magnetic subsystems. The first subsycorresponds to the Cu2+ paramagnetic ions and the secoone to the manganese sublattice. In this latter one, the mganese ions are coupled by an exchange interactionJ . Asmentioned above, the value ofx can be approximated by thfractional valuex = 12/37, which corresponds to an aveage composition of Sr49Cu12Mn25O111. It is therefore pos-sible to assume that the manganese spin lattice is forme11 dimers plus one linear trimeric unit.

The total susceptibility of Sr1.3244Cu0.3244Mn0.6756O3can be expressed as:

χcalc(T )= (12/37) · χp(T )+ (11/37) · χDim(T )

(1)+ (1/37) · χTrim(T ),

where χp(T ) is the paramagnetic contribution of Cu2+,χDim(T ) the magnetic susceptibility of the dimeric unitsMn4+ coupled by an exchange interactionJ , andχTrim(T )

the magnetic susceptibility of the linear trimeric unitsMn4+ with an exchange interactionJ .

χDim(T ) and χTrim(T ) have been calculated usingHeisenberg Dirac Van Vleck model whereJ is the spinexchange parameter between two Mn4+ ions(S = 3/2).

χDim(T ) is given by:

χDim(T )= 0.375g2

T

× [28exp(4.5x)+ 10exp(−1.5x)+ 2exp(−5.5x)][exp(−7.5x)+ 7exp(4.5x)+ 5exp(−1.5x)+ 3exp(−5.5x)]

wherex = J/kT .The corresponding susceptibility of the linear trime

unit is given by:

χTrim(T ) = 0.375g2

T

N

D,

where

N = [47+ 17.5 exp(3x)+ 5 exp(−2x)+ 0.5 exp(−5x)

+ 42 exp(6x)+ 17.5 exp(−x)+ 5 exp(−6x)

+ 0.5 exp(−9x)+ 82.5 exp(9x)+ 17.5 exp(−7x)

+ 5 exp(−12x)]

and

D = [12+ 6 exp(3x)+ 4 exp(−2x)+ 2 exp(−5x)

+ 4 exp(−6x)+ 8 exp(6x)+ 6 exp(−x)

+ 2 exp(−9x)+ 10 exp(9x)+ 6 exp(−7x)]

+ 4 exp(−12x) .

A. El Abed et al. / Solid State Sciences 5 (2003) 59–71 71

sus-icman-

the-ly

re

tion

t).gedeintalic

ownnottioner a

995)

ter.

35.kx,

. 136

998)

ka,

4.em.

ic,

999)

rg.

e,

e,

m.

ez-

01)

ate

er.

cta

07

zio,

ana,

87)

5)

00.950,

99)

38

) 60.,

.

in,

Fig. 15. Experimental (circles) and calculated (solid line (d)) magneticceptibility of Sr1+xCuxMn1−xO3 (x = 0.3244). The calculated magnetsusceptibility of the manganese trimers (a), the copper (b) and theganese dimers (c) are shown.

The calculated susceptibilityχcalc(T ) (solid line) based ona least square fit and the experimental susceptibilityχexp(T )

(square symbols) are given in Fig. 15. In the refinementg-factor of Mn4+ was fixed atg = 1.96 and the paramagnetic susceptibility of Cu2+ was set equal to the spin-oncontribution. The total susceptibility is expressed as:

χcalc(T ) =m1(0.375/T )+m2 · χDim(T )+m3 · χTrim(T ),

wherem1, m2 andm3 and the spin exchange interaction arefinable parameters.

The refinement leads to a spin exchange interacJ/k = −43(4) K, m1 = 0.29(8), m2 = 0.31(5) andm3 =0.01(5). The value ofm1, m2, andm3 are in good agreemenwith the expected values corresponding to the formula (1

It is worth noting that the value of the spin exchanparameterJ/k = −43 K is close to the value observein Sr4Mn2NiO9 (J/k = −35.5 K), where the manganesions are coupled in a similar fashion [19]. As shownFig. 15, this simple model is able to fit the experimensusceptibility very well. The contributions of the dimerunits (curve c) and the trimeric units (curve a) are also shin Fig. 15. It can be seen that 3D magnetic ordering isobserved down to 2 K, which corroborate the assumpthat the two magnetic sublattices are independent ovwide temperature range.

References

[1] J. Darriet, M.A. Subramanian, J. Mater. Chem. 5 (1995) 543.[2] C. Dussarat, F. Grasset, J. Darriet, Eur. J. Solid State Inorg. 32 (1

557.

[3] P.D. Battle, G.R. Blake, J. Darriet, J.G. Gore, F. Weill, J. MaChem. 7 (1997) 1559.

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