Hole and electron attractor model: An explanation of clustered states in manganites

Progress in Solid State Chemistry 38 (2010) 38e45

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Hole and electron attractor model: An explanation of clustered states in manganites R. Cortés-Gil a, b, J.M. Alonso b, c, J.M. Rojo d, A. Hernando b, d, M. Vallet-Regí b, e, M.L. Ruiz-González a, J.M. González-Calbet a, b, * a

Departamento de Química Inorgánica, Facultad de Químicas, Universidad Complutense, 28040-Madrid, Spain Instituto de Magnetismo Aplicado, UCM-CSIC-ADIF, Las Rozas, P.O. Box 155, 28230-Madrid, Spain Instituto de Ciencia de Materiales, CSIC, Sor Juana Inés de la Cruz s/n, 28049-Madrid, Spain d Departamento de Física de Materiales, Facultad de Físicas, Universidad Complutense, 28040-Madrid, Spain e Departamento de Química Inorgánica y Bioinorgánica, Facultad de Farmacia, Universidad Complutense, 28040-Madrid, Spain b c

a b s t r a c t Keywords: Manganites Hole and electron attractor model Phase segregation FM clusters

A previously proposed model, based on the attractor role of doping cations, is extended to account for the electric and magnetic behavior on La1-xCaxMnO3 manganites in the whole compositional range (0 < x < 1). From this model, the spontaneous magnetization value is predicted quantitatively over the entire compositional range of the solid solution. By further including as basic parameters the tolerance factor and the band-width, the model is expanded to give an overall description of other Ln1-xTxMnO3 systems (Ln ¼ lanthanide, T ¼ alkaline-earth metal) with special emphasis in explaining the asymmetry and complexity of the magnetic phase diagrams. Those basic parameters are accounted for, in turn, by compositional variations, x, as well as by effects due to the different size of substitutional atoms. The model also sheds some light on the current issue of explaining the phase segregation and allowing the prediction of the spontaneous magnetization values in Ln1-xTxMnO3 systems. Ó 2010 Elsevier Ltd. All rights reserved.

Contents 1. 2.

3.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.1. The La1-xCaxMnO3 system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.1.1. The La-rich side (x < 0.5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.1.2. The Ca-rich side (x > 0.5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.2. Other systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.2.1. Lanthanide ion substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.2.2. Alkaline-earth ion substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.2.3. A general picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

1. Introduction

* Corresponding author. Departamento de Química Inorgánica, Facultad de Químicas, Universidad Complutense, 28040-Madrid, Spain. E-mail address: [email protected] (J.M. González-Calbet). 0079-6786/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.progsolidstchem.2010.09.002

The peculiar correlation between magnetic and electric properties in Ln1-xTxMnO3 (Ln ¼ lanthanide, T ¼ alkaline-earth) solid solutions, initially studied by Jonker and Van Santen [1e3], were soon explained by C. Zener [4,5] on the basis of his pioneer model of double exchange. This model properly describes the physics of the

R. Cortés-Gil et al. / Progress in Solid State Chemistry 38 (2010) 38e45

is different: although the solid solution in La1-xCaxMnO3 exists over the whole compositional range, it does only for x < 0.8e0.9 in the equivalent La1-xSrxMnO3 system [36,37]. In fact, for x ¼ 1, a 4HSrMnO3 hexagonal polytype is stabilized [38]. Secondly, the orthorhombic distortion is higher in the Ca system resulting in Mn3þ- O - Mn4þ bonding angles smaller than 180 whereas these angles are closer to 180 in the Sr system. This situation results in a more efficient orbital overlapping in the Sr compounds leading to wide-band systems whereas the Ca compounds give rise to intermediate-band ones. In earlier publications, we have argued that for the La1xCaxMnO3 system a simple model based on the attractor role of dopant cations can explain the FM vs AFM behavior of the corresponding manganite [30,32]. We have also shown that the same model can account for the magnetization in terms of the dopant concentration in the Ca-rich side of the series [39]. In this paper, we make two extensions of the referred model: first, we extend it to the whole range 0 < x < 1 and show that the same physical mechanisms operate when the holes or the electrons are the exchange particles and that the magnetization behaviour can be described therewith; second, we show that by just considering the tolerance factor and the band width, the model can be expanded to encompass systems containing other alkali-earth and lanthanide cations. 2. Experimental The basic lines of preparing and characterizing the La1-xCaxMnO3 have been reported in a series of previous papers [18,30,39]. Particular attention has been paid to controlling the vacancies in either sub-lattice as they can modify the total number of holes (or electrons) in the system with respect to the number induced by only the substituting impurity. The magnetization vs magnetic field (H) curves (T ¼ 5 K and Hmaximun ¼ 5 T) reported [17,18,30,39] were obtained after subtracting the AFM component from the raw magnetization measurements and, after that, the spontaneous magnetization vs x was represented, as shown in Fig. 1. The spontaneous magnetization refers to the cluster’s spontaneous moment multiplied by the corresponding fraction of volume that they occupy. Note that, under these conditions, when we refer to spontaneous magnetization we refer to the spontaneous magnetic moment of each FM cluster whereas the external field is used to align the different moments. The total measured magnetization corresponds, then, to the spontaneous magnetic moment of a cluster

4,5 4,0 3,5 3,0

m ( µB)

ferromagnetic (FM) and metallic (M) state observed along the 0.2 < x < 0.5 range on the assumption that an eg electron in Mn3þ can only jump to an empty neighbor vacant state, belonging to Mn4þ, if the t2g electrons of both cations have the same spin orientation, i.e., if the t2g orbitals are polarized. In addition, the discovery of colossal magnetoresistance (CMR) [6e8] kindled the interest on manganese related perovskites disclosing a much more complex behavior due to the competence between lattice, spin charge and orbital ordering. Many of the intricacies of these systems have been explained on the basis of the so-called phase segregation model [9e11] which proposes the presence of clusters, either of nanometric [12e19] or submicrometric [20,21] size, which correspond to an FM-M phase or to an antiferromagnetic (AFM) - insulator (I) one. In the corresponding clusters, the AFM-I phase can also involve a charge ordering (CO) state characterized by an ordered array of holes (Mn4þ) in every other Mn ion [22]. Phase diagrams representing the magnetic and CO temperature variation versus  are generally used for describing this electric and magnetic behavior [23e29] being  the T concentration. According to these diagrams the alkaline-earth concentration coincides to the one of Mn4þ introduced. Nevertheless, it has also been proposed [30] that in addition to providing holes to the band, the divalent substituting cations act as effective attractors for these holes. This effect, which is not accounted for by the standard phase segregation model [31], affects the magnetic response as the Mn4þ location around Ca creates nanosize clusters which affect the total magnetic moment. In fact, this localization effect allows the coexistence of Mn3þ and Mn4þ around the doping cation, leading to double exchange interactions and, consequently, to FM and locally M cluster formation. Note that, under those assumptions, the electrons can freely move all over the lattice only if a critical xc concentration of the doping cation is reached, giving rise to cluster percolation. This role of calcium is experimentally evidenced since materials with the same electronic density but different magnetic and electronic properties can be prepared [17,18,30]. For instance, the creation of cationic vacancies in La0.5Ca0.5MnO3 ((La1-xCax)zMn4þ0.5Mn3þ0.5O3) allows modifying its CE-type AFM and I behaviour with CO state [30] to an FM-M one while the Mn4þ percentage is kept constant. Similarly, an FM material with a 28% of Mn4þ can exhibit an M or I behaviour depending on the Ca2þ concentration [17,18]. This lead to threedimensional phase diagrams since both Mn4þ and Ca2þ ions’s concentration must be taken into account [32]. Either these two dimensional or three-dimensional phase diagrams are very complex due to the wide variety of behaviors inside represented, making a systematic comparison among the different systems becomes a fearsome task. Although many unknowns remain about the various mechanisms underlying the different kinds of ordering [31,33], valuable insight into the phase segregation processes can be gained from simply analyzing magnetization curves. As each phase has a characteristic magnetic moment, the explanation of the measured magnetization versus composition, x, curve can become a test to check the soundness of any model intending to account for the phase segregation phenomena. According to the hole-attractor model the Mn4þ location around Ca creates clusters which affect the total magnetic moment. In this sense, analyzing the cluster magnetic moment all over the compositional range would provide a rational pathway for a better understanding of the La1-xCaxMnO3 which could be extended to other related systems. When a different alkaline-earth cation is substituted for, structural, electric and magnetic properties are modified. For example, when Sr is substituted for Ca, the average cation size increases [34]. This provokes an important change in the solid solution Ln1xTxMnO3 (T ¼ Ca, Sr) since the tolerance factor [35], which depends on the average cation size, is modified. First of all, the stability range

39

2,5 2,0 1,5 1,0 0,5 0,0 0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

2+

x (Ca ) Fig. 1. Experimental magnetization, m, vs  curve corresponding to La1-xCaxMnO3 system.

40

R. Cortés-Gil et al. / Progress in Solid State Chemistry 38 (2010) 38e45

multiplied by the corresponding fraction of volume that clusters occupy. As reported before [17,18], for a certain range of x values, percolation takes place and the whole sample becomes FM. Here we have not attempted to pinpoint the onset of percolation; we have concentrated on the analysis of only the cluster magnetization. 2.1. The La1-xCaxMnO3 system This section deals first with the effect of Ca on the orthorhombic perovskite LaMnO3 matrix. In agreement to previous reported data [23,29,33], the system exhibits a wide variety of magnetic and electric behaviors. Actually, it is I for x < 0.16 whereas changes to AFM with FM clusters in the 0 < x < 0.07 range being FM for 0.07 < x < 0.16 [17,18,40]. Between 0.16 and 0.5, the system exhibits M behaviour and two phases, an FM-M and another AFM-I with CO, coexist [20,21]. In the Ca-rich region (x > 0.5), the system is AFM and I, nanometric FM clusters only appearing for very low doping concentration [15,16,39]. In spite of this diversity, the magnetic moment has a more regular variation, increasing continuously to reach a maximum value at x z 0.2 and, after that, decreasing, until x z 0.5 (Fig. 1). At the La-rich end of the graph (x/0 limit), Ca impurities feed holes into the band whereas at the Ca-rich one (x/1 limit), La impurities feed electrons. According to the hole attractor model, at both ends of the magnetization vs divalent impurity concentration curve shown as Fig. 1, these holes or electrons via double exchange set up a local FM order, involving local spin reversal, and contribute to the total magnetic moment of the sample. This mechanism results in a cluster of magnetic Mn ions around each foreign cation at both ends of the solid solution. Note that the different magnetic ordering (A- and G-type) sustaining the AFM array in both limits implies that the size of the magnetic cluster may be different in the La-rich and Ca-rich regions. In this sense, the magnetic moments in the A-type AFM structure (Fig. 2a) of LaMnO3 are FM ordered in two space directions whereas along the third direction [41] the ordering is AFM. In CaMnO3 matrix, Mn4þ magnetic moments are antiferromagnetically ordered in the three space directions (G-type AFM) [41] and consequently there are not any FM interactions (Fig. 2b). In both cases, the dopant cation induces the appearance of a nanometric size cluster which has different chemical composition and physical properties due to the presence of Mn4þeMn3þ double exchange interactions localized around Ca (La-rich region) or La (Ca-rich region). In order to

calculate the magnetic moment of the material, the corresponding moment of the cluster must be obtained. Notice, however, that due to the different AFM matrices, the interactions of the FM clusters with those matrices must be also different in each limit of the solid solution. This is clearly evidenced by the experimental hysteresis loops, depicted in Fig. 3. Actually, Fig. 3a, corresponding to the hysteresis loops of LaMnO3 and La0.995Ca0.005MnO3, shows that the introduction of 0.5% of Ca2þ on LaMnO3 induces an increasing of the magnetization whereas the introduction of 1% of La3þ in the CaMnO3 matrix does not lead to any increase of the magnetization. 2.1.1. The La-rich side (x < 0.5) An expanded view of the spontaneous magnetization vs  curve is shown as Fig. 4a. A well-defined maximum appears at an impurity concentration of xmax z 0.20. If we design by m the magnetic moment per Mn ion in units of mB, at the maximum, we measure mmax ¼ 4. In the quenched orbital moment limit, the projected value of the individual magnetic moment of an ion along the external field direction, again in units of mB, would be equal to gS, where S is the spin of the ion and g ¼ 2 the Landé factor. The corresponding values, for Mn3þ and Mn4þ are, respectively, 4 and 3, resulting in an average value of mav ¼ 3.8 for x ¼ 0.2. Within the experimental error, the experimental value of mmax is, then, consistent with an alignment of virtually all Mn spins along the direction of the external field. Furthermore, the m vs x curve of Fig. 4a grows almost linearly in the 0 < x < 0.18 range. This linearity strongly suggests that an individual FM cluster is being nucleated around each divalent impurity. If one writes:

m ¼ ax

[1]

from the slope of the experimental curve, we get a ¼ 20. A small deviation of linearity in the x/0 limit might be ascribed to the presence of a certain number of cationic vacancies. A small contribution from a DzyaloshinskieMoriya interaction [42,43] might result in a residual magnetization in the undoped limit. These effects would also lead to a slightly higher value of a. Even more, in our simplified scheme, the influence of Griffiths phases [44,45] has not

0,8 0,6

m (µB)

0,4 0,2

LaMnO3 La0.995Ca0.005MnO3

a

T=5K

0,0 -0,2 -0,4 -0,6

m ( µB)

0,08 0,04

b

CaMnO3 Ca0.99La0.01MnO3 T=5K

0,00

-0,04 -0,08 -0,12

-40000 -20000

0

20000 40000

H (Oe) Fig. 2. Schematic representation of (a) A-type AFM structure of LaMnO3 and (b) G-type AFM structure of CaMnO3.

Fig. 3. Comparative hysteresis loops of (a) LaMnO3 and La0.995Ca0.005MnO3; (b) CaMnO3 and La0.01Ca0.99MnO3.

R. Cortés-Gil et al. / Progress in Solid State Chemistry 38 (2010) 38e45

41

4,5 4,0

Exp Eq. 2

a

3,5

m ( µB)

3,0 2,5 2,0 1,5 1,0 0,5 0,0 0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

Fig. 5. Schematic representation of possible FM clusters nucleated in the (a) La-rich and (b) Ca-rich regions of the La1-xCaxMnO3 system.

2+

x (Ca ) 1,0 0,9 0,8

In order to understand the evolution of the m vs x curve for higher x values, the CO phenomena must be considered. For high concentrations of divalent impurities, Ca2þ cations will sit adjacent to other already incorporated. These might well become nuclei for the CO phase by forming local arrays of alternating Mn3þ and Mn4þ ions. The formation and growth of this new state requires, as already reported, the presence of three neighbou Ca2þ cations [46]. Since the Mn4þ is localized in this surrounding, the appearance of CO is favoured. The phase development is given by the following expression,

Exp m

b

m ( µB)

0,7 0,6 0,5 0,4 0,3 0,2

x1 ¼ Cx3

0,1

where x1 designs the CO volume. Concerning the magnetization growth stage, due to magnetic moment clustering around impurities, it is clear that this process must reach saturation when all the magnetic moments are aligned (i.e. at the maximum por x ¼ xmax). In other words, equation [1] is valid for x xmax. A simple model, incorporating the above assumptions, can be readily formulated. It combines the building-up of the magnetic moment of the sample by means as described by equation [1] with the destruction of magnetic moment due to the building up of CO.

0,0 0,75

0,80

0,85

0,90

0,95

1,00

2+

x (Ca ) Fig. 4. Expanded view of the m vs  curve for (a) La-rich region and (b) Ca-rich region in the La1-xCaxMnO3 system. The fitting curves, corresponding to Eqs. [1,2] (for Fig. 4a) and [3,4] (for Fig. 4b), are drawn superimposed.

been taken into account. In particular, clusters could start forming well above the Curie temperature since it is known that phase competition can enhance Griffiths effects. The ratio of a and mav, equal to 5.2 in units of mB, represents the average magnetic moment of each cluster. As each reversed spin in the AFM lattice results in a local magnetic moment of twice the average value of a manganese magnetic ion, one can conclude that the number of magnetic moments reversed in every FM cluster, n z 2.6, a value compatible with an average number of three manganese ions whose magnetic moments are reversed in each cluster. A simple picture can account for this value (Fig. 5): assume that the Mn4þ hole is located in a manganese ion in the spinedown plane (see Fig. 5a, red filled arrow) and that this spin flips to a spinup orientation as a result of doubleeexchange interaction with the spin-up placed underneath. Then, the hole can be exchanged with two nearest-neighbor Mn3þ in-plane resulting in a total of three spins in the upper plane having reversed their orientations. Notice that although these three inversed spins belong to the same unit cell, in which Ca2þ triggers the hole’s location, the number of unit cells affected by this inversion is higher. Actually, as represented in Fig. 5a, in terms of nearest-neighbor cells, such an inversion conforms a cluster of 16 cells, whose size is similar to that observed by Hennion et al. [40] by means of neutron scattering in La1xCaxMnO3 (x ¼ 0.05 and 0.08).

mðxÞ ¼ SðxÞ  aCx3 ekx

[2]

Where S(x) ¼ a x if x < xmax, and S(x) ¼ a xmax if x > xmax. An exponential factor has been added to the second term to take into account the fact that as the CO phase grows less available space is being left. The curve corresponding to Eq. [2] is drawn in Fig. 4a superimposed to the experimental data corresponding to the first maximum of Fig. 1. We have used the parameter a ¼ 20, as discussed above and leave C and k as fitting parameters. The best values are, respectively, C ¼ 3.6 and k ¼ 1.5. Note that the present parameter C has the same value than the one that we derived in a previous publication [32] in which the onset of FM phases was analyzed. Note that the model presented here accounts for the maximum value of m and its position. It also in agreement with the asymmetrical shape of the curve m (x). 2.1.2. The Ca-rich side (x > 0.5) In this side of the curve, as shown in the expanded view of Fig. 4b, the maximum in the m vs y graph (y stands for 1ex) is much smaller. The origin and evolution of the clusters can be, again, explained on the basis of the electronic defects location. In this sense, when Ca2þ is substituted by La3þ, Mn3þ and Mn4þ cations coexist around the La3þ leading to double exchange which, in agreement with the Goodenough model [47], develops on the

R. Cortés-Gil et al. / Progress in Solid State Chemistry 38 (2010) 38e45

FM-M nanometric clusters formation which exhibit different chemical composition and properties comparing to the CaMnO3 matrix (Fig. 2b). Nevertheless, the absence of FM interactions (Fig. 2b) in CaMnO3 matrix, compared to the LaMnO3 matrix in Fig. 2a, leads to less pronounced clusterematrix interaction and in agreement with the hysteresis loops (Fig. 3) involves a smaller maximum compared to La-rich size. Its value, at y ¼ 0.07, is m ¼ 0.40, only slightly above 10% of the maximum value of the spontaneous magnetization. The experimental curve in the y/0 limit, can be written

m ¼ a’y

[3]

a linear curve with an slope a’ ¼ 7. This value is in good agreement with simple estimations [12,15,16] based on flipping one spin from AFM to FM orientation in the G-type AFM structure. We have also argued earlier [39] that if we assume a magnetic moment per cluster of the order of the flipping of one Mn ion spin, the value of mM ¼ 0.47 at y ¼ yM can be explained in terms of an electron-attractor model. We offer now a more quantitative account: we use the same model as in the previous x/0 limit, as described by Eq. [2]. Of course the parameters are different.

mðyÞ ¼ SðyÞ  a0 C 0 y3 eky

[4]

where, similarly, S(y) ¼ a’y if y < ymax, and S(y) ¼ a’ ymax if y > ymax As explained before we take a0 ¼ 7. By using the parameters C’ ¼ 32 and k z 0, we find an optimum fit of Eq.[4] to the curve corresponding to the Ca-rich side (see Fig. 4b). Note that all curves from other authors using different doping cations tend to have a very steep descent on the high y side of the maximum [48]. It might be that the residual value of m is due to some artefact, for example substitutional anionic vacancies [49]. The corresponding spin’s scheme is shown as Fig. 5b. Note that, in this side of the graph, the number of unit cells affected by the spin inversion is lower and, consequently, the cluster’s size becomes significantly smaller [16]. Although Eq.[4] is formally similar to Eq. [2], there is a significant difference between the x/0 and x/1 limits. Whereas in the x < 0.5 side, the magnetization reaches a maximum corresponding to an alignment of all the Mn ions, this is not case for the x > 0.5 systems where the maximum does not exceed about 10% of that value. This effect can be related to the much higher value of the constant C’, as compared with C. This is, in turn, consistent with the well-known rapid formation of the C-type AFM phase. It is likely that this AFM nucleates from the very first stages of La doping, rapidly restricting the effective area for FM cluster nucleation after moderate increases of the concentration y. For this reason, the first term of Eq.[4] reads a’yM, implying that further nucleation of FM is prevented after m reaching a maximum. 2.2. Other systems We analyze now the likelihood of extending the model which suitably describes the La1-xCaxMnO3 system to Ln1-xTxMnO3 compounds involving different T cations and different Ln ions. In particular, we examine whether Eqs. [1] and [2], which portray a two-phase model including a hole attractor interaction [18,32], correctly describes the variation of the spontaneous magnetization as a function of the dopant cation concentration x, at least for x < 0.5. One should note first that the electronic and magnetic properties of Ln1-xTxMnO3 are highly dependent on the band-width (BW) which, itself, is intimately related to the chemical composition [33]. It is hard to overemphasize the effect on the perovskite behavior of exchanging cations in the A sub-lattice (referred to the ABO3

lattice), which often leads to a rather complex behavior. The change of one T cation for other modifies the tolerance factor because the average A cation size is modified. For example, substituting Sr for Ca leads to the La1-xSrxMnO3 system which exhibits a higher tolerance factor. However, this system does not sustain a solid solution in the whole compositional range because the 2H hexagonal polytype is stabilized at around x > 0.8, as a consequence of the larger average size of the A cation [36,37]. Even a more complex situation is found when another lanthanide is substituted for La: in this case not only the tolerance factor is changed, as a consequence of the A cation size, but the compound magnetic moment is also modified due to the contribution of the magnetic moment of the rare-earth cation [50,51]. Undoubtedly, this effect can affect the model applicability. Also, for large lanthanides (CeeDy), Ln1-xCaxMnO3 crystallizes in an orthorhombic perovskite where the distortion increases as the lanthanide size decreases resulting in a tolerance factor which also decreases [33]. 2.2.1. Lanthanide ion substitution We discuss, first, lanthanide substitution. We choose the Pr1xCaxMnO3 system. The spontaneous magnetization, m, vs  curve (compiled from the saturated magnetization values obtained by different authors [28,52]) is displayed in Fig. 6. The appearance of two maxima of different intensity suggests a common behavior of both the Pr and La compounds. In fact, the presence of the two maxima at x ¼ 0.2 and around y z 0.09, in the hole and electron rich regions respectively is common to all the Ln1-xCaxMnO3 systems [28,53,54]. The CO state appears at x ¼ 1/3 (Pr0.67Ca0.33MnO3) [28]. Note, in this regard, that the CO state stability increases as the average cationic size in the A perovskite sub-lattice decreases and, in the Pr perovskite, it tends to appear at lower x values than in the La1xCaxMnO3 system. We check now the validity of equation [2]. In order to obtain the value of C, we proceed along the same lines than in reference 30. We take that for the CO state corresponding to the composition Pr0.67Ca0.33MnO3, the residual m ¼ 0.80 [28]. This is equivalent to saying that the FM volume ratio is 0.20. Therefore, the corresponding AFM is 0.80 and taking into account that the Ca proportion is 0.33, we end up with a ratio of Ca in CO positions of xCO ¼ 0.264. Using now Eq.[4] we obtain C ¼ 7.5. When this value is incorporated into Eq. [2] of the proposed model, we obtain a spontaneous magnetization (solid line) which can be compared in Fig. 6 to the magnetization experimental values (squares). It can be 4,5

Exp. Model

4,0 3,5 3,0

m (µB)

42

2,5 2,0 1,5 1,0 0,5 0,0

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

2+

x (Ca ) Fig. 6. Experimental and calculated [from Eq. [1] to [4]] m vs  curves corresponding to Pr1-xCaxMnO3 system.

R. Cortés-Gil et al. / Progress in Solid State Chemistry 38 (2010) 38e45

2.2.2. Alkaline-earth ion substitution Now, we discuss alkalineeearth ion substitution. In the case of Ln1-xSrxMnO3 system, as the lanthanide ionic radius increases, the MneOeMn angle gets closer to 180 and the CO state stability decreases disappearing for La1-xSrxMnO3. It is interesting to discuss how the model can be generalized to systems as La1-xSrxMnO3 which does not exhibit CO. The La1-xSrxMnO3 is a complex system. Previous magnetic studies [24] indicate an A-type AFM ordering (x ¼ 0) whereas, for x > 0.1 changes to an I-FM and, then, to an M-FM for x  0.2. For x > 0.5, the Sr system exhibits an A-type AFM behavior different from the CE-type observed in the Ca perovskite. This A-type AFM further changes to C-type for x ¼ 0.6. For x z 0.8e0.9, the system is no longer a solid solution due to the appearance of hexagonal layers. Actually, the SrMnO3 phase crystallizes in the 4H structural type [38] which is formed by dimmers of octahedra sharing faces linked by corners according to a .chch. hexagonal stacking sequence, where c and h refer to cubic and hexagonal layers, respectively. Considering that LaMnO3 is an orthorhombic perovskite constituted by octahedra sharing corners following a cubic stacking sequence .ccc., a solid solution between LaMnO3 and SrMnO3 along the whole compositional range cannot be stabilized. In spite of that complex behavior, the magnetization curve of the Sr system can be explained in terms of our simple mode in the 0 < x < 0.6 range. Fig. 7 shows the magnetic moment versus  representation for the experimental and theoretical values, the latter derived from the hole attractor model [Eq. (1)]. As for the Ca system, in the 0 < x < 0.20 interval a linear relationship is observed. Besides, the slope, a, of the linear stage of the curve is very similar in both systems (for the Sr system the fitting gives a ¼ 21 with an error that certainly encompasses the corresponding value for the Ca system). In the 0.2 < x < 0.4 range the magnetization value slowly decreases as the Mn4þ concentration increases, i.e., as the Sr content is higher, up to x ¼ 0.4. After this value,

4,5 Exp. Model

4,0 3,5 3,0

m (µB)

observed that the model reproduces the general behavior of the system: it shows a maximum at x ¼ 0.2, followed by an m decreasing due to the appearance of CO. The magnetization value corresponding to the first maximum (x ¼ 0.2) is slightly lower than expected considering the average manganese oxidation state. In spite of the general qualitative agreement between experimental and calculated data, for very low calcium concentration, i.e., small x values, the experimental values of m tend to be higher than predicted. The origin of this discrepancy must be found on the already mentioned fact that, contrary to La, most of the rare-earth elements, as Pr, have their own magnetic moment that can, obviously, alters the magnetic moment of the compound. For the adjacent lanthanides (NdeDy), which also crystallize in the perovskite structure, the discrepancy is even larger, being also related to structural factors. Actually, the decrease of the ionic radius provokes an enhancement of the co-operative rotation of the MnO6 octahedra characterized by the decrease of the MneOeMn bond angle. This causes a significantly decreasing in the magnetic ordering temperature, TN, when the A-type AFM ordering changes to the E-type [55e59]. All the Ca perovskites, Ln1-xCaxMnO3, exhibit a CO state. The compositional range along which this state can exist, as well as the range of its stability against external magnetic fields, depend on the ionic radius of the lanthanide cation [33]. The smaller this cation the broader the compositional range and, also, higher fields are required for the disappearance of the CO state. This behavior can be understood on the basis of the distortion of the 180 MneOeMn ideal angle: as the lanthanide size decreases the electronic jump between the manganese neighbors becomes more difficult consequently favoring localization effects [22].

43

2,5 2,0 1,5 1,0 0,5 0,0 0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

2+

x (Sr ) Fig. 7. Experimental and calculated (from Eqs [1] and [5]) m vs  curves corresponding to La1-xSrxMnO3 system.

a pronounced decreasing of the magnetization value takes place according to:

m ¼ 3:6 þ a’x’

ða’ ¼ 18 and x’ ¼ 0:4  xÞ

[5]

as a consequence of the previously remarked FM to A-type AFM transition. 2.2.3. A general picture In this landscape we discuss the role of the A cation at the ABO3 lattice taking into account the La/Ca, Ln/Ca and La/Sr pairs. Actually, the A average size changes in each system leading to a modification of the tolerance factor. As mentioned in the introduction, this factor controls the BW since the bond angle MneOeMn depends on the A cation. [31,33,60,61] The bond angle is 180 for La1-xSrxMnO3 providing an effective overlapping and then leading to a wide-band system [62]. For the other systems, the smaller A average size involves higher orthorhombic distortion leading to a decreasing of the MneOeMn bond and, then, to a less effective overlapping characteristic to intermediateband systems or even narrow-band systems [62e67]. To further elucidate the role of tolerance factor and to propose a generalized phase diagram for perovskite-type manganites, several authors have explored samples with fixed doping levels in which the average ionic radius of the A site has been systematically varied [65,66]. To better understand the structural tuning effects in magnetic properties, the tolerance factor for the La1-xSrxMnO3, Pr1xSrxMnO3, Nd1-xSrxMnO3, Sm1-xSrxMnO3, and equivalent with calcium systems, has been represented versus  (Fig. 8). It should be recalled that previous reports do not allow for a dependence of the BW on composition [62] for different Ln1-xTxMnO3 systems. In this kind of analysis, graphs of BW vs x are indeed a set of parallel lines to the horizontal axis. Albeit, BW and tolerance factors are closely related parameters and it is difficult to understand how some authors use a constant value of the BW in the Ln1-xTxMnO3 systems since LnMnO3 (LaMnO3, for example) and TMnO3 (CaMnO3, for example) have different tolerance factors (Fig. 8 a). In our representation, BW reach higher values when going from Pr/Ca (narrow-band system) to La/Sr (wide-band system), passing through a system La/Ca of intermediate BW. We argue that between these limiting values, a gradual variation for the tolerance factor is expected, as is also expected for the band-width (t vs x lines in Fig. 8a not being horizontal but inclined). Notice that in this representation, left and right axes represent lanthanide and alkalineeearth tolerance factors, respectively.

44

R. Cortés-Gil et al. / Progress in Solid State Chemistry 38 (2010) 38e45

Fig. 8. Schematically representation of the tolerance factor, t, vs  for the Ln1-xCaxMnO3 (dashed lines) and Ln1-xSrxMnO3 (solid lines) systems (Ln ¼ La, Pr, Nd, Sm and Eu). The magnetic behavior of these systems is summarized here through areas of different colours (yellow ¼ A-AFM; blue ¼ FM; red ¼ CO; grey ¼ C-AFM; light yellow ¼ G-AFM.) The green region is a mixture of A-AFM and FM. The purple area corresponds to a mixture of FM and CO states.

In terms of these parameters, Fig. 8 schematically summarizes the evolution of the magnetic properties of Ln1-xTxMnO3 as a function of both x and t at low temperatures. It is patent that independently of the system, the tolerance factor, and consequently the band-width, increases as  (electronic holes) increases. Furthermore, the figure also evidences that the variation of the tolerance factor, and, consequently, of the band-width is different for each system: the La1-xCaxMnO3 system, a system showing an intermediate band-width, is the one exhibiting the lowest slope change in the whole compositional range. It is also worth stressing that Sr systems have been considered as wide-band systems [60,62,68,69]. Nevertheless, Fig. 8 clearly shows that this is only partially true. Actually, for x < 0.2 the band-width in La1-xCaxMnO3, a system which has been considered as an intermediate-band width system, is broader than in most of Ln1-xTxMnO3 systems. Starting at the low hole doping concentration region, 0 < x < 0.2, it can be observed that all the systems show the same evolution of the magnetic and electric behavior (see yellow and green areas in Fig. 8a). For x ¼ 0, the compounds are A-type AFM but as x increases nanometric size FM conducting clusters appear, their number increasing linearly up to xw0.1(Fig. 8b). For higher x, magnetic percolation takes place and the systems become FM (Fig. 8c). Notice also that, in this interval, 0 < x < 0.2, the spontaneous magnetization can be represented by equation [1]. Let us remark that this behavior is similar in both narrow and broad-band systems and happens in the low doping concentration region in which the change of the tolerance factor is quite small [17,18,24,28,48,70,71]. Differences on the electric and magnetic behavior between narrow and broad-band systems become evident for x > 0.2. In this sense, a clear separation can be made between systems with BW higher and lower than the corresponding to the La1-xCaxMnO3 system [23]. In the first case, i.e., for Ln1-xSrxMnO3 (Ln ¼ Pr and La) [24,28] an FM-M ordering appears (see blue area in Fig. 8a as well as in Fig. 8d) at x > 0.2. In this case, the spontaneous magnetization values agree with the average oxidation Mn state. For x > 0.4, A-type AFM clusters start appearing and for xw0.5 both systems become AFM (see yellow and grey areas on the upper right hand size of Fig. 8a) being the spontaneous magnetization described by equation [5] in the 0.4 < x < 0.5 range. A different situation is

observed in the second case, i.e., the tight band systems. In these systems, Ln1-xCaxMnO3 (Ln ¼ Pr, Nd, Sm and Eu) [28,52,53,55], and Ln1-xSrxMnO3 (Ln ¼ Nd, Sm and Eu) [28], a CO state nucleates (see red area in Fig. 8a as well as in Fig. 8d) leading to a gradual decrease of the spontaneous magnetization represented by equation [2] in the 0.2 < x < 0.5 range. For x > 0.5, the FM behavior disappears whereas the CO state is maintained. Finally for x > 0.85, (equation [3] and [4]), FM ordering, due to FM nanoclusters embedded on a G-type AFM matrix, appears (Fig. 8 e) [15,16,28,39,48,72]. 3. Conclusions In summary, we have extended a previously proposed model for La1-xCaxMnO3, based on an attractor effect of impurities versus electrons or holes, to encompass the whole interval 0 < x < 1 of the m vs  curve. In particular, signatures of the nucleation of AFM and FM phases have been identified and employed to follow the evolution of the magnetic response of the system. In the alkaliearth substituted La1-xSrxMnO3, the model gives also a satisfactory agreement with the experimental curve for x < 0.6. In most cases, the substitution of another rare-earth for La maintains the general trends of the spontaneous magnetization vs x curve but some departures from the model are recognized as a consequence of the competition between the magnetic moments of manganese and the rareeearth. Most of the different experimental behaviors discussed here are revealed in the graph of Fig. 8 where the different behaviors associated to different band-width are summarized. It is observed that the less distorted perovskite system, corresponding to the Sr compounds, exhibits the higher tolerance factor. Conversely, as the average A cation decreases, i.e., for smaller T and/or Ln cations, the tolerance factor rapidly decreases. For low tolerance factor values, the systems can be described as A-type AFM with small FM imbibed. As the tolerance factor increases, the FM cluster’s size increases, leading to CO in the central region of the diagram. This description recognizes that the band width in each system Ln1xTxMnO3 is strongly dependent on the composition, x, contrary to the hitherto extended assumption that the band width is a constant of the system.

R. Cortés-Gil et al. / Progress in Solid State Chemistry 38 (2010) 38e45

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