Charge, Spin, and Orbital Ordering in the Perovskite Manganates, Ln1

Jun 2, 2000 - xCaxMnO3 perovskite ... Superconductor Science and Technology 2002 15 (3), 423-426 ...
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J. Phys. Chem. B 2000, 104, 5877-5889

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FEATURE ARTICLE Charge, Spin, and Orbital Ordering in the Perovskite Manganates, Ln1-xAxMnO3 (Ln ) Rare Earth, A ) Ca or Sr) C. N. R. Rao* Chemistry & Physics of Materials Unit and the CSIR Centre of Excellence in Chemistry, Jawaharlal Nehru Centre for AdVanced Scientific Research, Jakkur P.O, Bangalore 560 064, India ReceiVed: February 7, 2000; In Final Form: March 29, 2000

Charge ordering occurs in some mixed-valent transition metal oxides. The perovskite manganates of the formula Ln1-xAxMnO3 (Ln ) rare earth; A ) Ca, Sr) are especially interesting because long-range ordering of the Mn3+ (t32g e1g) and Mn4+ (t32g e0g) ions in these materials is linked to antiferromagnetic spin ordering, and also to the long-range ordering of the Mn3+ (eg) orbitals and the associated lattice distortions. Charge ordering occurs at a higher temperature than spin ordering in some of the manganates (TCO > TN), whereas in some others TCO ) TN. Orbital ordering occurs without charge ordering in the A-type antiferromagnetic manganates, but in the manganates where charge ordering occurs, antiferromagnetism of CE-type is found along with orbital ordering. The subtle relations between charge, spin, and orbital ordering are discussed in the article, with special attention to the effects of cation size, chemical substitution, dimensionality, pressure, and magnetic and electric fields. Unusual features such as phase separation and electron-hole asymmetry are also examined.

Introduction Charge ordering is a phenomenon generally observed in mixed-valent transition metal oxides. When differently charged cations (i.e., 2+ and 3+) in an oxide order on specific lattice sites, the hopping of electrons between the cations is no longer favored. One therefore observes an increase in the electrical resistivity at the charge-ordering transition, often accompanied by a change in crystal symmetry. Because transition metal ions also carry spins, it is interesting to examine the magnetic (spin) ordering in the solids in relation to charge ordering. A wellknown example of charge ordering is found in Fe3O4 (magnetite) where it occurs at a temperature well below spin ordering.1,2 Charge and spin ordering in real space in metal oxides received renewed attention because of their role in cuprate superconductors.3 In recent years, charge and spin ordering have been discovered in a few other transition metal oxides,4 typical examples being La1-xSrxFeO3, La2-xSrxNiO4, and LiMn2O4. Charge ordering in the rare earth manganates of the perovskite structure, with the general composition La1-xAxMnO3 (Ln ) rare earth; A ) alkaline earth), is considerably more interesting, because it is closely associated with spin and orbital ordering, giving rise to fascinating properties.5-7 The perovskite manganates originally became popular because of the discovery of colossal magnetoresistance (CMR).5,6 CMR and related properties essentially arise from the double-exchange mechanism of electron hopping between the Mn3+ (t32g e1g) and Mn4+ (t32g e0g) ions.8 In this mechanism, lining up of the spins (ferromagnetic alignment) of the incomplete eg orbitals of the adjacent Mn ions is directly related to the rate of hopping of the electrons, giving rise to an insulator-metal transition in the material at the ferromagnetic Curie temperature, Tc. In the * For correspondence: e-mail: [email protected].

ferromagnetic phase (T < Tc), the material becomes metallic, but is an insulator in the paramagnetic phase (T > Tc). In the insulating phase, a Jahn-Teller distortion associated with the Mn3+ ions favors the localization of electrons. Charge ordering of the Mn3+ and Mn4+ ions competes with double-exchange and promotes insulating behavior and antiferromagnetism. It may be recalled that the Mn3+-O-Mn3+ and Mn4+-O-Mn4+ superexchange interaction, through the eg orbitals, is antiferromagnetic. Although charge ordering in the rare earth manganates was investigated by Jirak et al.9 as early as1985, the subject has received renewed attention only in the past 5 years, for reasons described below. Charge ordering occurs through a fairly wide range of compositions of Ln1-xAxMnO3, provided the Ln and A ions are not too large. Large Ln and A ions (e.g., La, Sr) favor ferromagnetism and metallicity, whereas the smaller ones (e.g., La, Ca, or Pr, Ca) favor charge ordering. Charge ordering and spin (antiferromagnetic) ordering may or may not occur at the same temperature. Besides, the Mn3+ (dz2) orbitals and the associated lattice distortions develop long-range order (as illustrated later in this article). Such orbital ordering may or may not occur with charge ordering in the manganates, but it generally accompanies antiferromagnetic (spin) ordering. In this article, we discuss the interplay of charge, spin, and orbital ordering in the rare earth manganates in some detail, and highlight some of the important recent results. Before discussing the manganates, we shall briefly review the properties of a few of the other transition metal oxides that exhibit charge ordering. Examples of Charge and Spin Ordering in Oxides. Fe3O4 has a spinel structure, represented as Fe3+[Fe2+, Fe3+]O4 in which one third of the cations are tetrahedrally coordinated (Asites) and two thirds of the cations are octahedrally coordinated (B-sites). It is ferrimagnetic below 858 K (TN), with the spins

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Figure 1. Verwey transition in Fe3O4 caused by charge ordering (from Honig1b).

Figure 3. Structure showing charge and spin ordering in La0.33Sr0.67FeO3 (from Battle et al.10b).

Figure 4. Spin and charge modulation in the NiO2 planes of La2-xSrxNiO4+y with increasing hole concentration. Here, the modulation wavenumber, , is equivalent to the hole concentration, p ) x + 2y (from Tranquada et al.11a). Spin density on nickel ions is shown by arrows, and charge density on oxygen ions is shown by circles.

Figure 2. Temperature variation of electrical resistivity and magnetization of La0.33Sr0.67FeO3 showing marked changes on charge ordering (TCO ) TN) (from Park, Yamaguchi and Tokura, as quoted by Imada et al.4).

of the A- and B-sublattices being antiparallel. Around 120 K (TV), Fe3O4 shows a sharp increase in resistivity, commonly referred to as the Verwey transition (Figure 1). Below TV, the Fe2+ and Fe3+ ions are considered to be ordered, thereby giving rise to high electrical resistivity. Above TV, conduction occurs on the B site sublattice. It actually turns out, however, that charge ordering in Fe3O4 is much more complicated, with some short-range ordering present even above TV. Even today, there is argument about the symmetry of the low-temperature ordered phase. The Verwey transition in this oxide has been reviewed excellently by Honig1 and Tsuda et al.2 La1-xSrxFeO3 (x ) 0.67) undergoes charge ordering at approximately 207 K (TCO), at which temperature it also exhibits antiferromagnetic spin ordering. Thus, TCO is also the Ne´el temperature (TN) in this oxide. The resistivity shows a marked increase at TCO ) TN (Figure 2). Although the formula requires the presence of Fe3+ and Fe4+ ions, the Fe4+ ions disproportionate to give Fe3+ and Fe5+ ions.10 The charge- and spin-ordered structure of La0.33Sr0.67FeO3 is shown in Figure 3. Quasi two-dimensional La2-xSrxNiO4+y undergoes cooperative ordering of the Ni spins and of the charge carriers below a temperature (TCO). Charge ordering occurs at nearly all doping levels (p ) x + 2y), in the insulating regime of the material (p < 0.7). Spin and charge modulations are observed in the NiO2 plane and these vary with the hole concentration (p value). This nickelate system is a typical instance of microscopic phase separation wherein the charge carriers (holes) localize in the domain walls in an antiferromagnetic system. Such phase

separation causes stripe modulations. Here, the ordering may be viewed as alternating stripes of antiferromagnetic and holerich regions.11 In Figure 4, we show the spin and charge modulations in the NiO2 planes at two hole concentrations. The  ) 1/4 case corresponds to La2NiO4.125 (p ) 0.25), where the interstitial oxygens form a superlattice with a unit cell of 3a × 5b × 5c. The compositional dependence of resistivity of La2-xSrxNiO4 shows peaks at x ) 0.33 and 0.25, owing to charge ordering, which in the x ) 0.33 composition occurs at 240 K. At 240 K, various properties show anomalies, as depicted in Figure 5. Superlattice peaks show up in the electron diffraction pattern at this temperature. Antiferromagnetic spin ordering in the nickelate occurs at a lower temperature (180 K). It appears that ordering is driven by charge. Charge ordering of holes, accompanied by spin ordering or the segregation of holes and spins in the stripe form, also occurs in La2-xAxCuO4 (A ) Sr, Ba, x ) 0.125), causing anomalous suppression of superconductivity.3 LiMn2O4 is a spinel with equal proportions of 3+ and 4+ Mn cations. It has been shown recently to undergo a Verweytype transition with a resistivity anomaly at approximately 290 K where there is a structural (cubic-tetragonal) transition. Around 65 K, the material exhibits a complex long-range magnetic order.13 Clearly, this charge-ordering transition requires further study. A Brief Description of the Different Types of Ordering in the Manganates. LaMnO3 has a layered antiferromagnetic structure, referred to as A-type antiferromagnetic ordering14 (Figure 6a). Because there is a doubly degenerate eg orbital in each Mn3+ ion (t32g e1g), LaMnO3 and the other analogous rare earth compounds such as NdMnO3 show a fine interplay between spin and orbital ordering. The orbital ordering is coupled to the Jahn-Teller (JT) distortion. Figure 6b describes the JT distortion in LaMnO3. The distortion disappears above

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Figure 7. Charge, spin, and orbital ordering in (a) CE-type and (b) A-type AFM Ln1-xAxMnO3. In part a, the broken line shows the unit cell for the CE-type AFM CO order. Mn4+ ions are shown by circles.

Figure 5. Normalized sound velocity (∆ν/ν), specific heat (c), as well as temperature derivatives of resistivity (F) and magnetic susceptibility (χ) showing anomalies at the charge ordering transition (240 K) in La1.67Sr0.33NiO4 (from Ramirez et al.12).

Figure 6. (a) A-type AFM ordering, (b) JT distortion, and (c) orbital ordering in LaMnO3. The orientation of eg orbitals shown in panel c is consistent with the 5 Å lattice spacing.

750 K. Orbital ordering of 3x2 - r2 or 3y2 - r2 type accompanied by the JT distortion leads to a superexchange coupling in LaMnO3, which is ferromagnetic (FM) in the planes and antiferromagnetic (AFM) between the planes (Figure 6a).15 Orbital ordering in LaMnO3 is shown in Figure 6c. Without the JT distortion, LaMnO3 would have been a FM insulator; it is an A-type AFM insulator instead. In Ln1-xAxMnO3, besides orbital and spin ordering, we can have charge ordering because of the presence of Mn3+ and Mn4+ ions. Small Ln and A ions stabilize the charge-ordered (CO) state. Thus, Pr0.7Ca0.3MnO3, charge-orders around 230 K in the paramagnetic state, becoming AFM at 170 K; it is an insulator and does not show ferromagnetism in the absence of a strong

magnetic field. La0.7Ca0.3MnO3, on the other hand, is a FM metal below the Curie temperature (Tc ≈ 230 K) and a paramagnetic insulator above Tc. La0.5Sr0.5MnO3 is metallic both in the FM and paramagnetic states, whereas Nd0.5Sr0.5MnO3 shows a transition from a ferromagnetic metallic (FMM) state to an AFM charge-ordered state on cooling. The CO states in these manganates are associated with CE-type AFM ordering.14 In the CE-type ordering, Mn3+ and Mn4+ ions are arranged as in a checker board and the Mn3+ sites are JT distorted.15 Along the c-axis, the in-plane arrangement mentioned above gets stacked and the neighboring planes are coupled antiferromagnetically. The exchange coupling between the Mn3+ and Mn4+ ions depends on the type of eg orbital at the Mn3+ site, and hence the nature of orbital ordering becomes important. The CE-type AFM CO state in Ln1-xAxMnO3 is associated with the ordering of 3x2 - r2 or 3y2 - r2 type orbitals at the Mn3+ site. The JT distortion that follows such orbital ordering stabilizes the CE-type AFM state (relative to the FMM state). In Figure 7a, we show the spin, charge, and orbital ordering in the CEtype AFM state. The CO states in the manganates exhibit CEtype AFM ordering at the same temperature as the chargeordering transition or at a lower temperature (TCO g TN). That is, spin ordering occurs concurrently or after charge ordering. Complete orbital ordering is achieved when there is both charge and spin ordering. Orbital and spin ordering occur without charge ordering in some of the manganates showing A-type antiferromagnetism. The A-type AFM state described earlier in relation to LaMnO3 (Figure 6a) is also encountered in the Ln1-xAxMnO3 system. This state generally is not accompanied by charge ordering, because some electron transfer can occur between the Mn cations in the ab plane. Orbital ordering in A-type AFM ordering is depicted in Figure 7b. Here, the x2 - y2 type orbital is present at the Mn3+ site. Pr0.5Sr0.5MnO3 transforms from a FMM state to a A-type AFM state on cooling. Nd0.45Sr0.55MnO3 is a A-type antiferromagnet, unlike Nd0.5Sr0.5MnO3, which is a CE-type antiferromagnet exhibiting charge ordering at low temperatures; the former shows conductivity in the ab plane and is not chargeordered. Evidence for charge ordering can be observed in crystal structures at low temperatures. Thus, in La0.5Ca0.5MnO3, the Mn4+ environment is nearly isotropic, with all the Mn-O distances being nearly equal (∼1.92 Å). In the Mn3+O6 octahedra, one of the Mn-O bonds is much longer (∼2.07 Å) than the other bonds (∼1.92 Å), consistent with orbital ordering. It must be noted that the Mn-O distances in the ab plane of the manganates are much longer than in the c-direction,

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Figure 8. (a) Structure of charge-ordered Nd0.5Ca0.5MnO3 in the ab plane at 10 K. Mn4+ (black) located at (1/2, 0, 0) and Mn3+ (grey) located (0, 1/2, 0) can be distinguished. The structure has zigzag chains with alternate long and short Mn-O distances. The distances are 1.921 and 2.021 Å 〈110〉 and 1.881 and 2.020 Å along 〈-110〉 (from Vogt et al.16). (b) Charge-ordered structure of Nd0.5Sr0.5MnO3. The Mn3+ ions are the filled circles, and Nd/Sr ions are large open circles. Oxygens are small open circles. The long Mn3+-O bonds shown in black also represent the orientation of the eg orbitals. Mn4+-O octahedra are shown in polyhedral representation (from Woodward et al. 50).

Figure 9. Phase diagram of La1-xCaxMnO3 (following Cheong). CAF, canted antiferromagnet; CO, charge-ordered phase; FMI, ferromagnetic insulator; PMI, paramagnetic insulator; FMM, ferromagnetic metallic state; CO AFMI, charge-ordered antiferromagnetic insulator; COI, charge-ordered insulator. Notice electron hole asymmetry by comparing the x < 0.5 and x > 0.5 regimes.

particularly in the AFM state. In Figure 8a, we show the projection of the structure of charge-ordered Nd0.5Ca0.5MnO3 down the c-axis to illustrate the definitive identification of the unique sites occupied by Mn3+ and Mn4+ ions in the CO state. The structure of charge-ordered Nd0.5Sr0.5MnO3, where the Mn4+-centered octahedra are represented in polyhedral notation, is shown in Figure 8b. Representative Phase Diagrams of the Manganates. In Figure 9 we show the phase diagram of La1-xCaxMnO3. In this system, charge ordering occurs in the x ≈ 0.5-0.8 range. In Figure 10 we show the phase diagrams of Pr1-xCaxMnO3 and Pr1-xSrxMnO3. The latter system shows no charge ordering, but Pr1-xCaxMnO3 exhibits charge ordering over the x ≈ 0.3-0.8 range. Note that Pr0.7Ca0.3MnO3 exhibits charge ordering but La0.7Ca0.3MnO3 does not. All such variations are essentially due to the effect of the size of the A-site cations, the smaller size favoring charge ordering. From Figures 9 and 10, we also see that the CO regime is prominent at large x. In fact, the x > 0.5 compositions in Ln1-xCaxMnO3 are almost entirely in the CO regime both when Ln ) La and Pr. This regime can be considered as the electron-doped regime (substitution of trivalent rare earth in CaMnO3), whereas the x < 0.5 compositions may be considered as the hole-doped regime (substitution of divalent Ca in LnMnO3). Clearly, there is electron-hole asymmetry in these manganates. It is surprising that ferromagnetism is not encountered in the electron-doped regime (x > 0.5). Effects of magnetic and electric

Figure 10. Phase diagrams of (a) Pr1-xSrxMnO3 and (b) Pr1-xCaxMnO3. Notice the wide charge ordering regime and electron-hole asymmetry in part b and the absence of charge ordering in part a. In part b, there is spin-glass or CAF behavior when x g 0.8.

fields on the hole- and electron-doped manganates (e.g., Pr0.7Ca0.3MnO3 and Pr0.3Ca0.7MnO3) are also different. There are some similarities between the hole- and electron-doped regimes. For example, in Pr1-xCaxMnO3, the charge-ordering transition temperature increases with hole concentration in the 0.3 < x e 0.5 regime and with electron concentration in the 0.5 e x e 0.8 regime. Case Studies. To understand typical scenarios of chargeordered manganates, it is instructive to examine the properties of two manganates with different sizes of the A-site cations. For this purpose, we choose Nd0.5Sr05MnO3 with a weighted average radius of the A-site cations, 〈rA〉, of 1.24 Å and Pr0.6Ca0.4MnO3 with an 〈rA〉 of 1.17 Å (Shannon radii are used here).

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Figure 13. Temperature-magnetic field phase diagram for Nd0.5Sr0.5MnO3 (from Tokura et al.18).

Figure 11. Temperature variation of (a) the magnetization and (b) the resistivity of Nd0.5Sr0.5MnO3 (from Kuwahara et al.17).

Figure 14. CO gap in Nd0.5Sr0.5MnO3 as revealed by vacuum tunneling measurements (from Biswas et al.19). Figure 12. Effect of magnetic fields on the charge ordering transition of Nd0.5Sr0.5MnO3 (from Kuwahara et al.17).

Nd0.5Sr0.5MnO3 is a ferromagnetic metal with a Tc of ∼250 K and transforms to an insulating CO state at about 150 K (Figure 11). The CO transition is accompanied by spin ordering, and the CO insulator is a CE-type antiferromagnet.17 The orbital ordering therefore involves 3x2 - r2/3y2 - r2 orbitals as in Figure 7a. Application of a magnetic field of 7T destroys the CO state, and the material becomes metallic (Figure 12), the sharpness of the transition decreasing with increasing strength of the field. The transition is first-order, showing hysteresis, and is associated with changes in unit cell parameters. The unit cell volume of the CO state is considerably smaller than that of the FMM state. The properties of Nd0.5Sr0.5MnO3 can be described in terms of the phase diagram shown in Figure 13. The Imma space group of this manganate renders the Mn-OMn angle in the ab plane closer to 180°, promoting the overlap of the Mn(eg) and O(2p) orbitals. Vacuum tunneling measurements19 show that a gap of 250 meV opens up below TCO (Figure 14). The gap collapses on applying a magnetic field, suggesting that a gap in the density of states at EF is necessary for the stability of the CO state. Photoemission studies indicate a sudden change in electron states at the transition and give an estimate of 100 meV for the gap.20 These estimates of the gap are considerably larger than the Tco (12 meV); it is not clear how a magnetic field of 6T (1.2 meV) can destroy the CO state. Nd0.5Sr0.5MnO3 shows anomalous magnetostriction behavior, with a large positive magnetovolume effect (Figure 15), owing

Figure 15. Temperature variation of the maximum volume magnetostriction in Nd0.5Sr0.5MnO3 at 13.7T (from Mahendiran et al.21).

to the magnetic field-induced structural transition accompanying a change from the AFM CO state to the FMM state.21 Pr0.6Ca0.4MnO3 is an insulator at all temperatures and becomes charge-ordered at about 230 K (TCO). At this temperature, anomalies are found in the magnetic susceptibility, as well as in the resistivity, as shown in Figure 16. In the CO state, the Mn3+ and Mn4+ ions are regularly arranged in the ab plane with the associated ordering of the 3x2 - r2/3y2 - r2 orbitals. On cooling, AFM ordering (CE-type) occurs at 170 K (TN). At about 40 K, Pr0.6Ca0.4MnO3 exhibits canted AFM ordering. Application of an external magnetic field transforms the CO state to a FMM state, as shown in Figure 16, but the field required is much larger than in Nd0.5Sr0.5MnO3. The transition

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Figure 18. Charge and orbital ordering in La1-xCaxMnO3: (a) x ) 0.50, (b) x ) 0.67. Open circles represent Mn4+ and lobes show eg orbitals of Mn3+. Charge modulation wavelengths are ∼11 and 16.5 Å for x ) 0.50 and 0.67, respectively (following Cheong).

Figure 16. Temperature variation of (a) resistivity and (b) magnetic susceptibility of Pr0.6Ca0.4MnO3 (from Tomioka et al.22a and Lees et al.22b).

Figure 17. Temperature-magnetic field phase diagram for Pr0.6Ca0.4MnO3 (from Tokura et al.18).

is associated with hysteresis. The properties of Pr0.6Ca0.4MnO3 can be represented by the phase diagram in Figure 17. The basic features of the CO state in Pr0.6Ca0.4MnO3 are exhibited by several other rare earth manganates with relatively small A-size cations, in that the CO state is the ground state. Thus, Nd0.5Ca0.5MnO3 (〈rA〉 ) 1.17 Å) is a paramagnetic insulator with a charge-ordering transition at about 240 K. Charge ordering occurs in the paramagnetic state in Pr1-xCaxMnO3 (0.35 e x e 0.5) with the TCO increasing with x. The paramagnetic state is characterized by FM spin fluctuations with a small energy scale.23 At TCO, these fluctuations decrease and disappear at TN. Electron diffraction and darkfield transmission electron microscopy (TEM) images show the presence of incommensurate charge ordering in the paramagnetic insulating state (180-260 K) of the x ) 0.5 composition.24 At TN, there is an incommensurate-commensurate CO transition. In the incommensurate CO structure, partial orbital ordering is likely to be present. Similar charge, orbital, and spin ordering has been found in the 0.3 composition as well.25 Optical conductivity spectra of the x ) 0.4 composition show evidence of spatial charge and orbital ordering at 10 K.26 The CO state

Figure 19. Temperature-〈rA〉 phase diagrams for (a) Ln0.5Sr0.5MnO3 and (b) Ln0.5Ca0.5MnO3 (from Woodward et al.31).

has a gap of ∼0.2 eV, and the gap remains up to 4.5T. The gap value is the order parameter of the CO state and couples with spin ordering. Pr0.67Ca0.33MnO3 shows thermal relaxation effects from the metastable FMM state (produced by the application of 10T magnetic field) to the CO state.27 A metal-insulator transition is observed as an abrupt jump in resistivity at a well-

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Figure 20. Effect of internal pressure on the properties of (a) Pr0.7Ca0.3-xSrxMnO3 and (b) Pr0.7-xLaxCa0.3MnO3. Note that substitution by a larger A-site cation renders the material FM (see insets). An insulator-metal transition is also observed (from Rao et al.33).

defined time, depending on the temperature. This observation seems to indicate a percolative nature of current transport. Charge and orbital ordering in the manganates give rise to stripes.28 In Figure 18 we show the modulation that can arise in La1-xCaxMnO3 with x ) 0.50 and 0.67. At x ) 0.50, the same number of Mn3+ and Mn4+ ions exist and diagonal stripes with a spacing of 11 Å are, therefore, to be expected (Figure 18a). When x ) 0.67, there are twice as many Mn4+ ions as Mn3+ ions. Ordering of diagonal rows of Mn3+ and Mn4+ ions, besides the orientational ordering of the orbitals, would give rise to the striped pattern in Figure 18b, with a periodicity of 16.5 Å. Paired JT distorted stripes or bistripes are believed to be present in La0.33Ca0.67MnO3.29 A supercell based on such ordering has been proposed, but a detailed structural investigation30 has shown that the diffraction data can be explained satisfactorily without bistripes. Apparently, owing to orbital disordering, a mixture of paired and unpaired stripes seems to occur in La0.5Ca0.5MnO3. Because such charge stripes generally are observed by electron microscopy, it is not clear whether these structures truly represent the bulk composition.

Cation Size Effects. In the manganates exhibiting CMR, the ferromagnetic Tc increases with the average radius of the A-site cations, 〈rA〉. Increasing 〈rA〉 is equivalent to increasing the hydrostatic pressure and is therefore accompanied by an increase in the Mn - O - Mn angle and the eg bandwidth. If there is considerable mismatch in the radii of the different A-site cations, however, the Tc does not increase with 〈rA〉. Charge ordering is also highly sensitive to 〈rA〉 and the TCO generally increases with decrease in 〈rA〉. The sensitivity of TCO to 〈rA〉 has been examined7,31,32 and is generally attributed to an increased tilting of the MnO6 octahedra as the 〈rA〉 decreases. In Figure 19 we show that the phase diagrams31 of Ln0.5Sr0.5MnO3 and Ln0.5Ca0.5MnO3 illustrate some of the important features. (Here, the 〈rA〉 is varied by changing the Ln ion.) The Mn-O(eq)-Mn and Mn-O(ax)-Mn bonds are identical in Ln0.5Ca0.5MnO3 (excect when Ln ) La). For La0.5Ca0.5MnO3 and all the Ln0.5Sr0.5MnO3 compounds, the Mn-O(eq)-Mn angle is significantly larger (by 2-6°) than the Mn-O(ax)-Mn angle. Although the Ln0.5Ca0.5MnO3 manganates crystallize in the Pnma symmetry, there is an evolution from Pnma to I4/mcm through Imma in the Ln0.5Sr0.5MnO3 manganates, with increase

5884 J. Phys. Chem. B, Vol. 104, No. 25, 2000 in 〈rA〉. The changes in the octahedral tilt system have consequences on the low-temperature magnetic structure. This is seen in Nd0.5Sr0.5MnO3 where the charge ordering in the CEtype AFM state is associated with the Imma structure. As pointed out earlier, the CO states of Nd0.5Sr0.5MnO3 (〈rA〉 ) 1.24 Å) and Pr0.6Ca0.4MnO4 (〈rA〉 ) 1.17 Å) are destroyed by magnetic fields. The field required to melt the CO state varies with 〈rA〉 and the manganates with very small 〈rA〉 remain charge-ordered even on the application of high magnetic fields.32 Thus, Y0.5Ca0.5MnO3 (〈rA〉 ) 1.13 Å) has a robust CO state that is not affected by very high magnetic fields (>25T). We can thus distinguish three different categories of manganates with respect to their sensitivity to magnetic fields: (a) manganates that are FM and become charge-ordered at low temperatures (e.g., Nd0.5Sr0.5MnO3 when TCO ) TN), with the CO state transforming to a FMM state on the application of a moderate magnetic field; (b) manganates that are charge-ordered in the paramagnetic state (TN < TCO), and do not exhibit an FMM state, but transform to a FMM state under a magnetic field (e.g., Pr1-xCaxMnO3); and (c) those that are charge-ordered in the paramagnetic state (TN < TCO) as in b, but are not affected by magnetic fields up to 15T or greater (e.g., Y0.5Ca0.5MnO3). Category c is encountered when 〈rA〉 e 1.17 Å. The apparent one-electron bandwidth estimated on the basis of the experimental Mn-O-Mn angle and the average Mn-O distance in Ln0.5A0.5MnO3 does not vary significantly with 〈rA〉, which suggests that other factors may be responsible for the sensitivity of the CO state to 〈rA〉. One possibility is a competition between the A- and B-site cations for covalent mixing with the O(2p) orbitals.32 By increasing the size of the A-site cations or by the application of pressure, the CO state in the manganates can be transformed to the FMM state.33,34 In Figure 20, we show the effect of internal pressure on the CO state of Pr0.7Ca0.3MnO3 wherein Ca is substituted by the larger Sr or Pr is substituted by La. The Tc in the Pr0.5Sr0.5-xCaxMnO3 system, decreases with an increase in x or a decrease in 〈rA〉 up to x ) 0.25; TCO ) TN from x ) 0.09 to 0.25. When 〈rA〉 is decreased further, TCO increases from 180 K for x ) 0.25 to 250 K for x ) 0.30; for 0.30 e x e 0.50, TCO > TN.35 The effect of cation size disorder on the ferromagnetic Tc of rare earth manganates exhibiting CMR has been investigated in detail. The disorder is quantified in terms of the variance in the distribution 〈rA〉, as defined by Attfield.36 The variance σ2 is defined by, σ2 ) Σxiri2 - 〈rA〉2, where xi is the fractional occupancy of A-site ions and ri is the ionic radius. The ferromagnetic Tc decreases significantly with the variance, σ2, based on the studies of rare earth manganates with fixed 〈rA〉. A similar study of the variation of TCO with σ2 in Ln0.5A0.5MnO3, for fixed 〈rA〉 values of 1.17 and 1.24 Å, has shown that TCO is not very sensitive to the size mismatch.37 It appears that JT distortion and Coulomb interactions play a prominent role in determining the nature of the CO state in these materials. Considering that the rare earth manganates with large 〈rA〉, as exemplified by Nd0.5Sr0.5MnO3 (〈rA〉 ) 1.17 Å), exhibit entirely different characteristics of the CO state, and that 〈rA〉 ) 1.17 Å categorizes the manganates with respect to their insensitivity to magnetic fields, we would expect interesting and unusual properties in the intermediate range of 〈rA〉 of 1.20 ( 0.20 Å. In this regime TCO approaches Tc, leading to a competition between charge ordering and ferromagnetism. Thus, La0.5Ca0.5MnO3 (〈rA〉 ) 1.20 Å) exhibits a region of coexistence of ferromagnetism and charge ordering (Tc ) 225 K, TCO ) 135 K). At 135 K, the material also becomes AFM (CE-

Rao

Figure 21. Temperature variation of the CO gap in Nd0.25La0.25Ca0.5MnO3 (closed circles) and Nd0.5Sr0.5MnO3 (closed triangles). Inset shows a typical tunneling conductance curve (from Arulraj et al.40). Shaded region represents the coexistence regime.

Figure 22. Temperature variation of the (a) magnetic susceptibility and (b) resistivity of Nd0.5Ca0.5Mn1-xRuxO4 (from Vanitha et al.46b).

type) and the orbital ordering becomes commensurate.38 In (Nd1-xSmx)0.5Sr0.5MnO3, Tc decreases from 255 K to 115 K as x increases from 0.0 to 0.875, as expected of a decrease in 〈rA〉.39 The TCO also decreases from 158 K to 0 K as x changes from 0.0 to 0.875. This unusual behavior wherein TCO is suppressed as Tc approaches TCO is interesting. Nd0.25La0.25Ca0.5MnO3 (〈rA〉 ) 1.19 Å) reveals an intriguing sequence of phase transitions.40 On cooling, this manganate develops an incipient CO state below 220 K. The formation of this state is accompanied by an increase in electrical resistivity and the opening up of a gap in the density of states near EF. The orthorhombic distortion also increases, as a consequence of cooperative JT distortion of the lattice and short-range

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Figure 23. Temperature variation of the (a) magnetization and (b) resistivity of Nd0.5Sr0.5Mn1-xRuxO4 (from Vanitha et al.46b).

ordering of the Mn3+ and Mn4+ ions. At about 150 K, the incipient CO state becomes unstable and the material undergoes a reentrant transition to the FMM state. The transition is characterized by a sharp decrease in resistivity, collapse of the CO gap, development of FM ordering, and an abrupt decrease in the orthorhombic distortion. There is a two-phase coexistence region (150-220 K) around the CO-FMM transition. We show the fascinating reentrant transition in Figure 21 where the CO gap, obtained by vacuum tunneling measurements,40 is plotted against temperature. Effects of Substitution in the Mn Site and by 18O. Substitution of 16O by 18O (generally up to 85-90%) has a marked effect on the magnetic properties and CMR of the manganates, indicating the important role of electron-phonon coupling. Substituting 18O for 16O in La0.175Pr0.525Ca0.3MnO3 destroys the insulator-metal transition and renders the material insulating down to 4 K.41 The CO transition in La0.5Ca0.5MnO3 increases by 9 K upon replacing 16O by 18O; the isotope shift increases with the magnetic field in La0.5Ca0.5MnO3 and in Nd0.5Sr0.5MnO3.42 In Pr0.67Ca0.33MnO3, the magnetic field-induced insulator-metal transition occurs at a higher field on 18O substitution; the heavier isotope favors the insulating state.43 The isotope effect on TCO is greater in Nd0.5Sr0.5MnO4 than Pr0.5Ca0.5MnO3, indicating the role of 〈rA〉 as well.44 Substitution of Mn by cations such as Al3+ and Fe3+ in charge-ordered manganates destroys charge ordering at moderate

doping (x g 0.03), but the materials remain insulating. However, substitution by Cr3+ readily destroys charge ordering and renders the material FM and metallic.45,46 In Sm0.5Ca0.5Mn1-xCrxO3, the TCO (275 K when x ) 0.0) decreases with increasing x and charge ordering disappears at x ) 0.05. The x ) 0.05 composition shows an insulator-metal transition when the material becomes FM.47 The effectiveness of Cr3+ in destroying the CO state is considered to be due to its favorable electronic configuration (t32g), which is the same as that of Mn4+. However, Cr3+ in the Mn3+ site would be surrounded immediately by Mn4+ ions, which would not allow for near-neighbor electron hopping. Hopping would be more favored if Mn4+ were substituted by an appropriate quadrivalent cation such as Ru4+ (t42g e0g). Recent studies have shown that substitution of Mn by Ru in Nd0.5Ca0.5MnO3 destroys charge ordering and renders the material FM, with the Tc increasing with Ru content; the material also shows an insulator-metal transition46 (Figure 22). The marked effect of Ru substitution is also seen in Nd0.5Sr0.5MnO3 where the Tc increases with the Ru content to well above 300 K, but charge ordering is destroyed (Figure 23). Phase Separation. The formation of FM clusters in an AFM host matrix in the rare earth manganates has been noticed by many workers. Thus, spin glass behavior has been encountered in the Ln1-xAxMnO3 system at either extreme, corresponding to large or small x. Electronic phase separation is also evidenced

5886 J. Phys. Chem. B, Vol. 104, No. 25, 2000

Figure 24. Variation in the percentage of the different phases of Nd0.5Sr0.5MnO3 with temperature: FMM phase (diamonds); orbitally ordered A-type AFM phase (circles); charge-ordered CE-type AFM phase (squares) (from Woodward et al.50).

in the manganates. Thus, an electron microscopic study of La1-x-yPryCaxMnO3 (x ) 0.375) has shown electronic phase separation into a submicrometer-scale mixture of CO insulator regions and FMM domains. Perculative transport could occur between the two states.48 The coexistence of FM and CO states has been observed in La0.5Ca0.5MnO3 and Nd0.25La0.25Ca0.5MnO3.38,40 Some phase separation is likely in many of the charge-ordered manganates. In Cr-doped Nd0.5Ca0.5MnO3, submicrometer FMM domains are embedded in an AFM CO state, so the material shows a relaxor behavior.49 Nd0.5Sr0.5MnO3, which shows evidence for separation into three macroscopic phases, is particularly interesting. These are the high-temperature FMM phase (Imma), the A-type AFM intermediate-temperature phase (Imma), and the CE-type AFM CO low-temperature phase (P21/m).50 The A-type AFM phase starts manifesting itself around 220 K, whereas the CE-type CO phase first appears at 150 K. In Figure 24, we show the phase compositions at different temperatures. There are three phases at the so-called CO transition at 150 K. The presence of the high-temperature FMM phase, even at very low temperatures, is noteworthy. These results are of significance in interpreting many of the properties of this manganate. The fact that such phase separation is seen by X-ray/neutron diffraction implies that even the minority phases have large domains (g100 nm). The FMM phase of Nd0.5Sr0.5MnO3 has a larger volume than the average volume or the volume of the low-temperature CO phase. The phase-separation behavior of this system and the relative stabilities of the structures seem to depend crucially on the Mn4+/Mn3+ ratio. Thus, the regime Mn4+/Mn3+ > 1 seems to stabilize the orbitally ordered AFM (A-type) phase. Unlike Nd0.5Sr0.5MnO3, Nd0.45Sr0.55MnO3 has an A-type AFM state below TN (220 K) and metallicity is confined to the ferromagnetic ab plane below TN, whereas the material is insulating along the c-axis. The large anisotropy in this material implies that the carriers are confined to the FM layer by magnetic and orbital ordering.51 An interesting experiment on phase-separated Nd0.5Sr0.5MnO3 at low temperatures was performed recently wherein the phase composition was determined by neutron diffraction in the absence and presence of a magnetic field.52 The results show how on applying a magnetic field, the CO state at low temperatures, by and large, transforms to the FMM state (Figure 25). For some reason, a small proportion of the intermediatetemperature A-type AFM phase persists. Effect of Electric Fields. Charge-ordered manganates such as Pr1-xCaxMnO3 (x ≈ 0.3-0.4) undergo a CO-FMM transition

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Figure 25. Effect of magnetic field (6T) on phase-separated Nd0.5Sr0.5MnO3 at 125 K (from Ritter et al.52).

Figure 26. Electric current induced insulator-metal transition in Nd0.5Ca0.5MnO3 films deposited on Si(100) at different values of the current. Inset show I-V curves at different temperatures (from Rao et al.54).

on application of moderate magnetic fields. However, manganates with small 〈rA〉 such as Y0.5Ca0.5MnO3 are, for all practical purposes, unaffected by magnetic fields. Laser irradiation has been reported to cause an insulator-metal transition in Pr0.7Ca0.3MnO3, generating a localized conduction path, although the bulk of the sample is insulating.53 It has been found recently that small d.c. currents induce insulator-metal transitions in thin films of several charge-ordered rare earth manganates, including Y0.5Ca0.5MnO3, Nd0.5Ca0.5MnO3, and Pr0.7Ca0.3MnO3.54 The current-voltage characteristics are nonohmic and show hysteresis. The I-M transition temperature decreases with increasing current (Figure 26). The hysteretic I-M transition in Figure 27 is specially noteworthy in that there is a reproducible memory effect in the cooling and heating cycles. The current-induced I-M transition occurs even in Y0.5Ca0.5MnO3,

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Figure 28. Charge ordering in La0.5Sr1.5MnO4 showing oxide ion displacements. Mn3+ (eg) orbitals are shown (from Ishikawa et al.56a).

when x ) 0.7. La0.5Sr1.5MnO4 shows ordering of the Mn3+ and Mn4+ ions at about 220 K, accompanied by the ordering of the eg orbitals (Figure 28). The material becomes antiferromagnetic at 110 K and exhibits anisotropic properties arising from orbital ordering.56 At the 220 K CO transition, a significant change occurs in the conductivity spectrum. The order parameter for orbital ordering increases at TCO, grows further with decreasing temperature, and decreases on spin ordering at TN. The order parameters for charge and orbital ordering seem to evolve together. Application of high magnetic fields gives rise to metamagnetic transitions below TCO, and charge and orbital ordering are destroyed by the magnetic field. Charge ordering in LaSr2Mn2O7 (n ) 2) has been observed by electron diffraction.57 There is a need to study charge ordering in this as well as in other rare earth analogues, including the calcium derivatives. Figure 27. (a) Temperature variation of resistance of an oriented Nd0.5Ca0.5MnO3 film deposited on LaAlO3(001) for different values of the current; (b) resistance-temperature plots for three current values recorded over cooling and heating cycles showing memory effect. Inset in part a shows I-V curves at different temperatures (from Rao et al.54).

which is not affected by large magnetic fields. Furthermore, there is no need for prior laser irradiation to observe the currentinduced I-M transitions. It is proposed that electric fields cause depinning of the randomly pinned charge solid. There appears to be a threshold field in the CO regime beyond which nonlinear conduction sets in along with a large broad-band conductivity noise.55 Threshold-dependent conduction disappears around TCO, which suggests that the CO state gets depinned at the onset of nonlinear conduction. At small currents or low magnetic fields, resistance oscillations occur because of temporal fluctuations between resistive states. Layered Manganates. The interplay of spin, orbital, and charge ordering in the rare earth manganates in determining their properties becomes even more prominent in the layered manganates. In the Ruddlesden-Popper series of manganates, (Ln, A)n+1MnnO3n+1, the n ) ∞ phases are the three-dimensional perovskites. The n ) 2 phases, such as La2-2xSr1+2xMn2O7, show a metallic ground state for x g 0.17 and high CMR; they also exhibit interesting properties arising from the layered nature of the materials. The n ) 1 member, Ln1-xSr1+xMnO4, with the quasi two-dimensional K2NiF4 structure, becomes metallic only

Concluding Remarks The rare earth manganates exhibit a variety of properties and phenomena, with an extraordinary sensitivity to various factors such as cation size, pressure, and magnetic and electric fields. In particular, the mutual relations between orbital ordering, charge ordering, and spin ordering in the rare earth manganates is truly fascinating. It is because of this interplay that charge ordering in these materials has turned out to be such an attractive area of research. In manganates such as Pr0.6Ca0.4MnO3 and Nd0.5Ca0.5MnO3 (〈rA〉 ≈ 1.17 Å), charge ordering occurs in the paramagnetic state, and commensurate orbital ordering accompanies a transition to the CE-type AFM state. In the paramagnetic CO state, there could be some orbital ordering that would be incommensurate, and FM correlations or clusters are generally present. In Nd0.5Sr0.5MnO3 (〈rA〉 ) 1.24 Å), where charge ordering occurs on cooling a FMM state, however, it is possible to delineate transitions associated with orbital and charge ordering. In La0.5Ca0.5MnO3 (〈rA〉 ) 1.20 Å), charge ordering and orbital ordering occur when the FM state transforms to an AFM state (CE type) on cooling. In the regime where the FM and CO states coexist, there is no long-range orbital ordering. As expected, the La0.5Ca0.5MnO3 system gives rise to complex lattice images. In La0.33Ca0.67MnO3, however, there is a clear-cut charge ordering transition (260 K) accompanied by orbital ordering, and followed by a transition to

5888 J. Phys. Chem. B, Vol. 104, No. 25, 2000 a CE-type AFM state, and paired stripes of Mn3+O6 octahedra have been observed in the lattice images. In manganates such as Nd0.5Ca0.5MnO3 and Y0.5Ca0.5MnO3 with a small 〈rA〉, it is not clear whether ordered single or bistripes would be present. It is important to ensure that bistripes and other features found by electron miscroscopy truly represent the bulk structure. Lowtemperature lattice imaging of these materials with highresolution electron microscopy would be of great value. Although we are able to distinguish spin, charge, and orbital ordering transitions, we do not understand some aspects. It is not entirely clear whether commensurate orbital ordering occurs only in the AFM (CE) state. The electron-hole asymmetry in the manganates, with respect to the FM and CO states, needs to be explained properly. Is it certain that we can never encounter ferromagnetism in the electron-doped materials? Also, what is the type of AFM ordering in the electron-doped CO manganates? Phase separation in the manganates is especially interesting. Phase separation generally involves the formation of clusters of one phase in another (e.g., FM clusters in a CO or AFM phase). Macroscopic phase separation involving the presence of distinct domains of fairly large sizes (g100 nm) with Bragg peaks in the diffraction patterns is, however, different from the formation of clusters or stripes. Such inhomogeneous distributions of CO or FM (charge and spin) phases in a material requires understanding. Coulomb forces would prevent accumulation of charge in a phase-separated regime in the absence of the means to compensate the charge. Electronic phase separation is known in La2NiO4+δ and La2CuO4+δ.3,11,28 In the rare earth manganates, there is increasing evidence for the coexistence of FM and AFM (CO) phases. Although it is possible that small changes in the Mn3+/Mn4+ ratio could affect phase separation, we do not understand the mechanism. Although one can consider the presence of large domains (e.g., CO and FM) of different phases of a given composition as a criterion for phase separation, the effects of phase separation, in contrast to those of chemical inhomogenieties or cluster formation, need to be investigated in greater detail. The 〈rA〉 regime of 1.20 ( 0.02 Å in Ln0.5A0.5MnO3, which exhibits complex phenomena and properties, including reentrant transitions, deserves further study. It is useful to examine such systems with fixed 〈rA〉 and variable cation size mismatch. Charge ordering in the layered manganates has to be investigated in detail. We do not yet have a full understanding of the extraordinary effect of electric fields on the CO state. Acknowledgment. The author is thankful to the Department of Science and Technology and the Science Office of the European Union for support of this work. References and Notes (1) (a) Honig, J. M. In The Metallic and the Nonmetallic States of Matter; Edwards, P. P., Rao, C. N. R., Eds.; Taylor and Francis: London, 1985. (b) Honig, J. M. Proc. Indian Acad. Sci., Chem. Sci. 1986, 96, 391. (2) Tsuda, N.; Nasu, K.; Yanase, A.; Siratori, K. Electronic Conduction in Oxides; Springer: Berlin, 1991. (3) (a) Kivelson, S. A.; Fradkin, E.; Emery, V. J. Nature (London) 1998, 393, 550. (b) Tranquada, J. M.; Sternleib, B. J.; Axe, J. D.; Nakamura, Y.; Uchida, S. Nature (London) 1995, 375, 561. (4) Imada, M.; Fujimori, A.; Tokura, Y. ReV. Mod. Phys. 1998, 70, 1039. (5) (a) von Helmolt, R.; Holzapfel, B.; Schultz, L.; Samwer, K. Phys. ReV. Lett. 1993, 73, 2331. (b) Chahara, K.; Ohno, T.; Kasai, M.; Kozono, Y. Appl. Phys. Lett. 1993, 63, 1990. (6) (a) Rao, C. N. R.; Raveau, B., Eds. Colossal Magnetoresistance, Charge Ordering and Related Properties of Manganese Oxides; World Scientific: Singapore, 1998. (b) Ramirez, A. P. J. Phys: Condens. Matter 1997, 9, 8171.

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