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Journal of Physics and Chemistry of Solids 61 (2000) 1543–1551 www.elsevier.nl/locate/jpcs A new ferromagnetic perovskite: LaMn1/2Rh1/2O3 C. Schinzer...

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Journal of Physics and Chemistry of Solids 61 (2000) 1543–1551 www.elsevier.nl/locate/jpcs

A new ferromagnetic perovskite: LaMn1/2Rh1/2O3 C. Schinzer 1 Institut de chimie de la Matie`re Condense´e de Bordeaux, I.C.M.C.B., UPR CNRS 9048, 87, Avenue du Docteur A. Schweitzer, 33608 Pessac cedex, France Received 25 May 1999; accepted 22 February 2000 Dedicated to Prof. Sibylle Kemmler-Sack, †10 February 1999

Abstract The new, ferromagnetic perovskite type oxide LaMn1/2Rh1/2O3 has been synthesized by conventional ceramic techniques. Rietveld refinements from X-ray diffraction data confirm a slight GdFeO3-type distortion and a disordered cation arrangement  b ˆ 7:845…3† A  and c ˆ 5:553…2† A:  on the B-sites. The space group is Pnma (No. 62) with lattice parameters a ˆ 5:582…2† A; DC magnetic measurements and hysteresis loops show ferromagnetic behavior at temperatures below 120 K. Due to domain effects divergences occur between zero-field-cooled and field-cooled magnetization curves at low fields. The anisotropy is investigated using AC techniques. Domains of short-range cationic order between Mn II and Rh IV lead to ferromagnetic properties. q 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Oxides; A. Magnetic materials; D. Electrical properties; D. Magnetic properties

1. Introduction Only few oxides exist that show ferromagnetic properties due to the parallel alignment of spins in a long-range magnetic ordering. Among these are mainly double perovskites A2MM 0 O6 and spinels. Within the framework of localized moments in the double perovskite, the magnetic interaction between different cations can be predicted from superexchange theory by applying the Goodenough– Kanamori rules [1,2]. Generally, ferromagnetic couplings are only possible between differently occupied d-orbitals (half-filled/empty or full/half-filled). The coupling takes place through two types of interactions, s- or p-interactions, at 1808 bonding angle between M, O and M 0 , thus forming linear M–O–M 0 bonds. Oxygen 2p-orbitals are involved in both, the strong s-interaction, where all the participating orbitals lie in the bonding line between M, O and M 0 , and the weaker p-interaction, where the interacting orbitals do not lie on the bonding line but in the same plane with it. 1 Present address: Hahn–Meitner-Institut, Glienicker Straße 100, D-14109 Berlin, Germany. Also at the Institut fu¨r Kristallographie, Charlottenstraße 33, D-72070 Tu¨bingen, Germany. Tel.: 1 497071-2976389; fax: 1 49-7071-45938. E-mail address: carsten.schinzer@ uni-tuebingen.de (C. Schinzer).

It is a matter of fact, that the electronic population of the d-orbitals of a transition metal depends on two factors: the formal oxidation state of the element and the corresponding local symmetry and crystal field [3]. The splitting energy of the crystal field increases with the oxidation state. Furthermore, the splitting energy and the cation size increase from 3d- to 5d-elements for a given oxidation state. In a crystal field of cubic symmetry (Oh), a low-spin configuration is therefore expected for the 4d 5 cation Rh IV and high-spin configurations are expected for 3d elements in a lowoxidation state. In order to obtain a strong ferromagnetic interaction, only high-spin 3d cations that possess at least one half-filled eg-orbital are of interest. However, 3d cations with only one half-filled eg-orbital (high-spin 3d 4, low-spin 3d 7 and 3d 9) usually show a strong Jahn–Teller effect and consequently the crystal field symmetry is distorted. In our case, M II should therefore be one of Mn II, Fe II or Ni II. Ferromagnetic perovskites containing Ir IV, the higher homologue of Rh IV, have been reported by several authors. Among the known compounds are La2MnIrO6 with a Curie temperature around 130 K [4] and La2MIrO6 …M ˆ Co; Ni) [5,6]. Another problem is involved in the chemistry of Rh IV oxides. The tetravalent oxidation state of Rh is about as stable as the (diamagnetic) trivalent one. For divalent cations that in octahedral coordination are also stable in the trivalent state, e.g. Fe II, one cannot expect the

0022-3697/00/$ - see front matter q 2000 Elsevier Science Ltd. All rights reserved. PII: S0022-369 7(00)00036-6

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Table 1 Expected super-exchange interactions for ordered LaMn1/2Rh1/2O3 (AF, antiferromagnetic; FM, ferromagnetic) Rh IV 4d 5, LS

O

Mn II 3d 5, HS

Result

s-interaction (strong) 2 eg –

ps

2 eg

FM

p-interaction (weak) Half 1 t2g 2 t2g Full

calcination with intermediate grindings were performed. The progress of the reaction was followed by X-ray diffraction. A single-phase product resulted after a total calcination time of 72 h. 2.2. Chemical analysis

pp pp

3 t2g 3 t2g

Half Half Half

AF FM

assumption of a pure II/IV-charge distribution to be valid. As for the other mentioned 3d metals attention must therefore be paid, whether the oxidation states do really correspond to the expected ones. In the framework of our work on Rh-containing perovskites [7,8], we have been able to study several chemical compositions likely to generate ferromagnetic couplings. II IV Perovskites of general formula LaM1/2 Rh1/2 O3 have been II selected. Often the doubled formula La2M Rh IVO6 is used when cation ordering occurs. M II is a magnetic cation able to couple ferromagnetically with tetravalent rhodium in the low-spin state. In this study, the results obtained for M ˆ Mn II are reported. The expected magnetic interactions between d-orbitals of low-spin Rh IV and high-spin Mn II in an ordered arrangement on the B-sites and split in a cubic crystal field of symmetry Oh have been worked out and are presented in Table 1.

EDX and volumetric titration were used to analyze the samples. A Cameca FX 100 calibrated with appropriate standards was used for the EDX analysis. Table 2 reports the mean values from 15 points that were statistically distributed over the sample surface. The reported oxygen percentage is calculated by difference. Iodometric titration was used to determine the oxygen content of the samples. The applied procedure is a variation of the Bunsen method. A part of the sample was cooked in boiling hydrochloric acid. The aliquot of elementary chlorine formed due to the reduction of the cations to stable oxidation states in the solution (Mn II and Rh III in our case) is caught in a beaker charged with iced potassium iodide solution. When the reduction and the accompanying dissolution of the samples is complete, the amount of elementary iodine formed in the potassium iodide solution is determined using a 0.1 N sodium thiosulfate solution. The EDX results reported in Table 2 show that the cation ratios of La, Mn and Rh are 2:1:1 as it is expected for the given nominal stoichiometry. The complementary information from the iodometric titration confirms the EDX results concerning the oxygen content and it can be concluded that the sample stoichiometry is LaMn1/2Rh1/2O3.

2. Synthesis and characterization

2.3. X-ray diffraction and Rietveld refinement

2.1. Synthesis

A Philips PW 3040/00 X’Pert MPD system was used to register the diffraction pattern of the sample. Ka radiation from a ceramic Cu tube operated at 40 kV/50 mA was applied in a Bragg–Brentano setup equipped with an analyzer crystal (PG). For the Rietveld refinements, the FullProf 3.1 software package [10] was used. The accurate standard deviation of the refined values was estimated by applying Brear’s formula [11] and multiplying its result to the precision of the parameters as reported in the final cycle of the refinement. The obtained product is a single phase with the perovskite structure. Preliminary profile-matching runs assuming ideal structure factors have been used to determine the space

Powder samples of LaMn1/2Rh1/2O3 were prepared using La2O3 (Prolabo, 99.9%), MnO (Strem Chemicals) and Rh2O3·5H2O (Johnson Matthey Alfa Products, .99%). La2O3 was precalcined overnight at 9008C. The transformation of Rh2O3 into RhO2 was undertaken in an autoclave applying sufficient pressure and temperature according to Ref. [9] (100 bar O2; 8008C) for 20 h. Stoichiometric amounts of La2O3, MnO and RhO2 were then mixed and thoroughly ground in an agate mortar. The powder was placed in platinum boats and calcined at 11008C in oxygen atmosphere. In order to gain a phase pure product, several Table 2 Results of chemical analysis for LaMn1/2Rh1/2O3 EDX-microanalysis %atom La

Iodometry %atom Mn

%atom Rh

%atom O

Oxygen per FU

Found

Calc

Found

Calc

Found

Calc

Found

Calc

20.7(5)

20

9.1(9)

10

10.5(9)

10

60.3(4)

60

3.002(5)

C. Schinzer / Journal of Physics and Chemistry of Solids 61 (2000) 1543–1551 Table 3 Rietveld refinement results for LaMn1/2Rh1/2O3 (space group Pnma;  b ˆ 7:845…3† A;  c ˆ 5:553…2† A:  Overall temperaa ˆ 5:582…2† A;  2 ; R-values see text) ture factor: B ˆ 0:08…2† A Atom

Site x

y

z

Occupancy

La Mn Rh O(1) O(2)

4c 4b 4b 4c 8d

1/4 0 0 1/4 20.045(3)

0.0080(8) 1/2 1/2 20.086(7) 20.220(5)

1.0(–) 0.5(–) 0.5(–) 1.0(–) 1.0(–)

0.0417(4) 0 0 0.485(4) 0.210(4)

group and unit cell parameters of the product. It is found that LaMn1/2Rh1/2O3 obeys space group P2 1 =n21 =m21 =a with cell  b ˆ 7:8493…8† A  and parameters being a ˆ 5:6155…6† A;  Rietveld refinements were started introduc ˆ 5:5537…6† A: cing the positional parameters found for disordered LaNi1/ 2Rh1/2O3 [8]. In the final state, R-values of Rp ˆ 13:9%; Rwp ˆ 17:8% and RBragg ˆ 4:96% could be achieved with an expected R-value of Rexp ˆ 12:6%: Complementary refinements in the monoclinic space group of the B-site-ordered orthorhombic perovskites as reported for La2MRhO6 …M ˆ Mg; Zn) [7] led to higher R-values when cation ordering was considered. The refinements in this ordered structural model led to similar Rvalues only when complete disorder was introduced by setting the B-cation sites to half-occupancy by Mn and Rh each …Rp ˆ 14:4%; Rwp ˆ 18:1%; RBragg ˆ 5:04%†: The results of the refinement are reported in Table 3 and the final plot of the refinement is shown in Fig. 1. The Rietveld refinements allow for two conclusions: (i) the unit cell is derived from the cubic perovskite type by a slight

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GdFeO3-type distortion and (ii) no long-range cationic ordering is observed. 2.4. Magnetic properties The DC magnetic susceptibility for LaMn1/2Rh1/2O3 was measured using a Quantum Design SQUID magnetometer equipped with the 5 T magnet. For temperature-dependent measurements, the sample was introduced in zero field and cooled down to the starting temperature of 5 K. Once the temperature stabilizes, the desired field is applied and measurements are taken while heating the sample up to RT resulting in the ZFC (zero-field cooled) curves. FC (field cooled) curves are registered when cooling the sample down again. Hysteresis loops were recorded at a fixed temperature and varying field using a special (faster) damping mode to adjust the field. Samples were inserted into the sample chamber at zero field and cooled down to the measuring temperature. Then the field was first increased stepwise to 5 T, reverted to -5 T and again raised to 5 T in order to complete a full hysteresis loop. The temperature dependence of the mass magnetization, s , as recorded at 0.5 T is shown in Fig. 2. The slope of the FC curve indicates a ferromagnetic behavior with a Curie temperature T C < 80 K: The exact value of TC is determined by the numerical analysis of the point of inflection, where the first derivative 2s=2T has a maximum at TC and the second derivative 2 2 s=2T 2 is zero. A TC of 72(1) K is found here. Further magnetic measurements were undertaken in order to elucidate the magnetic transition. Fig. 3 shows hysteresis loops at different temperatures. Even at 5 K, a complete saturation of the specific magnetization is

Fig. 1. Final plot of the Rietveld refinement of LaMn1/2Rh1/2O3 in space group Pnma …Rp ˆ 13:9%; Rwp ˆ 17:8%; Rexp ˆ 12:6%; RBragg ˆ 4:96%†:

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Fig. 2. Temperature variation of DC mass magnetization of LaMn1/2Rh1/2O3 at 0.5 T.

not observed in the magnetic field range accessible by the apparatus used here …H max ˆ ^5 T†: The 5 K hysteresis does not indicate a strong remanent behavior of the sample. At 200 K, a linear dependence of s vs. H is observed and consequently paramagnetic behavior can be assumed at T . 200 K:

Additional DC measurements were performed at 1 mT and 5 T. The thermal variation of s at these fields is shown in Fig. 4. Second derivative curves are plotted at the bottom of the graphs. They show a clear dependence of the magnetic behavior on the applied field. At very low fields of 1 mT (upper graph

Fig. 3. Hysteresis loops of LaMn1/2Rh1/2O3 at different temperatures.

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Fig. 4. DC mass magnetization of LaMn1/2Rh1/2O3 at 1 mT (upper graph) and 5 T (lower graph) as a function of temperature. The bottom part of each graph shows the second derivative of the measured data; the zero line is dotted.

in Fig. 4), three points of approximately zero slope are detected at 57(1), 99(1) and 126(2) K. On the other hand, only one TC is seen at 95(1) K in the 5 T measurement. At 1 mT, only the effect at 57(1) K is attributed to the ferromagnetic transition. The approximate saturation values estimated from the field cooled curves are s 0 K;1 mT < 0:517 A m2 kg21 ; s 0 K;0:5 T < 25:8 A m2 kg–1 and s 0 K;5 T < 38:1 A m2 kg–1 : From these results, it is possible to estimate the magnetic exchange integral J using the formula given by Selwood in

Ref. [12]: TC ˆ

2JzS…S 1 1† 3k or J ˆ T 3k 2zS…S 1 1† C

where k is the Boltzmann constant and S…S 1 1† is accessible from the Curie constant (the spin-only value was chosen here). Assuming the number of neighboring magnetic cations, z ˆ 6; the exchange integral thus rises from 24.9(4) to 31.5(9) J mol 21 and to 41.6(4) J mol 21 at 1 mT, 0.5 T and 5 T, respectively. Assuming that the exchange

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Fig. 5. Real part s 0 AC and imaginary part s 00 AC of AC mass magnetization from AC measurements applying 0.3 mT field amplitude at 1.25 Hz alternation frequency. The bottom part of each graph shows the first derivative of the data; the zero line is dotted as a guide to the eye.

Fig. 6. Inverse molar susceptibility at different magnetic fields. The line represents the best fit to the Curie–Weiss law in the paramagnetic regime.

C. Schinzer / Journal of Physics and Chemistry of Solids 61 (2000) 1543–1551 Table 4 Magnetic properties of LaMn1/2Rh1/2O3 Paramagnetic domain …T . 200 K† spin-only values 2.375 emu K mol –1 C 1.94(1) emu K mol –1 C a m eff 3.94(3) mB m S.O. 4.359 mB Q 126(2) K Ferromagnetic domain H 1 mT TC 57(1) K Jb 24.9(4) J mol –1 m 5 K b 1.67(1) mB a b

0.5 T 72(1) K 31.5(4) J mol –1 1.67(1) mB

5T 95(1) K 41.6(4) J mol –1 1.67(1) mB

II IV Mean spin-only value: C S:O: ˆ 1=2 (CS.O., Mn 1 CS.O., Rh). Cf. text for explanation.

integral J simply depends on the sum of all competing magnetic interactions, where positive and negative J, respectively, depict ferromagnetic and antiferromagnetic interactions, it can be concluded that an increasing field suppresses the antiferromagnetic interactions. As a result, the values for both, TC (and hence the magnetic exchange integral) and s 0 K, increase with rising external field. The determination of the Curie–Weiss parameters of the compound was performed on the inverse molar susceptibility, 1/x mol. The values of x mol from the high-field measurements at 0.5 and 5 T were corrected for atomic diamagnetism using the tables given by Selwood [12]. A plot of the best fit together with the experimental DC data is shown in Fig. 6. The numerical fit-results are reported in Table 4. AC susceptibility measurements at 1.25 Hz field alternation frequency are presented in Fig. 5. Several relaxation processes are detected at different temperatures. The bottom part of each plot shows the first derivative, indicating

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changes in the slope of the measured data. In the real part s 0 AC, a broad maximum at 49(1) K and a shoulder at 102(2) K are observed. The imaginary part s 00 AC is characterized by four maxima at 38(2), 56(2), 73(2) and 92(2) K. 2.5. Electrical conductivity Conductivity measurements were performed on a pellet of LaMn1/2Rh1/2O3. For this purpose, the powdered sample was pressed and re-calcined at preparation temperature for 4 h. Four contacts were applied to the surface and the conductivity is measured by cooling down from RT until the resistance exceeds the capacity of the measuring equipment. A Keithley nanovoltmeter and current source have been used. Temperature and equipment were controlled by a LabViewe application running on a personal computer. The result of this measurement is shown in the form of the Arrhenius plot in Fig. 7. The specific conductivity s near RT is rather low …s 280 K ˆ 0:685…2† mS†: A linear dependence of log s vs. T 21 is observed in the whole range of temperature (112–285 K) thus indicating a semiconducting behavior of the sample with a rather low-activation energy of E a ˆ 8:52…4† kJ mol21 (0.0883(4) eV). 3. Discussion It is evident from the analytical results that the composition of the investigated compound is the expected one. Only a slight distortion of the ideal cubic perovskite unit cell is observed. This is in full agreement with earlier reports on LaB1/2Rh1/2O3 perovskites [7,8]. The slight distortion is explained by the misfit of the Goldschmidt tolerance factor t ˆ 0:92 (radii from Ref. [13]). No distortion indicating the

Fig. 7. Variation of specific electrical conductivity s of LaMn1/2Rh1/2O3 as a function of inverse temperature (Arrhenius plot).

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Fig. 8. Decomposition of the hysteresis loop at 5 K (W) into a ferromagnetic contribution s ferro (—) and a paramagnetic one s para (- - -). The hysteresis loop at 200 K (A) is added for comparison

presence of Mn III, a 3d 4 high-spin ion exhibiting a strong Jahn–Teller effect, is observed. A charge distribution of Mn II/Rh IV can therefore be assumed. The fact that no long-range order is observed in the X-ray diffraction pattern is somehow contradicted by the magnetic properties. They clearly indicate an ordered arrangement of the cations, because only the magnetic interactions in a regular, ordered array of Mn II and Rh IV lead to ferromagnetic behavior as indicated in Table 1. If the cations on neighboring B-sites are identical, an antiferromagnetic interaction is expected. However, in an intermediate situation where only a part of the neighboring cations is of the same species as the center ion, antiferromagnetic and ferromagnetic interactions between identical and different species compete. This leads to a complex magnetic behavior. Such a competition between different exchange interactions is probably indicated by several relaxation processes and by a varying magnetic exchange integral. It is believed that an important fraction of the investigated sample is well described by the disordered structural model derived from the Rietveld analysis. The ferromagnetic effect is due to domains where a 1:1 ordering of Mn II and Rh IV is observed. An ordering of the B-site cations is expected from the differences in charge and radii, too. The magnetic properties of LaMn1/2Rh1/2O3 in the paramagnetic domain support the assumption of a Mn II/Rh IV charge distribution since the observed Curie constant C and the effective magnetic moment m eff derived from it are close to the spin-only values. The values might be slightly reduced for two reasons: (i) the accuracy of the data in the paramagnetic domain 200–300 K is not sufficient to determine the correct values; or (ii) the values are reduced due to some antiferromagnetic interactions between neighboring Mn II –Mn II or Rh IV –Rh IV. The first argument is probably valid here since 200 K is not far above the

Curie temperature and interferences cannot be excluded. Moreover, the absolute number of data points is not very high. The ferromagnetic behavior of the sample is clearly confirmed by both temperature and field variation experiments. However, the Curie temperature changes with the applied field and the Weiss constant Q indicates a TC higher than any value determined by the numerical analysis of the point of inflection. The fact that TC and Q do not coincide is often observed in ferromagnets [12]. Unfortunately, the electrical measurements could not be performed at temperatures less than 112 K. This is the more disappointing, since the point measured at 112 K …ˆ 0:00893 K 21 † seems to indicate a change of slope where all other resistivity points measured do follow the Arrhenius law. In order to determine the saturation properties, the hysteresis at 5 K was analyzed in more detail. The fact that saturation is not achieved even at high-magnetic fields might indicate that only a fraction of the sample obeys an ordered cation arrangement. Consequently, only a part of the volume shows a transition to a ferromagnetic state and the rest remains in a paramagnetic state. Such an occurrence of two magnetic phases gives rise to a field-dependant contribution to s even at 5 K. The hysteresis loop obtained at 5 K is thus decomposed into two fractions: a ferromagnetic and a paramagnetic one. The paramagnetic contribution was estimated by fitting a line to the nearly linear extremes of the hysteresis at 4–5 T and 24 to 25 T. The slope of this line was multiplied with the magnetic field. The resulting values are considered to represent a good estimate of the contribution of the paramagnetic volume fraction to mass magnetization, s para,5 K. The experimental s was subsequently corrected for s para,5 K resulting in a hysteresis that reaches a saturation at approximately 3 T. The entire decomposition is demonstrated in Fig. 8. Note that s para,5 K is 66 ^ 2% the value of s 200 K at any field, thus indicating

C. Schinzer / Journal of Physics and Chemistry of Solids 61 (2000) 1543–1551

that a volume fraction of about 2/3 possibly remains paramagnetic below TC. The saturation moment at 5 K, m 5 K,∞, has been estimated from s ferro,5 K using the relation between m 0,∞ and the saturation magnetization s 0,∞

m 0;∞ ˆ

M s 0;∞ NmB

Replacing the variables by the molar weight, M, the Avogadro number, N, and the value of the Bohr magneton, a saturation moment of m5 K;∞ ˆ 1:67…1† mB is derived. The ferromagnetic volume fraction, Vferro, can thus be estimated via two independent routes: from the ratio of s para,5 K and s 200 K we have found V ferro < 33%: From the comparison of m 5 K,∞ with the spin-only value, we get Vferro < 38%: A mean value of approximately 35% ferromagnetic volume fraction can thus be considered. As was described above, Vferro is at the same time an estimate of the fraction of cation-ordered domains in the sample. Since the X-ray diffraction analysis is an integral method, it is quite evident that such a small fraction of ordered domains must remain undetected. Moreover, the strong domain effects present in weak magnetic field indicate that magnetic domains are loosely connected with statistical orientation at insufficient field strengths. The B-site ordered, homologous compound La2MnIrO6 shows a ferromagnetic transition, too [4]. The Curie temperature of 130 K indicates a stronger exchange interaction, a fact that is explained by the higher exchange integral expected when replacing a 4d by a 5d metal cation of identical d-electron configuration [14]. The saturation magnetization of La2MnIrO6 is extrapolated to 4.0 mB at 0 K [4] and a similar value can be expected for completely ordered La2MnRhO6. It is therefore believed that the reduced value and the field dependence of s at 5 K as found here are explained by domains with ordered cation arrangement. The remaining disordered regions in the sample exhibit a more complex magnetic behavior as is evident from the AC measurement presented in Fig. 5. The shoulder in s 0 AC at 102(2) K is possibly accompanied by a maximum in s 00 AC at 92(2) K. This behavior is attributed to domain effects, since the orientation of the ferromagnetic domains relative to the field-direction cannot directly follow the alternating field. The maximum of s 0 AC at 38(2) K, however, cannot be explained by such a mechanism and must be of a different origin. It is believed that competing antiferromagnetic and ferromagnetic interactions between identical and different species of neighboring cations in the statistically ordered domains, are responsible for this behavior. However, this effect is not accompanied by any visible change in s 0 AC or the DC measurements and the hypothesis of ferromagnetically ordered domains coexisting with an important paramagnetic volume fraction is therefore valid. Neutron

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diffraction experiments are under way in order to analyze the magnetic structure of LaMn1/2Rh1/2O3 at low temperatures and possibly give more insight into the magnetic interactions.

4. Conclusion The perovskite-type compound LaMn1/2Rh1/2O3 has successfully been prepared and studied. The crystal structure is orthorhombic and no long-range cationic order is observed between Mn II and Rh IV. A ferromagnetic transition is observed at T ˆ 118 ^ 1 K and is possibly accompanied by a change in resistivity. The hysteresis loop at 5 K probably consists of a superposition of a paramagnetic and a ferromagnetic contribution. DC and AC temperature variation measurements indicate two coexisting magnetic phases in the low-temperature domain. The value of the ferromagnetic volume fraction is estimated to be of approximately 35%.

Acknowledgements This work was supported by a TMR Marie-Curie Research Training Grant of the European Union (Contract no. ERB FMB ICT 961859). The assistance of E. Lebraud (X-ray diffraction), I. Alves (microanalysis) and E. Marquesteaut (electric measurements) is gratefully acknowledged. The author is indebted to Prof. G. Demazeau (E.N.S.C.P.B., Bordeaux) for valuable discussions.

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