Spin, Charge, and Lattice States in Layered Magnetoresistive Oxides

© Copyright 2001 by the American Chemical Society

VOLUME 105, NUMBER 44, NOVEMBER 8, 2001

FEATURE ARTICLE Spin, Charge, and Lattice States in Layered Magnetoresistive Oxides J. F. Mitchell,* D. N. Argyriou, A. Berger, K. E. Gray, R. Osborn, and U. Welp Materials Science DiVision, Argonne National Laboratory, 9700 S. Cass AVenue, Argonne, Illinois 60439 ReceiVed: April 17, 2001; In Final Form: August 6, 2001

Colossal magnetoresistive materials are perovskite-related mixed-valent (Mn3+/Mn4+) manganese oxides that exhibit both spontaneous (at a Curie transition) and magnetic field-induced insulator-metal transitions. In concert with the dramatic changes in electrical conductivity, these oxides exhibit large lattice anomalies, ferro- and antiferromagnetism, charge ordering of the Mn3+/Mn4+ sites, etc. In this article, we discuss how a particular class of these manganite materials, naturally layered manganites La2-2xSr1+2xMn2O7, has allowed us to experimentally probe many of these tightly coupled phenomena. In particular, we examine the structureproperty relationships that determine the critical magnetic ground states, we discuss how conductivity and its field dependence can test prevailing models for the magnetoresistance effect, and we explore the interplay and competition between charge- and magnetic-order on both long- and short range length scales. Finally, we present evidence from neutron and X-ray scattering that these short range charge correlations are essential to the mechanism of colossal magnetoresistance in naturally layered manganites.

1. Introduction Transition metal (TM) oxides, particularly those related to the perovskite structure (Figure 2), have provided a fertile ground for condensed matter physics for more than half a century. There are many reasons why these materials have captured our fascination. They exhibit exotic electronic phenomena, such as insulator-metal transitions and superconductivity. They adopt a wide range of magnetic structures, both long- and short-range, static and dynamic. They often adopt relatively simple crystal structures that can be modified with almost infinitesimal precision by appropriate chemical substitutions. Such control opens the door to detailed study of a wide expanse of exotic physics. Finally, TM oxides already exist as or hold substantial promise for advanced technological applications, such as magnetic sensors,1 superconducting devices,2 and ferroelectric memories.3 As a result of such exciting features, this broad class of materials has captured considerable attention in condensed matter science worldwide. They are inherently complex, and the inter-relationships among their spin, charge, and structural degrees of freedom pose deep and fundamental 10.1021/jp011419u

questions about the nature of the metallic state, the nature of phase stability, and the energetics of exotic coupling phenomena in correlated systems. An underlying reason for all of these spectacular phenomenas particularly among the perovskite oxides of the first transition seriessis the delicate balance between one- and two-electron terms in the energy and the implications for electron correlation in the solid state. This balance naturally leads to multiple electronic and magnetic ground states that compete at similar energy scales. Which state prevails in this competition becomes a sensitive function of both intrinsic chemical-structural features (e.g., dopant ion size, charge, oxygen stoichiometry, strain, etc.) and external parameters (temperature, pressure, magnetic field). The TM oxides thus provide a spectacular laboratory for exploring how competing ground states sort themselves out, how particular structures and/or states can be biased both intrinsically and extrinsically, and how these phenomena can be harnessed for practical application. One particularly compelling group of transition metal oxides that has garnered tremendous attention in the past several years

This article not subject to U.S. Copyright. Published 2001 by the American Chemical Society Published on Web 10/16/2001

10732 J. Phys. Chem. B, Vol. 105, No. 44, 2001

Figure 1. Fab(T) for La1.2Sr1.8Mn2O7 (x ) 0.4) bilayer manganite in 0, 3, and 7 T.

is the doped rare-earth manganites, R1-xAxMnO3, where R ) trivalent lanthanide and A ) divalent alkaline earth.4-6 These materials, first carefully studied in the 1950s,7,8 have enjoyed a renaissance in recent years because they exhibit colossal magnetoresistance (CMR), the spectacular decrease of electrical resistivity in an external magnetic field illustrated in Figure 1. While this effect and its potential technological impact have generated renewed interest in manganite research, the scientific community quickly realized that the fundamental physicss thought to be understood decades earliershad only begun to be explored. In addition to the magnetic field-induced insulatormetal (I-M) transition, CMR manganites reside at a nexus of myriad coupled physical processes: zero-field I-M transitions in the presence of a concomitant para- to ferromagnetic (PMFM) transition, enormous structural rearrangements, electronic phase separation, and charge-ordering on various length-scales are foremost in importance among these processes. Three classes of manganites shown in Figure 2 have shown CMR: the related 3-D perovskites (e.g., La1-xCaxMnO3)9 and 2-D Ruddlesden-Popper (R-P)10 phases (La2-2xSr1+2xMn2O7) and the pyrochlore Tl2Mn2O7.11,12 While all three systems share the common structural motif of vertex-sharing MnO6 octahedra linked in the solid state, the pyrochlore differs from the perovskite and R-P phases by being undoped by cation substitution. That is, the perovskite and R-P phases rely on aliovalent cation substitution (e.g., La3+ for Sr2+) to generate a mixed-valent Mn3+/Mn4+ array. As we shall see, this mixedvalent state and its generation of mobile carriers are critical to understanding the behavior of the perovskite-related manganites. It is believed that the pyrochlore generates its small carrier concentration (∼0.001-0.005 carriers/Mn 11) by self-doping of the Mn bands via overlap of low-lying Tl 6s states.13 Because the pyrochlore is sufficiently different from the perovskite and R-P phases, the remainder of this review will focus only on these latter doped, mixed-valent manganites. As alluded to above, the R1-xAxMnO3 perovskite structure allows for virtually infinite tunability of physical properties by suitable cation substitutions and/or oxygen stoichiometry control. Indeed, most of the rare earth and alkaline earth cations can be combined into perovskite manganites. Such manipulations of the chemical composition manifest themselves in structural modifications to the ideal cubic structure shown in Figure 2. This yields lower-symmetry structures characterized by cooperatively rotated and/or distorted MnO6 octahedra. The ability to tune the magnitude of such distortions allows for systematic investigation of the connections among structural, magnetic, and electronic degrees of freedom in TM oxides. In the case of the CMR oxides, the nominally cubic perovskite structure is often

Mitchell et al. quite strongly distorted by the combined influence of cation size mismatch and electronic instability (Jahn-Teller distortion of Mn3+ ion). The size mismatch results in cooperative rotations of the MnO6 octahedra, yielding an orthorhombic structure, while the Jahn-Teller distortion leads to an anisotropic bondlength distribution within the octahedra. As discussed throughout this review, the crystal structuresand its response to changing magnetic and/or electronic statessplays an extremely important role in the physics of manganites. As shown in Figure 2, the R-P phases are derived from the perovskite structure by interleaving double blocks of rocksalt structure, (La,Sr)O, between the electronically and magnetically active perovskite sheets. The usual symmetry of these naturally layered structures is I4/mmm, the body-centering operation implying that the octahedra from neighboring perovskite blocks are staggered with respect to one another. The generic formula for the R-P phases is An+1MnnO3n+1, where n designates the number of perovskite layers per block. In the manganites, the n ) 1 phase La1-xSr1+xMnO4 is known but shows no FM metallic ground states. Rather, it is characterized either by antiferromagnetic (AFM) or spin-glass (SG) insulating states.14,15 The n ) 2 phase La2-2xSr1+2xMn2O7, however, shows a variety of magnetic and electronic states,16-18 potentially due to the greater bandwidth afforded the bilayer structure. Unlike the perovskites, to date only the La,Sr series has been observed to show FM and I-M transitions, although compounds with other rare-earth ions have been prepared. The MnO6 octahedra in these materials are less distorted and do not rotate as severely as in the perovskites (typical Mn-O-Mn angles in the planes are 179°), both factors ameliorating band-narrowing in the electronically active bilayers. Furthermore, the reduced dimensionality of this structure vis-a`-vis the 3-D perovskite is expected to amplify the magnetic, electronic, and orbital fluctuations in the temperature regime immediately above the Curie transition. It is this fluctuation regime where external fieldssmagnetic, electric, pressurescouple most strongly to modify the physical behavior of manganites. Thus, the naturally layered manganites are a powerful resource for studying the CMR effect and its associated physics. The Jahn-Teller distortion is extremely important to understanding the physics of both perovskite and naturally layered manganites, as it is the principal cause of the self-trapping of carriers into polaronic states (vide infra). Figure 3 shows a simplified orbital energy level diagram for octahedrally coordinated Mn ion. With four d electrons and under the influence of the weak crystal field of the oxygen octahedron, Mn3+ adopts a high-spin (S ) 2) configuration with three unpaired electrons in the nonbonding t2g orbitals and a single electron in the degenerate, antibonding eg orbitals. This single eg electron results in an orbitally degenerate electronic state for Mn3+ that is unstable to a distortion along a vibronic coordinate that lifts the orbital degeneracy, typically by generating octahedra with two long (>2 Å) Mn-O bonds and four short ( TC to the FM state at T < TC can be shown to increase the conductivity by a factor of two, rationalizing why the I-M transition coincides with the Curie point. Likewise, for T slightly above TC, application of field will tend to align the spins, increasing the conductivity and leading to a large magnetoresistance. Note that a simple DE picture would predict that the transition temperature should follow x(1 - x), where x is the fraction of Mn4+ and 1 - x the fraction of Mn3+. Thus, the DE model would predict a composition dependence of TC symmetric about a maximum at x ) 0.5. In practice, the phase diagram of manganites is distinctly asymmetric around x ) 0.5, requiring modifications to the DE picture. As we shall

see, these modifications largely arise from the strong electronlattice coupling characteristic of the manganites. Early in the modern study of CMR manganites, Millis et al.22,23 pointed out that the factor of two limitation on CMR is inconsistent with typical experimental results in which CMR in excess of a factor of 1000 was reported.4 They invoked the strong electron-lattice coupling inherent to the Jahn-Teller system to develop a theory of polaronic transport. The carriers become self-trapped by the Jahn-Teller distortion surrounding Mn3+; the relaxation of these lattice distortions, engendered by the double-exchange interaction, provides the necessary mechanism to account for the colossal magnetoresistance. Using this model, they were able to calculate magnetoresistance in reasonable quantitative agreement with experiment. They also predicted that anomalous changes in oxygen Debye-Waller factors should occur at the I-M transition, a prediction that was rapidly verified by several neutron scattering groups.24,25 Subsequently, several transport26-28 and scattering29-31 studies have amplified and greatly expanded the understanding of polarons and lattice distortions in the CMR mechanism. Indeed, as discussed in section 5.2, the naturally layered manganites provided the first direct evidence of polaron formation and collapse through the I-M transition.32 It should also be noted that in simple terms the concentration of Jahn-Teller distorted sites depends linearly on the Mn3+ concentration, providing the asymmetry needed to begin explaining the compositional dependence of the phase diagram. In the polaronic regime, carriers reside on the Mn3+ sites on time scales longer than typical optical phonon frequencies, allowing the distortion to “lock in.” In special cases, such as when the Mn3+/Mn4+ ratio is unity, the self-trapped polarons form an ordered superstructure, or a charge-ordered (CO) phase. Such is the case of Nd0.5Sr0.5MnO3, a perovskite with this 50% Mn3+ composition. Below TC ∼ 270 K, the material is a FM metal, but at TCO ∼ 160 K, a dramatic increase in resistivity, accompanied by an AFM transition, is observed. Electron diffraction shows the appearance of superlattice reflections consistent with a supercell of alternating Mn3+ and Mn4+ sites.33 Furthermore, crystal structure studies of the related La0.5Ca0.5MnO3 unequivocally show this checkerboard pattern in real space.34 The CO lattice can be “melted” in applied magnetic fields or under pressure. Indeed, extremely large CMR effects can be found in these systems at a temperature just slightly below TCO. Here, the FM metallic state is only slightly less stable than the charge-ordered insulator, and relatively small fields can produce orders-of-magnitude decreases in resistivity.35 CO is also found in the naturally layered manganites near x ) 0.5,36 where it competes with incompatible magnetic structures as a function of temperature (see section 5.1).

10734 J. Phys. Chem. B, Vol. 105, No. 44, 2001 Recent theoretical37-41 and experimental42-44 studies of the manganites have suggested that CO on short-range length scales, that is, below the coherence length measured by Bragg diffraction, may be a critical aspect of CMR. These results suggest that the I-M transition occurs as a percolative phenomenon in a phase-segregated system: FM metallic regions grow (either in field or as TC is approached from above) at the expense of CO regions until a percolation threshold is reached, beyond which the material becomes metallic. Because of differential volumes between the (smaller) FM and (larger) CO regions, the importance of strain on the phase segregation has also been emphasized by a number of research groups.45,46 As discussed in section 5.2, scattering studies of naturally layered manganites in our laboratories have corroborated the view that short-range charge correlations are a critical ingredient in the understanding of CMR. Finally, a more exotic featuresan orbital degree of freedoms must be introduced, as it too impacts the highly interconnected physics of manganites. The occupied eg orbital on Mn3+, either x2-y2 or z2, imparts a local lattice strain (Jahn-Teller distortion). Often, a cooperative long-range ordering of these orbitals develops to accommodate the strain, as seen in LaMnO3,47 La0.5Ca0.5MnO3,48 La0.5Sr1.5MnO4,15 etc. In the case of incommensurately doped materials, e.g., La1.2Sr1.8Mn2O7 discussed later, the orbital order may appear on short-range length scales and/ or be dynamic. Importantly, magnetic interactions and orbital arrangements are closely connected, as codified in Goodenough’s rules for 180° Mn-O-Mn magnetic exchange.49,50 Simply put, these rules state that FM interactions occur when occupied Mn3+ orbitals overlap with unoccupied orbitals (either Mn4+ or orthogonal Mn3+ states) on neighboring ions. Indeed, as we shall see, these rules are extremely useful for predicting the magnetic structures of orbitally ordered manganites. This brief introduction has identified the pertinent issues in manganite physics: the CMR effect and the associated I-M and FM transitions, double exchange, Jahn-Teller distortions, polaronic transport, and charge- and orbital-ordering. It is clear from this list that the manganites sit at the center of a richly interconnected web of the some of the most compelling fundamental issues in condensed matter physics, explaining why such attention has been lavished on these materials. Naturally, many questions can be asked on the basis of the issues outlined above. Some of these include: how do orbital and magnetic structures evolve with chemical composition and what connections can be drawn? Does the double-exchange rule really apply in these materials given the strong evidence for lattice effects? Are the materials really metals in their ground state? What is the nature of the magnetic phase transition (conventional or not)? What direct evidence can be found for polarons and/or for shortrange charge/orbital ordering? And finally, what is the impact of such features on the mechanism of CMR? As argued above, we have focused on layered manganites in the effort to answer these questions. The reduced dimensionality of these structures is anticipated to enhance the magnetic and electronic fluctuations in the critical temperature region just above TC. It is in this region where external fields can harness these fluctuations to generate ordered phases and the CMR effect. The goal of this article will be to discuss how layered manganites synthesized and studied in our laboratories are answering fundamental questions about CMR and manganite physics. In the next sections, we will explore the broad structural and magnetic phase diagram of naturally layered manganites to show the critical linkage between long-range orbital and magnetic structures. We will then describe transport measure-

Mitchell et al. ments on strategically chosen single crystals to demonstrate that (a) double-exchange is indeed an appropriate description for the field dependence of electronic transport and (b) the lowtemperature behavior of these materials is consistent with a metallic ground state. Next, we will highlight the role of magnetic correlations, discuss the nature of the magnetic phase transition, and explore a first order spin-flop transition associated with low-field magnetoresistance. By combining results of neutron and X-ray scattering studies on single crystal samples, we will provide direct evidence of polarons and their shortrange correlations. Such observations are consistent with models of short-range charge order and can provide a unified picture of the CMR effect. Finally, we will look forward, identifying significant outstanding questions and describing some approaches we are taking to answer them with naturally layered manganites. 2. Crystal and Magnetic Phase Diagram of Layered Manganites Figure 4 shows the complete structural, electronic, and magnetic phase diagram of La2-2xSr1+2xMn2O7 in the region where samples have been successfully prepared, 0.3 < x e 1.0.17,51,52 As is readily seen, these compounds show an impressive array of structural, electronic, and magnetic states as a function of temperature and composition. The interesting FM metallic (FMM) region extending from x ) 0.3 to x ) 0.4 was quickly studied, as these compounds could be readily synthesized by conventional solid state techniques, and growth of crystals suitably large for neutron scattering (several mm on an edge) was not extremely difficult using floating-zone optical image furnaces.10,17,53,54 However, the highly Mn4+ region beyond x ) 0.5 has required more complex synthetic approaches developed in our laboratories;55,56 unfortunately, crystal growth of materials beyond x ) 0.6 has thus far proved unsuccessful. This region is important because here the connection between orbital ordering and magnetism is most clearly expressed. In this section, we will discuss the descriptive physics of the various phases, then seek understanding for their stability by appealing to connections between structure and magnetism described in the 50s by Goodenough and more recently in theories developed independently by Akimoto57 and Maezono.58 2.1. Evolution of Structure with Doping: The Phase Diagram 0.3 e x < 0.5. The Mn3+-rich portion of the La2-2xSr1+2xMn2O7 phase diagram, 0.3 e x < 0.5, has been reported by several groups using solid-state synthesis.51,52,59,60 However, the pioneering report of single-crystal synthesis and the CMR effect by Moritomo et al.61 cemented the importance of the layered manganites as a new class of CMR compounds. We and other groups grew crystals in this regime to map out the composition dependence of TC as well as to facilitate transport and magnetization studies (vide infra). In the process, we have uncovered a rich variety of magnetic structures, and a connection between structural distortions and the doping dependence of TC. Neutron diffraction has revealed four kinds of long-range magnetic structures in the FM region of the phase diagram, shown in Figure 5. With the exception of the x ) 0.5 composition, all structures have in common a ferromagnetic intrabilayer coupling. In contrast, the interbilayer coupling abruptly changes from AFM (x ) 0.3) to FM (0.32 e x < 0.5). Likewise, the magnetization direction lies parallel to the c-axis at low Sr concentration (x < 0.33) but moves into the a-b plane as Sr is added. At x ) 0.5, the intrabilayer coupling has now become AFM. Several competing terms in the magnetic energy

Feature Article

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Figure 4. Structural and magnetic phase diagram of the bilayer manganite La2-2xSr1+2xMn2O7 in the range 0.3 e x e 1.0 determined by neutron powder diffraction. Solid markers represent the magnetic transition temperature (TC or TN,); open squares delineate the tetragonal to orthorhombic transition. Several magnetic phases are identified: ferromagnetic metal (FM), canted antiferromagnet (CAF), and A-, C-, and G-type antiferromagnetic insulators (AFI) (see sections 2.1 and 2.2 and Figure 5 for details). The region marked “No LRO” has no magnetic diffraction peaks at T > 5 K. Samples in the region marked “CO” exhibit long-range charge ordering reflections in X-ray and/or electron diffraction. A temperature range schematically indicated by the yellow square shows how this long-range charge-ordered state grows then disappears at low temperature.

Figure 5. Low temperature (5 K) magnetic structures of bilayer manganites La2-2xSr1+2xMn2O7 (0.3 e x e 1.0) determined by neutron powder diffraction. Arrows represent direction of Mn spins. Labels for structures refer to the phase diagram of Figure 4.

determine these structures: crystal field and dipolar magnetic energies are particularly important. A study by Welp et al.62 on several of our crystals has shown that crystal-field effects are an essential ingredient, reflecting a possible shift of charge from z2 to x2-y2 orbitals with increasing Sr content. In a tetragonal system, the magnetic anisotropy energy can be written

E ) K1 sin2 θ + K2 sin4 θ + K3 sin4 θ sin2 φ cos2 φ (2) where θ is measured from the c-axis and φ from the [100]

direction. K1 and K2 are the first and second-order uniaxial anisotropy constants, and K3 is the in-plane anisotropy. These anisotropy constants can be deduced from magnetization measurements along the principal axes of the crystal. In layered structures such as these, K1 includes both an “intrinsic” contribution from the electronic structure and a contribution resulting from dipolar interactions between the Mn moments in neighboring perovskite blocks. This latter term can be evaluated analytically: it is small and negative for all compositions, favoring in-plane orientation of the Mn moments. Subtracting the dipolar contribution from K1 gives ku, the intrinsic magnetocrystalline anisotropy. A plot of ku and K2 versus composition reveals that K2 is always small and positive but that ku is large and changes sign from positive for x< 0.34 to negative for x > 0.34. A positive ku indicates c-axis anisotropy; a negative ku indicates in-plane anisotropy. These results are in excellent agreement with the magnetic structures determined by neutron diffraction. The diffraction experiments show that the distortion of MnO6 octahedra is consistent with a shift of electron density from 3z2-r2 (axial) to x2-y2 (planar) orbitals as Sr doping increases, as well as with the measured change in ku. The phase diagram of Figure 4 shows that TC varies approximately parabolically with x in the region 0.3 < x < 0.4, maximizing at x ∼ 0.36. As is typical of CMR manganites, as the temperature is lowered through TC, a lattice anomaly is observed in which the thermal expansion deviates strikingly from an extrapolation of the high-T data. For example, in the x ) 0.4 layered material, the a-axis dramatically shrinks (by ∼0.2%), and the c-axis expands (by ∼0.1%). Kimura noted from strain gauge measurements that the sign of this lattice anomaly reversed on passing through the composition of maximum TC.63 A neutron powder diffraction study in our laboratories64 showed conclusively that the octahedral distortion is strongly correlated to the composition dependence of TC, providing a rationale for the macroscopic strain gauge measurements and a hypothesis for why TC maximizes at this composition. The distortion of the MnO6 octahedron can be parametrized by a Jahn-Teller mode, Q, and its temperature-dependent differential ∆Q (see eqs 3 and 4; T′ is the temperature at which Q deviates from a linear extrapolation of the high-temperature


Mitchell et al.

Figure 6. Curie temperature as a function of MnO6 octahedral distortion through the insulator-metal transition, ∆Q. Circles are TC vs ∆Q, solid line joining squares is TC vs Sr content, x.

behavior, and l, m, and s are, respectively, the long, medium, and short Mn-O bonds in the MnO6 octahedron). Note that ∆Q measures the microscopic rearrangement of the MnO6 octahedron as the system passes through the concomitant PMFM and I-M transitions:

Q ) 4{(l + m)/2 - s]

(3)

∆Q ) Q(20K) - Q(T′)

(4)

Figure 6 shows TC as a function of ∆Q and immediately demonstrates on microscopic grounds (a) that the sign reversal at x ) 0.36 observed macroscopically by Kimura has its origin in the octahedral distortion and (b) that the maximum TC coincides with the minimal lattice rearrangement at the transition. Remarkably, examination of the individual Mn-O bonds making up the octahedron shows that for x < 0.36 and x > 0.36 these bonds show pronounced lattice anomalies, but at the optimum composition none of these bonds shows any thermal expansion anomaly at TC. One possibility then is that in these layered materials the system that is best structurally prepared for the transition, i.e., requires the least structural modification to accommodate the FMM state, will be able to do so at the highest temperature. It is also possible, however, that this maximum arises fundamentally as a compromise in the competition between DE (which should increase TC as x approaches 0.5) and the tendency for CO (which should depress TC as x approaches 0.5) and that the lattice monitors this competition. This possibility will be explored further in section 5.2. 2.2. Evolution of Structure with Doping: The Phase Diagram 0.5 e x e 1.0. As Sr is progressively added to the bilayer manganite (x > 0.5), the number of Mn3+-Mn4+ pairs is diluted, resulting in fewer FM interactions and a crossover to superexchange-mediated antiferromagnetism.49 Nonetheless, a variety of magnetic structures is still found in this Mn4+-rich end of the phase diagram, and the configuration of these magnetic structures can be understood by appealing to orbitalordering models inferred from the crystal structures.49,50 As can be seen from the phase diagram of Figure 4, there is also an unexpected “gap” region 0.66 < x < 0.74 in which no longrange magnetic order is observed by neutron diffraction as low as 5 K. We speculate on what might be going on in this fascinating region and how we are exploring it in section 6. It should be noted that the synthesis of these Mn4+-rich materials is not trivial. Routine solid-state preparations of these compositions (firing metal oxides and/or carbonates at 1300-

1400 °C) yields mixed phase samples containing perovskites, single-layer material, and bilayer material of a composition different than that of the starting mixture. We found that firing at extremely high temperature (1650 °C) followed by quenching to room temperature was required to stabilize these materials as single-phase, albeit in an oxygen deficient form, La2-2xSr1+2xMn2O7-δ.56,65 The oxygen nonstoichiometry, δ, depends systematically on Sr content, apparently reflecting a tendency to stabilize an average Mn oxidation state close to 3.5.65 Fortunately, the oxygen vacancies can be completely filled in a few hours at low temperature (12 h, 400 °C) without disrupting the underlying cation sublattice. Thus, the bilayer phases in this portion of the composition diagram are metastable below T ∼ 1600 °C but can be kept indefinitely at room temperature because of the kinetic obstacle to metal-ion diffusion. Obviously, these samples are all polycrystalline powders; single-crystal growth of compositions x > 0.6 has thus far been unsuccessful. Concentrating initially on the magnetic phase diagram, we find considerable similarity to the perovskite phase diagram rationalized by Goodenough.49 To reiterate Goodenough’s model, ferromagnetic exchange arises from the overlap of occupied and unoccupied d orbitals in the 180° Mn-O-Mn unit, requiring that at least one member of the pair be Mn3+. All Mn4+-Mn4+ interactions are antiferromagnetic, as are interactions involving Mn3+ pairs in which the occupied eg orbital is directed orthogonal to the Mn-O-Mn axis. In the present system, we see a progression of magnetic structures (Figure 4) with increasing Mn4+ concentration from A-type (ferromagnetic sheets coupled antiferromagnetically) through C-type (ferromagnetic rods coupled antiferromagnetically) to G-type (all five Mn-Mn neighbors antiferromagnetically coupled). Thus, in accordance with Goodenough’s picture, the increasing concentration of Mn4+ in the lattice leads to progressively less ferromagnetism (sheets f rods f points) as the number of unoccupied eg orbitals increases. We would now like to explore the connection between crystal structure and long-range magnetic ground state.18 This is most easily illustrated by samples taken from the region 0.74 < x < 0.90, which adopt the C-type (ferromagnetic rods) magnetic structure. Note that Figure 4 shows a crystallographic phase transition from tetragonal (I 4/mmm) to orthorhombic (I mmm) symmetry at temperatures approximately 100 K above the Nee´l temperature throughout this region. Detailed study shows that the structural phase transition is consistent with an orbital ordering that “locks-in” the material for the specific C-type magnetic structure. First, consider the orthorhombic structure. The rather substantial splitting of the a- and b-axis lengths (e.g., a ) 3.789 Å and b ) 3.864 Å for x ) 0.80 at 10 K) indicates that substantial electron density is being added to antibonding orbitals directed along b. In fact, at T ∼ 20 K, the a-axis exhibits virtually no concentration dependence in the orthorhombic regime. From these observations, we suggest that doped electrons enter 3y2-r2 orbitals, precipitating a strain-driven structural phase transition when their concentration is sufficient. Within the Goodenough framework, the interaction of these occupied directed orbitals with adjacent unoccupied Mn4+ sites along the b-axis should yield ferromagnetic rods at sufficiently low temperature. Because the orbitals are lined up preferentially along the b-axis, occupied orbitals on Mn sites from adjacent rods will not overlap, yielding the antiferromagnetic arrangement characteristic of the C-type structure. Thus, the picture is of a high-temperature orbital orderingsobserved as a symmetrylowering structural transitionspreparing the system for its eventual magnetic ground state.

Feature Article In the case of the perovskite system described by Goodenough, the A-type structure is not found in the region x ∼ 0.5. However, the particular crystal structure of the layered material offers an opportunity to explain this discrepancy within the general framework of Goodenough’s magnetic exchange rules. Recent theoretical treatments by Akimoto57 and independently by Maezono58 have suggested that the occupied orbital state for x ∼ 0.5 is the x2-y2 planar orbital, while for 0.3 < x < 0.5 the axial 3z2-r2 orbital is predominantly occupied. Roomtemperature lattice constant data as a function of composition corroborate this view. As La is substituted for Sr in the Sr3Mn2O7 (x ) 1.0) end-member to produce Mn3+ centers, the a-axis expands, and the c-axis contracts. Below x ∼ 0.5, however, this trend reverses, and the c-axis rapidly expands while the a-axis saturates, contracting slightly as x approaches 0.3. These trends are consistent with the addition of electron density in the MnO2 planes for 0.5 < x e 1.0 accompanied by a shift to axial occupation for x < 0.5, in accordance with the theoretical predictions of Akimoto and Maezono. Since the structure remains tetragonal, our powder diffraction data cannot identify the symmetry of the occupied in-plane orbital in the A-type stability field. However, the x2-y2 orbital should give rise to ferromagnetic sheets, as all interactions between Mn3+ and Mn4+ sites within the plane will be ferromagnetic; the occupied orbital extends isotropically toward all four neighboring sites. Furthermore, these ferromagnetic sheets couple antiferromagnetically within the bilayer to yield the A-type structure since x2-y2 orbitals in adjacent planes of the bilayer have zero overlap. The crystal structure data thus provide an indirect signature of orbital ordering consistent with the A-type spin ordering. It should be noted that recently developed resonant X-ray scattering tools66 have identified that the x2-y2 orbital-ordered state is stable in the perovskite Nd0.45Sr0.55MnO3, a material that adopts the A-type magnetic structure.67 Finally, since we know that for 0.8 < x e 1.0 anisotropic 3y2 - r2 orbitals are occupied, it is important to identify and to explore how the system crosses over to occupation of x2-y2 orbitals, perhaps using probes of local structure (e.g., neutron pair distribution function analysis30,68-70) or the above-mentioned resonant X-ray scattering probes. 3. Electrical Transport and Microscopic Conductivity Models Electrical conductivity and its response to applied magnetic fields rest at the crux of the CMR effect. To understand CMR, the I-M transition, etc., we must measure and understand the macroscopic electrical conductivity of the manganites and then connect these measurements to microscopic models, such as the DE model, polaronic models, phase segregation models, etc. Naturally layered manganites are ideally for suited for this task. Because of their various magnetic structures (vide supra) and their anisotropic structure, fields and currents can be oriented in many permutations relative to the underlying magnetic sublattice. This flexibility is simply not available in the perovskites. The naturally layered manganites thus provide a unique opportunity to test the validity of the DE mechanism and to explore the nature of the low-temperature conductivity, i.e., is it really a metal? 3.1. Double Exchange Selection Rule. As discussed in section 2.1, an extremely rich variety of magnetic structures competes in the FM region of the La2-2xSr1+2xMn2O7 phase diagram. For the particular case of La1.4Sr1.6Mn2O7, i.e., x ) 0.3, the intrabilayer coupling is FM with spins aligned parallel to the c-axis. However, each ferromagnetic bilayer is coupled


Figure 7. Scaling of xσc with M/Ms in La1.4Sr1.6Mn2O7 (x ) 0.3) demonstrates the DE selection rule. Squares: M/Ms; Solid line: xσc; Dotted line: fit to model in ref 71. The field is applied parallel to the a-b plane.

AFM to its neighbors (Figure 5). Measurement of conductivity (σab and σc) reveals an anisotropy which surpasses 10 000 below 30 K that is consistent with this c-axis AFM ground state and DE. In high fields (∼7 T, either along the c-axis or in the a-b planes), the AFM coupling is overcome, and while the pathway to this FM end point involves a coherent spin rotation for inplane fields, it crosses through a mixed-state in which AFM and a spin-flop (SF) state coexist for fields parallel to the c-axis.71 The occurrence of the AFM c-axis order presents a unique opportunity for a definitive test of the DE selection rule for conductivity, σ. First, note that the virtual nature of AFM superexchange precludes it as a direct transport mechanism for conductivity. Thus, the conductivity is proportional to the square of the DE transfer matrix element, i.e., σ ∼ {to cos(η/2)}2, where η is the angle between neighboring spins. This definitive test is made possible because in-plane magnetic fields, Ha, result in a coherent rotation of the sublattice magnetization in alternating bilayers with a well-defined angle that is related to the in-plane magnetization, Ma(Ha) ) Ms cos(η/2), where Ms is the saturation magnetization. For the DE mechanism to be a valid descriptor for σc, it is necessary to establish that σc ∼ Ma2. In Figure 7, the dependence of xσc on Ma/Ms is plotted, showing extremely good agreement, except at the smallest fields where domain formation nulls the macroscopic magnetization but does not impact the local magnetic order that governs the conductance by the DE mechanism. For this x ) 0.3 composition, a sufficiently large c-axis applied field, Hc, will provide the necessary Zeeman energy to overcome the net AFM interbilayer exchange coupling. Indeed, σc versus H shows the onset of this process at H ∼ 1100 Oe; however, a linear increase in σc observed between 1100 and 5500 Oe reveals a new feature not found in 3-D perovskite manganites. The large value of the demagnetization coefficient for the platelike crystals typically used in the measurements (2.2 × 0.3 × 0.1 mm3) can favor a mixture of AFM and FM regions, akin to the intermediate state of type-I superconductors. Also, the lowest-energy state in the FM regions may be a spinflop (SF) state exhibiting finite angles (θ with respect to the c-axis which alternate in adjacent bilayers. To visualize this mixed-state, we have employed magnetooptic imaging,72 a technique that maps the spatial distribution of magnetic fields in the sample. Light areas represent regions of high field penetration, i.e., FM or SF regions, and dark areas are AFM. Imaging of the x ) 0.3 crystal at T ) 21 K, shown in Figure 8, demonstrates clearly how the mixed state forms at H ∼ 1100


Mitchell et al.

Figure 8. Magneto-optic imaging of a La1.4Sr1.6Mn2O7 (x ) 0.3) crystal at T ) 21 K as a function of field. (a) 806, (b) 1076, (c) 1165, and (d) 2351 Oe.

Oe and grows up to H ∼ 2400 Oe, the highest field value accessible in our imaging experiments. 3.2. Nature of the Electronic Ground State. A critical question surrounding all of manganite physics is that of the nature of the highly conducting state at low temperature. For instance, is it best considered as a band-metal with a Fermi surface, or is the low-T state better described as a high-mobility hopping process? In the case of layered manganites, evidence is mixed. For example, the very low values of the lowtemperature conductivity, σ, of layered manganites and their slightly semiconducting behavior are not obviously consistent with a metallic state. Nonetheless, as shown by the Tokura group,54 at very low temperatures, σ approximately follows a σ(0)[1 + AxT] dependence that is consistent with weaklocalization effects in disordered metals for a 3-D system, e.g., quantum corrections to the density of states due to electron interactions. Photoemission studies73 of the x ) 0.4 compound La1.2Sr1.8Mn2O7 have indicated the presence of a so-called “ghost” fermi-surface and a pseudogap in the electronic density of states, implying that a traditional band description is appropriate but perhaps not sufficient. Our field-dependent lowtemperature transport studies clearly show a positive xB correction to σ that is also consistent with 3-D weak-localization effects in disordered metals. That this xB behavior occurs for all field and current directions confirms the 3-D nature of the metallic state. Furthermore, the data agree reasonably well with the recent extension of the theory of quantum interference to highly anisotropic, layered metals developed by Abrikosov.74 From these results, one infers a quantum coherent nature to the diffusive transport, as opposed to thermally activated, since the phase of the wave function is necessarily preserved after numerous elastic collisions. This may be a reasonable definition of metallic conductivity since, e.g., it implies that a finite σ will be found at zero temperature. The investigation of the ground-state begins by measuring the magnetoconductance in both the c-axis and a-b plane. Positive magnetoconductance is found for both σab(H) and σc(H), and both display a strong temperature and field (both Hab and Hc) dependence. In all cases, they are linear in xHab and xHc, at low temperatures and high fields, as anticipated from the theoretical expression:

σ(H,T) - σ(0,T) ) βxH + 4πM(T)

(5)

where the σ(H,T) represent actual conductivities for various

Figure 9. Residual magnetoconductance at 10 K after subtracting the small contribution from the suppression of spin waves: open squares, σab(xBc); open diamonds, σc(xBc); open circles, σab(xBa). The solid curves are fits to the theory of ref 74.

values of H and T and β is a temperature-independent parameter for the quantum interference effect. The significant temperature dependence of the magnetoconductance arises from the suppression of thermally excited spin waves. For the case of double exchange, a particularly powerful and simple model has been derived75 that fits the spin-wave part of the data exceptionally well:

(

)

σ(H,T) σ(0,0) -1) - 1 (1 - exp[-gµH/kBT]) (6) σ(0,T) σ(0,T) This expression has a single temperature-dependent parameter, σ(0,0)/σ(0,T). Extrapolating eq 6 to low temperatures allows the temperature-independent quantum interference contribution (β of eq 5) to be determined. These resulting quantum interference data are displayed in Figure 9 for three of the four field and current directions (β of the fourth one is trivially related to another with an additional undetermined constant of the theory). In the general theory of quantum interference, the bare values of the conductances in the absence of quantum interference effects, σao and σco, are reduced by phase interference between the multiple possible phase-conserving, diffusive electron trajectories. Then, any loss of phase along these trajectories leads to an increase in σ. The phase can be disrupted by inelastic scattering, with mean time τφ, or by applied fields, when the flux enclosed by two interfering trajectories is the order of one flux quantum, Φo. Abrikosov74 has recently calculated this effect for a quasi2-D metal, to which the data of Figure 9 can now be compared. The resulting fits indicate that the carriers retain their phase through over 4000 elastic collisions and a path length of ∼5 µm, a path that must include significant excursions along the c-axis since the low-temperature conductance anisotropy is only ∼300. This result provides a compelling argument for the 3-D metallic nature of conduction.76 Our primary conclusion then is that the layered manganites exhibit 3-D metallic behavior at low temperatures. The excellent agreement of the data of Figure 9 with theory strongly supports the metallic behavior, but it is the data for fields parallel to the bilayers that emphasizes this by proving the 3D nature of σ.

Feature Article


4. Magnetic Behavior Because of the coupling among charge, lattice, and spin in CMR manganites, it might be expected that the magnetic phase transition itself would be unconventional. Indeed, much evidence has been mounting from neutron scattering from perovskite manganites that the magnetic transition is first order, with TC determined less by the divergence of the magnetic correlation length than by the freezing out of polarons.31,77 However, it is important to note that this conclusion is rather materials dependent, and the so-called “wide bandwidth” manganites, such as La1-xSrxMnO3, may not share this characteristic.78 The case of the naturally layered manganites seems to be somewhere between, exhibiting a second-order but rather unconventional magnetic phase transition. The sample magnetization as a function of composition, field, and temperature generates a picture of an extremely unusual FM transition accompanied by an exchange constant, J, that is both strongly magnetization dependent and substantially reduced in the paramagnetic phase. This unusual behavior becomes obvious in Figure 10a, in which the magnetization dependent susceptibility, χ(m), is displayed for the paramagnetic phase of a La1.28Sr1.72Mn2O7 (x ) 0.36) sample. The data, which exhibit an unusual χ(m) peak structure for |χ(m)| > 0, have been analyzed in terms of the Landau theory of phase transitions,79 which assumes that the free energy F can be expanded in a power series in the magnetization, m. We found it sufficient to fit a polynomial of sixth order to our experimental data, according to

1 1 1 F ) a‚m2 + b‚m4 + c‚m6 - h‚m 2 4 6

(7)

which corresponds to

χ(m) )

1 a + 3b‚m2 + 5c‚m4

(8)

for the magnetization-dependent susceptibility. This form can be fit to experimentally measured data at several temperatures to extract the parameters a, b, and c. The coefficient a is required to be positive in the paramagnetic phase (T > TC), as is c. However, the anomalous peak found in χ(m) can only be described by a negative b. This is of fundamental importance because b defines the order of the phase transition at TC. For positive b values, a conventional second-order phase transition is described; negative b values indicate that the phase transition will be discontinuous.80 Importantly, the sign of b changes in the immediate vicinity of TC, as shown in Figure 10b. At high temperatures, the system seems to be heading toward a firstorder ferromagnetic phase transition, but ultimately, a secondorder phase transition is observed, in accord with neutron scattering results.81 In terms of the free energy functional, F, the observed anomaly corresponds to a deformation of the conventional energy surface, in particular to an enhanced stabilization of the m ≈ 0 state. For small values of the magnetization, the anomalous state exhibits an unusually narrow minimum in F (see inset to Figure 10b), which can be explained either by a reduction of the magnetic moment per unit cell or by a reduction of the ferromagnetic exchange coupling, J. It seems unlikely that the magnetic moment is changed, as such changes are typically associated with large energies. This then implies a substantially reduced J for the paramagnetic state. Thus, the change in the electronic structure at TC reflects itself not only in the conductivity, as in all CMR materials, but through a

Figure 10. (a) Magnetic susceptibility, χ, vs magnetization measurement for composition x ) 0.36 as a function of temperature, T > TC. The thin solid lines connect the χ-peak positions for the individual curves; (b) Landau parameters a (filled circles) and b (open circles) vs temperature extracted from the experimental χ(m) data; the solid line is a linear fit of the high-temperature data for a. Inset: Schematic of the free energy for the paramagnetic state. The solid line illustrates the behavior of a conventional ferromagnet, while the dashed line corresponds to the distorted energy surface discussed in the text.

substantial reduction of the FM exchange coupling. As T ∼ TC, J grows, flattening the minimum in F and causing the critical b parameter to change sign in accordance with a second-order


Mitchell et al.

Figure 11. Incompatible orbital ordering patterns for the CE chargeordered phase and the A-type structure.

transition. It should be noted that the extent of the reduction in J increases with increased Sr concentration, indicative of a chemical trend that depends on some other energy scale. Our data also indicate that the full J can be restored by applying a sufficiently large field. A possible explanation for both of these observations is developed in section 5.2. 5. Charge-Order, Phase Competition, and the CMR Mechanism With the broad survey of crystal and magnetic structure, bulk transport phenomena, and the nature of the magnetic transition now in mind, we turn to microscopic features of the coupling among structure, magnetism, and charge that lead to the CMR mechanism. In particular, we now discuss how correlations among these degrees of freedom interact at the nanoscale to produce short-range ordered units that dramatically impact the I-M transition and the CMR phenomenon. 5.1. Charge Order and Magnetic Phase Competition: Orbital Incompatibility. As mentioned in the Introduction, perovskite manganites at the special composition where the ratio of Mn3+ to Mn4+ is unity frequently enter a charge-ordered (CO) state as they are cooled. Characterized by high resistivity and the appearance of superlattice diffraction spots from cooperative ordering of Jahn-Teller distorted Mn3+, this CO state persists to He temperature and below. Figure 11a shows the zigzag pattern of eg orbitals characteristic of an orbital- and spin-ordered arrangement known as the CE structure. This pattern has been established both in perovskites and in layered materials by neutron diffraction36,34 and by resonant X-ray scattering.82 This CE structure7 can be seen to satisfy the Goodenough rules for magnetic exchange: all interactions along the zigzag chain should be FM due to the alternating Mn3+/Mn4+ sites, but interchain interactions should be AFM because of orthogonal orbital overlap. The bilayer manganite LaSr2Mn2O7 (x ) 0.5) also has a similar CE configuration, but unlike the perovskites, this CE state is only stable in a narrow temperature window 100 < T < 225 K, as measured both by electrical conductivity and by diffraction.36,83 The “melting” of charge ordering in zero field can be explained by a phase competition between the CE state and its particular orbital ordering pattern and the eventual A-type magnetic ground state, whose orbital ordering pattern is incompatible with that of the CE state. The important data are shown in Figure 12. The top panel shows a measurement of F(T) on a single-crystal sample, highlighting the CO transition at T ∼ 225 K and then the I-M transition at T ∼ 190 K The intensity of the CE superlattice reflection measured by neutron diffraction (Figure 12b) tracks the resistivity: intensity sets in just as F(Τ) begins to increase rapidly, maximizes near the resistivity peak and then plummets

Figure 12. Behavior of LaSr2Mn2O7 (x ) 0.5) as a function of temperature: (a) resistivity, (b) intensity of charge-ordering reflection (1.75,2.25,0), (c) intensity of A-type antiferromagnetic reflection (1,1,1), and (d) temperature evolution of (0,0,10) reflection showing two-phase coexistence.

dramatically, vanishing at T ∼ 100 K. In Figure 12c, the order parameter for the A-type phase ((111) reflection) is plotted; it becomes nonzero at essentially the same temperature where the resistivity and superlattice intensities begin to decrease. Finally, in the bottom panel of Figure 12, a series of high-resolution powder X-ray diffraction patterns are plotted, showing the temperature evolution of the (0,0,10) reflection. This reflection is particularly sensitive to the c-axis, and its line shape has been used as a measure of sample homogeneity.84 In the present case, the (0,0,10) reflection shifts, develops a shoulder, broadens into a double peak, and then narrows and shifts again as the temperature passes through the CE region and into the A-type antiferromagnet. This behavior provides compelling evidence of a two-phase coexistence in the CO region, with the CE phase yielding to the A-type phase, which eventually occupies the entire sample. A rationale for this behavior can be found by considering the incompatible modes in which the occupied eg orbitals on Mn3+ order in the CE and A-type phases. As discussed above,

Feature Article the A-type phase requires a completely different kind of orbital ordering pattern, one in which x2-y2 orbitals are occupied. In fact, detailed structural studies36 have shown that the Mn sites are better described as having the electron density sketched in Figure 11b. This leads to enhanced DE coupling in the sheets and destabilizes the CE structure. Thus, a picture develops in which the planar orbital structure nucleates in the existing CE phase, bringing the A-type AFM in its wake. As mentioned above, quantitative calculations by Maezono58 and by Akimoto57 clearly support the planar x2-y2 orbital-ordered ground state. A possible physical picture for this is that charge can delocalize in 2-D with the x2-y2 pattern but is confined to 1-D in the zigzag chains. The greater kinetic energy gain in 2-D favors this planar orbital ordering state. 5.2. Short-Range Charge Order in Layered Manganites. The importance of CO as a general phenomenon impacting CMR manganites beyond the 50% Mn3+/Mn4+ compositions has recently been emphasized both theoretically and experimentally. Tomioka et al.85 have shown convincing evidence of CO from transport studies in the Pr0.7Ca0.3MnO3 perovskite, an x ) 0.30 composition. Likewise, in this same compound Cox,45 Radaelli,46 and Roy86 have presented powerful evidence for coexistence of the CO phase with a ferromagnetic metallic phase under high-field conditions. These experiments and others like them have shown conclusively that CO can exist as a longrange ordered phase despite the incommensurate (i.e., deviating from Mn3+/Mn4+ ) 1) dopant concentration. As noted earlier, large, low-field CMR is often found in the compositions showing this long-range CO, raising the intriguing possibility that short-range CO might play an important role in the general CMR effect. By using the naturally layered manganite La1.2Sr1.8Mn2O7 (x ) 0.4), we have obtained X-ray and neutron scattering evidence for this short-range order, developed a model for its structure, and connected its growth and disappearance with the I-M transition.32,87 These data provide a compelling, unified picture of the mechanism of CMR in these layered materials. Consider first the polaronic picture described in the Introduction for T > TC. A defining characteristic of polarons in the CMR manganites is a local Jahn-Teller distortion, whose lifetime exceeds that of typical phonon frequencies. Such lattice distortions should be observable by scattering techniques, and they are. Figure 13a shows a slice of reciprocal space interrogated by X-ray scattering on a single crystal of La1.2Sr1.8Mn2O7 at the Advanced Photon Source (APS) of Argonne National Laboratory.32 The symmetry-allowed Bragg reflections are easily seen at (0,0,8), (0,0,10), and (0,0,12). The narrow rod of scattering joining these peaks arises from a small (∼0.1%) concentration of intergrowths, an unavoidable byproduct of the crystal synthesis.88 Importantly, a large “butterfly” of diffuse scattering is clearly seen around each of the Bragg spots. This butterfly arises partly from thermal diffuse scattering (TDS) and partly from the long-range strain-field associated with an isolated point defect. The latter is known as Huang scattering and can be separated from the TDS by tracking the temperature dependence of the diffuse scattering intensity. Importantly, Huang scattering monitors the uncorrelated deviations of the structure away from a perfect tetragonal lattice and close to a Bragg reflection; it typically follows a q-2 dependence. In this case, the detailed shape of the anisotropic diffuse scattering can be quantitatively modeled32 assuming an in-plane Jahn-Teller distortion of the MnO6 octahedra. That is, locally the tetragonal symmetry is broken by the Jahn-Teller instability, consistent with the polaron picture.


Figure 13. Diffuse X-ray scattering from a La1.2Sr1.8Mn2O7 (x ) 0.4) crystal: (a) “butterfly” scattering from uncorrelated lattice distortions and (b) diffuse superlattice reflections from a correlated charge modulation.

As shown by the Huang scattering, at temperatures well above TC, these localized carriers and their associated distortion fields are uncorrelated. However, as the temperature is lowered, some of the charges and strain fields may well begin to overlap, producing a correlated defect in the structure. Indeed, the broad superlattice reflections shown in Figure 13b are an explicit marker of a short-range correlation, i.e., a modulated structure. The position of the reflections, (0,(0.3,(1) in units of (2π/ a,2π/a,2π/c), show that the modulation is confined to the a-b plane with a repeat unit of approximately 3a, but incommensurate with the lattice. The widths of the peaks are considerably broader than the instrumental resolution, allowing us to estimate the correlation length, ξ, to be approximately 26 Å in the a-b plane and ∼10 Å along the c-axis. The latter implies that only neighboring bilayers are correlated, while the former indicates that the range over which the lattice distortions influence one another in the a-b plane is only about six to seven lattice spacings. Note that the appearance of these reflections at odd integer values of l implies that the modulation is 180° out of phase in neighboring bilayer units. By measuring the integrated intensity of many of these superlattice reflections, it has been possible to develop a structural model for the short-range modulated structure.89 It is characterized by a spatially varying Jahn-Teller distortion and a bilayer phase shift that minimizes the strain fields engendered by the distortion. The structure of this short-range modulated structure is shown in Figure 14. Features to note include: (a)


Mitchell et al.

Figure 14. Crystallographic model for the short-range charge modulated units inferred from superlattice reflections in a La1.2Sr1.8Mn2O7 (x ) 0.4) crystal. The atomic displacements are exaggerated by a factor of 20 in order to make the more subtle features of the modulation visible.

the pronounced in-plane Jahn-Teller distortion of the Mn-O bond, whose amplitude varies with position (this is a measure of the “Mn3+ character” of the octahedron and shows that charge is inhomogeneously distributed in the unit); (b) a small rotation of the octahedra resulting in a buckled a-b plane, a distortion not present in the average structure; and (c) the 180° phase shift between neighboring bilayers that nestles long Mn-O bonds into short Mn-O “pockets” to reduce the lattice strain. It is important to reiterate that these charge-ordered clusters are extremely short-ranged, approximately six underlying lattice repeats. Nonetheless, inelastic neutron measurements unequivocally show that they are quasistatic, having lifetimes that exceed the picosecond periods typical of optic phonons.32 They are thus a “frozen” image of how charge, spin, and lattice interact on the nanoscale in CMR manganites. The charge modulation correlates strongly with the magnetic exchange reduction discussed in section 4. The modulation appears only in the paramagnetic phase, shows a maximum in intensity at T ≈ 1.1TC, and slowly disappears with increasing temperature. Furthermore, it can be suppressed by a magnetic field similar in strength to that necessary to restore the full exchange coupling. Thus, the paramagnetic phase has two distinct regions: (i) a charge modulated region with a reduced J for small applied field and (ii) a high-field region, in which J is restored and the charge modulation disappears. So, the ferromagnetic exchange competes not only with thermal fluctuations but also with the charge modulation as a second ordering mechanism. Such an interpretation of the modulation as a competitive ordering mechanism also agrees well with the observed chemical trend discussed in section 4. There, an increasingly suppressed J with higher doping level was found. One would expect such a doping dependence from the charge modulation mechanism as one moves closer toward x ) 0.50, where long-range CO is found. This competing interaction might also impact the x dependence of TC (section 2.1), which exhibits a maximum at x ) 0.36. The increasing importance of the charge modulation with its concomitant reduction in J may thus provide an explanation for the TC reduction as x increases beyond 0.36. Finally, the temperature and magnetic field dependences of the polaronic defects provide the link between the short-range charge-ordering and CMR. The polaron model predicts that upon delocalization of charge in the FMM phase, the static JahnTeller distortion should either vanish or at least become far less pronounced. Crystallographic and XAFS studies90,91 showed that this was indeed the case in perovskite manganites. Likewise, changes in Debye-Waller factors (“temperature factors”) show anomalies at the transition consistent with predictions by Millis et al.22 However, none of these results directly interrogates the polaronic strain field and its response to the I-M transition.

Figure 15. (a) Temperature dependence of the intensity of the diffuse “butterfly” Huang scattering and charge modulation reflection. In both cases, thermal diffuse scattering has been subtracted. Squares are the magnetic susceptibility enhancement (see section 4 of text); (b) Field dependence of the intensity of the charge modulation reflection at 125 K (∼1.1TC). Dotted line is Fab(T) in arbitrary units scaled for comparison to the scattering data.

The Huang scattering and its associated correlations provide this direct picture of the self-trapped charge and its strain field. The obvious prediction is that the strain field should vanish as the carriers become more mobile, i.e., hop more quickly than the lattice can trap them. Figure 15a shows that this is precisely what happens. As temperature is lowered, the carriers become progressively more localized, leading to increased intensity in both the “butterfly” and the superlattice scattering, which naturally track one another. At the Curie temperature, DE favors the delocalization of the carriers, and the intensity of both features abruptly and simultaneously vanishes as the JahnTeller strain fields are dispersed, concomitantly sweeping away the charge correlations. Note also the coincidence with the magnetic susceptibility enhancement discussed in section 4. These data, then, draw together all three critical degrees of freedom: lattice, charge, and spin.

Feature Article Finally, in Figure 15b, we link short-range charge correlations and CMR. This figure shows the superlattice reflection intensity as a function of applied field at a temperature just above TC, i.e., in the insulating phase. As the field is increased up to 2 T, the superlattice gradually decreases in intensity, tracking the reduced electrical resistivity. The physical picture is straightforward: applied field harnesses magnetic short-range order and pushes TC higher; the induced FM state precipitates the DE “melting” of the short-range CO state, leading to higher conductivitysprecisely the CMR effect. 6. Open Issues and Future Directions The efforts described above paint a vivid picture of how naturally layered manganites are answering fundamental questions in CMR physics. However, many questions are still unanswered, and much work remains. It has become increasingly clear that short-range ordering (charge, magnetic, structural) and phase segregation are among the most critical and complex aspects of manganite physics that must be addressed. The opportunity here is far-reaching, as such issues will impact not only CMR studies, but also the broader realm of TM oxides where these phenomena are also expected to play important roles. In this section, we briefly look forward to identify what somesbut by no means allsof the important questions might be and how naturally layered manganites will impact the understanding of these fundamental issues. As clearly shown in the phase diagram of Figure 4, there is an unexpected “magnetic gap” in the region 0.66 < x < 0.74. In this region no long-range ordered magnetic state is observed by neutron diffraction as low as 5 K despite the ordered A- and C-type phases on either side. We believe that the presence of these different ordered states may provide an explanation for the gap region. Since, the Mn spins have not vanished, we are considering several different possible reasons for this gap region. Of course, one can immediately speculate that the spins in this dopant concentration range exhibit glassy dynamics, but even if true, this begs the question of why it is so only in this narrow regime. We are speculating that the Mn spins adopt a mixedphase configuration in which short-range ordered A-type and C-type regions interpenetrate on length scales below the diffraction limit (∼1000 Å). To seek evidence for this model, we must look to the structures underlying the magnetic phases. As discussed above, the A-type phase adopts a planar x2-y2 orbital ordering and is tetragonal, while the C-type phase adopts a 3y2 - r2 orbital ordering, leading to an orthorhombic distortion. This orthorhombic distortion, although invisible to long-range diffraction, is expected to appear when local probes of structure are employed. Thus, the local structure becomes a signpost for the local magnetism. We are currently using neutron pair distribution function (PDF) analysis to explore this possibility. PDF has successfully identified the impact of local distortions in many CMR manganites and high Tc superconductors;70,92,93,68 here it will be used to understand not only short-range structure but also short-range magnetism and its influence on manganite physics. The importance of orbital interactions in stabilizing the charge-ordered state is shown by the dramatic influence of substitution by Cr3+ ions into perovskites at the 50% Mn3+/ Mn4+ concentration.94,95 Cr3+ ions with a d3 configuration are not Jahn-Teller-active, and therefore, they disrupt the delicate balance of Coulomb and orbital strain energies. Only a few percent are sufficient to break the charge-ordered oxide into ferromagnetic nanodomains in a paramagnetic matrix, a kind of phase segregation. Additionally, these systems have been

J. Phys. Chem. B, Vol. 105, No. 44, 2001 10743 dubbed “ferromagnetic relaxors” because of strong parallels with ferroelectric relaxor behavior such as frequency-dependent transitions and long relaxation times. Our interest in such substitutions will be 2-fold. We will explore how the shortrange charge correlations observed in the x ∼ 0.4 compositionss where I-M transitions are foundsrespond to small concentrations of “orbitally inactive” ions. This will give a powerful view of how orbital degrees of freedom impact CMR. In parallel, we will investigate long-range CO states (LaSr2Mn2O7, x ) 0.5) and the impact of these Jahn-Teller inactive ions on the delicate competition of orbital and charge ordering in reduced dimensions and how these competing forces impact the phase composition in the ground state. Finally, throughout this article, we have stressed the impact of reduced dimensionality of the naturally layered manganites on CMR physics. However, the exact nature of this dimensionality effect remains elusive. We propose two approachessone extrinsic, the other intrinsicsfor addressing this issue. Motivating both of these approaches is the observation that the singlelayer manganite, La1-xSr1+xMnO4, never shows an I-M transition. Rather, these compounds are either AFM or spin-glass insulators.14 Thus, the presence of the bilayer is important to stabilizing the FMM ground state. Consider first the A-type magnetic structure of the x ) 0.5 bilayer compound. The FM sheets of this compound are coupled antiferromagnetically within the bilayers, producing a barrier to intrabilayer transport within the DE framework. This effectively makes the bilayer into a pair of uncoupled single-layer sheets. Application of external magnetic fields of sufficient strength should rotate the sublattice magnetization, yielding either a FM or spin-flop state. Either possibility should remove the DE barrier and result in conductivity within the planes. That is, we will extrinsically precipitate a crossover into the conducting state by turning on coupling between the 2-D sheets. We also propose to interrogate this crossover from the other direction using oxygen vacancies to decouple the MnO2 sheets in the bilayer. As alluded to in section 2.2, oxygen vacancies in as-prepared materials locate in the apical position shared between the sheets in the bilayer. By generating and systematically controlling the concentration of these vacancies in compositions where I-M transitions are observed (0.3 e x e 0.4), it may be possible to isolate the MnO2 sheets magnetically and/or electronically. This chemical approach could also shed additional light on the factors needed to stabilize the short-range CO units critical to the CMR effect. 7. Conclusions The experimental results discussed above represent a substantial foray into our comprehensive exploration of naturally layered manganite physics. We have found strategic ways to make materials and exploit their unique structural, magnetic, and electronic pedigrees. We have mapped out an extremely rich phase diagram, interrogated the nature of electrical transport and magnetic coupling, and found direct connections among these degrees of freedom from sophisticated scattering measurements. In the process, we have identified similarities and differences with the perovskite relatives and exploited these relationships to explore the profound and complex connections among charge, spin, and structure in CMR manganites. It is a testimony to the initial concept of using layered manganites to amplify charge and magnetic correlations that the polaron strain fields and their melting were first observed in the layered materials and subsequently identified as important in 3-D compounds. Although a vastly wider chemical phase space is available to the perovskites, the anisotropic magnetic

10744 J. Phys. Chem. B, Vol. 105, No. 44, 2001 structures available to the layered materials more than overcome this apparent limitation. Importantly, many classes of TM oxides have such layered structures available to them: high Tc cuprate superconductors, low Tc superconducting ruthenates, magnetic cobaltates, titanates and vanadates, etc. Because of their spectacular coupling among charge, spin, and lattice interactions, the manganites will become a prototype for understanding the physics of this wide range of TM oxides. The lessons we have learned to date and will continue to learn in the future from CMR materials will provide a robust platform from which to launch similarly comprehensive studies of the many exciting aspects of the yet unexplored TM oxide physics. Acknowledgment. The work described in this article has been made possible by the substantial contributions of many researchers at Argonne National Laboratory and outside institutions. The authors would particularly like to acknowledge the work of Chris Ling, Julie Millburn, Marisa Medarde, Charlie Potter, Lida Vasiliu-Doloc, Jeff Lynn, Sunil Sinha, Branton Campbell, Qing’An Li, Heloisa Bordallo, Geoff Strouse, Stephan Rosenkranz, Joel Mesot, Jason Gardner, Sam Bader, Jim Jorgensen, Simine Short, Hong Zheng, and Carmen Kmety. The work has been sponsored by the US Department of Energy, Office of Science, under Contract No. W-31-109-ENG-38. References and Notes (1) Sun, J. Z. Manganate Trilayer Junctions: Spin-Dependent Transport and Low-Field Magnetoresistance. In Colossal MagnetoresistiVe Oxides; Tokura, Y., Ed.; Gordon and Breach: Amsterdam, 2000; Vol. 2, pp 331353. (2) In Layered Superconductors: Fabrication, Properties, and Applications; Shaw, D. T., Ed.; Materials Research Society: Pittsburgh, PA, 1992; Vol. 275. (3) Auciello, O.; Scott, J. F.; Ramesh, R. Phys. Today 1998, 51, 2227. (4) Caignaert, V.; Maignan, A.; Raveau, B. Solid State Commun. 1995, 95, 357. (5) Jirak, Z.; Krupicka, S.; Simsa, Z.; Dlouha, M.; Vratislav, S. J. Magn. Magn. Mater. 1985, 53, 153. (6) Urushibara, A.; Moritomo, Y.; Arima, T.; Asamitsu, A.; Kido, G.; Tokura, Y. Phys. ReV. B 1995, 51, 14103. (7) Wollan, E. O.; Koehler, W. C. Phys. ReV. 1955, 100, 545. (8) Yakel, H. L. Acta Crystallogr. 1955, 8, 394. (9) Schiffer, P.; Ramirez, A. P.; Bao, W.; Cheong, S.-W. Phys. ReV. Lett. 1995, 75, 3336. (10) Kimura, T.; Tomioka, Y.; Kuwahara, H.; Asamitsu, A.; Tamura, M.; Tokura, Y. Science 1996, 274, 1698. (11) Shimakawa, Y.; Kubo, Y.; Manako, T. Nature 1996, 379, 53. (12) Subramanian, M. A.; Toby, B. H.; Ramirez, A. P.; Marshall, W. J.; Sleight, A. W.; Kwei, G. H. Science 1996, 273, 81. (13) Mishra, S. K.; Satpathy, S. Phys. ReV. B 1998, 58, 7585. (14) Moritomo, Y.; Tomioka, Y.; Asamitsu, A.; Tokura, Y.; Matsui, Y. Phys. ReV. B 1995, 51, 3297. (15) Sternlieb, B. J.; Hill, J. P.; Wildgruber, U. C.; Luke, G. M.; Nachumi, B.; Moritomo, Y.; Tokura, Y. Phys. ReV. Lett. 1996, 76, 2169. (16) Kimura, T.; Tokura, Y. Annu. ReV. Mater. Sci. 2000, 30, 451. (17) Kubota, M.; Fujioka, H.; Hirota, K.; Ohoyama, K.; Moritomo, Y.; Yoshizawa, H.; Endoh, Y. J. Phys. Soc. Jpn. 2000, 69, 1606. (18) Ling, C. D.; Millburn, J. E.; Mitchell, J. F.; Argyriou, D. N.; Linton, J.; Bordallo, H. N. Phys. ReV. B 2000, 62, 15096. (19) Zener, C. Phys. ReV. 1951, 82, 403. (20) Anderson, P. W.; Hasegawa, H. Phys. ReV. 1955, 100, 675. (21) de Gennes, P.-G. Phys. ReV. 1960, 118, 141. (22) Millis, A. J.; Littlewood, P. B.; Shraiman, B. I. Phys. ReV. Lett. 1995, 74, 5144. (23) Millis, A. J.; Shraiman, B. I.; Mueller, R. Phys. ReV. Lett. 1996, 77, 175. (24) Dai, P.; Zhang, J. D.; Mook, H. A.; Liou, S. H.; Dowben, P. A.; Plummer, E. W. Phys. ReV. B 1996, 54, R3694. (25) Radaelli, P. G.; Marezio, M.; Hwang, H. Y.; Cheong, S.-W.; Batlogg, B. Phys. ReV. B 1996, 54, 8992. (26) Chun, S. H.; Salamon, M. B.; Tomioka, Y.; Tokura, Y. Phys. ReV. B 2000, 61, R9225. (27) Jaime, M.; Lin, P.; Salamon, M. B.; Han, P. D. Phys. ReV. B 1998, 58, R5901.

Mitchell et al. (28) Snyder, G. J.; Hiskes, R.; DiCarolis, S.; Beasley, M. R.; Geballe, T. H. Phys. ReV. B 1996, 53, 14434. (29) Ibarra, M. R.; Algarabel, P. A.; Marquina, C.; Biasco, J.; Garcı´a, J. Phys. ReV. Lett. 1995, 75, 3541. (30) Louca, D.; Egami, T. Phys. ReV. B 1999, 59, 6193. (31) Lynn, J. W.; Erwin, R. W.; Borchers, J. A.; Huang, Q.; Santoro, A.; Peng, J.-L.; Li, Z. Y. Phys. ReV. Lett. 1996, 76, 4046. (32) Vasiliu-Doloc, L.; Rosenkranz, S.; Osborn, R.; Sinha, S. K.; Lynn, J. W.; Mesot, J.; Seeck, O. H.; Preosti, G.; Fedro, A. J.; Mitchell, J. F. Phys. ReV. Lett. 1999, 83, 4393. (33) Miller, D. Private communication, 2001. (34) Radaelli, P. G.; Cox, D. E.; Marezio, M.; Cheong, S.-W. Phys. ReV. B 1997, 55, 3015. (35) Kuwahara, H.; Tomioka, Y.; Asamitsu, A. M.; Y.; Tokura, Y. Science 1995, 270, 961. (36) Argyriou, D. N.; Bordallo, H. N.; Campbell, B. J.; Cheetham, A. K.; Cox, D. E.; Gardner, J. S.; Hanif, K.; dos Santos, A.; Strouse, G. F. Phys. ReV. B 2000, 61, 15269. (37) Dagotto, E.; Yunoki, S.; Moreo, A. Mater. Sci. Eng., B 1999, 63, 65. (38) Moreo, A.; Yunoki, S.; Dagotto, E. Science 1999, 283, 2034. (39) Moreo, A. Int. J. Mod. Phys. B 1998, 12, 3369. (40) Yunoki, S.; Moreo, A.; Dagotto, E. Phys. ReV. Lett. 1998, 81, 5612. (41) Yunoki, S.; Hu, J.; Malvezzi, A. L.; Moreo, A.; Furukawa, N.; Dagotto, E. Phys. ReV. Lett. 1998, 80, 845. (42) Roy, M.; Mitchell, J. F.; Ramirez, A. P.; Schiffer, P. Phys. ReV. B 1998, 58, 5185. (43) Roy, M.; Mitchell, J. F.; Ramirez, A. P.; Schiffer, P. J. Phys.: Condes. Matter 1999, 11, 4843. (44) Uehara, M.; Cheong, S. W. Europhys. Lett. 2000, 52, 674. (45) Cox, D. E.; Radaelli, P. G.; Marezio, M.; Cheong, S. W. Phys. ReV. B 1998, 57, 3305. (46) Radaelli, P. G.; Ibberson, R. M.; Cheong, S.-W.; Mitchell, J. F. Phys. B 2000, 276, 551. (47) Rodriguez-Carvajal, J.; Hennion, M.; Moussa, F.; Moudden, A. H.; Pinsard, L.; Revcolevschi, A. Phys. ReV. B 1998, 57, 3189. (48) Radaelli, P. G.; Cox, D. E.; Marezio, M.; Cheong, S.-W. Phys. ReV. B 1997, 55, 3015. (49) Goodenough, J. B. Phys. ReV. 1955, 100, 564. (50) Goodenough, J. B. Magnetism and the Chemical Bond; John Wiley & Sons: New York, 1963. (51) Battle, P. D.; Green, M. A.; Laskey, N. S.; Millburn, J. E.; Murphy, L.; Rosseinsky, M. J.; Sullivan, S. P.; Vente, J. F. Chem. Mater. 1997, 9, 552. (52) Mitchell, J. F.; Argyriou, D. N.; Potter, C. D.; Jorgensen, J. D.; Hinks, D. G.; Bader, S. D. Mater. Res. Soc. Symp. Proc. 1997, 453, 343. (53) Mitchell, J. F.; Argyriou, D. N.; Jorgensen, J. D.; Hinks, D. G.; Potter, C. D.; Bader, S. D. Phys. ReV. B 1997, 55, 63. (54) Okuda, T.; Kimura, T.; Tokura, Y. Phys. ReV. B 1999, 60, 3370. (55) Mitchell, J. F.; Millburn, J. E.; Medarde, M.; Short, S.; Jorgensen, J. D.; Fernandez-Diaz, M. T. J. Solid State Chem. 1998, 141, 599. (56) Mitchell, J. F.; Millburn, J. E.; Medarde, M.; Argyriou, D. N.; Jorgensen, J. D. J. Appl. Phys. 1999, 85, 4352. (57) Akimoto, T.; Moritomo, Y.; Ohoyama, K.; Okamoto, S.; Ishihara, S.; Maekawa, S.; Nakamura, A. Phys. ReV. B 1999, 59, R14153. (58) Maezono, R.; Nagaosa, N. Phys. ReV. B 2000, 61, 1825. (59) MacChesney, J. B.; Potter, J. F.; Sherwood, R. C. J. Appl. Phys. 1969, 40, 1243. (60) Seshadri, R.; Martin, C.; Maignan, A.; Hervieu, M.; Raveau, B.; Ramachandra Rao, C. N. J. Mater. Chem. 1996, 6, 1585. (61) Moritomo, Y.; Asamitsu, A.; Kuwahara, H.; Tokura, Y. Nature 1996, 380, 141. (62) Welp, U.; Berger, A.; Vlasko-Vlasov, V. K.; You, H.; Gray, K. E.; Mitchell, J. F. J. Appl. Phys. 2001, 89, 6621. (63) Kimura, T.; Tomioka, Y.; Asamitsu, A.; Tokura, Y. Phys. ReV. Lett. 1998, 81, 5920. (64) Medarde, M.; Mitchell, J. F.; Millburn, J. E.; Short, S.; Jorgensen, J. D. Phys. ReV. Lett. 1999, 83, 1223. (65) Millburn, J. E.; Mitchell, J. F.; Argyriou, D. N. Chem. Commun. 1999, 1389. (66) Murakami, Y.; Hill, J. P.; Gibbs, D.; Blume, M.; Koyama, I.; Tanaka, M.; Kawata, H.; Arima, T.; Tokura, Y.; Hirota, K.; Endoh, Y. Phys. ReV. Lett. 1998, 81, 582. (67) Kuwahara, H.; Okuda, T.; Tomioka, Y.; Asamitsu, A.; Tokura, Y. Phys. ReV. Lett. 1999, 82, 4316. (68) Louca, D.; Egami, T.; Kwei, G. H. J. Supercond. 1999, 12, 291. (69) Egami, T. Abstr. Pap. Am. Chem. Soc. 1998, 215, 197-INOR. (70) Billinge, S. J. L.; DiFrancesco, R. G.; Kwei, G. H.; Neumier, J. J.; Thompson, J. D. Phys. ReV. Lett. 1996, 77, 515.

Feature Article (71) Li, Q. A.; Gray, K. E.; Mitchell, J. F.; Berger, A.; Osgood, R. Phys. ReV. B 2000, 61, 9542. (72) Welp, U.; Berger, A.; Miller, D. J.; Vlasko-Vlasov, V. K.; Gray, K. E.; Mitchell, J. F. J. Appl. Phys. 2000, 87, 5043. (73) Dessau, D. S.; Saitoh, T.; Park, C.-H.; Shen, Z.-X.; Villella, P.; Hamada, N.; Moritomo, Y.; Tokura, Y. Phys. ReV. Lett. 1998, 81, 192. (74) Abrikosov, A. A. Phys. ReV. B 2000, 61, 7770. (75) Li, Q. A.; Gray, K. E.; Mitchell, J. F. Phys. ReV. B 2001, 6302, 4417. (76) Note also that the fits yield a mean free path λ ∼ 1.4 nm. Since λ is considerably greater than the in-plane Mn-Mn spacing of 0.39 nm, the Ioffe-Regel limit is not violated. (77) Lynn, J. W. J. Supercond. 2000, 13, 263. (78) Ghosh, K.; Lobb, C. J.; Greene, R. L.; Karabashev, S. G.; Shulyatev, D. A.; Arsenov, A. A.; Mukovskii, Y. M. Phys. ReV. Lett. 1998, 81, 4740. (79) Tole´dano, J.-C.; Tole´dano, P. The Landau Theory of Phase Transitions; World Scientific: Singapore, 1987; Vol. 3. (80) Berger, A.; Mitchell, J. F.; Miller, D.; Bader, S. D. J. Appl. Phys., in press. (81) Rosenkranz, S.; Osborn, R.; Vasiliu-Doloc, L.; Lynn, J. W.; Sinha, S. K.; Mitchell, J. F. Phys. ReV. B, in press. (82) Wakabayashi, Y.; Murakami, Y.; Koyama, I.; Kimura, T.; Tokura, Y.; Moritomo, Y.; Hirota, K.; Endoh, Y. J. Phys. Soc. Jpn. 2000, 69, 2731. (83) Li, J. Q.; Matsui, Y.; Kimura, T.; Tokura, Y. Phys. ReV. B 1998, 57, R3205.

J. Phys. Chem. B, Vol. 105, No. 44, 2001 10745 (84) Battle, P. D.; Cox, D. E.; Green, M. A.; Millburn, J. E.; Spring, L. E.; Radaelli, P. G.; Rosseinsky, M. J.; Vente, J. F. Chem. Mater. 1997, 9, 1042. (85) Tomioka, Y.; Kuwahara, H.; Asamitsu, A.; Kimura, T.; Kumai, R.; Tokura, Y. Phys. B 1998, 246, 135. (86) Roy, M.; Mitchell, J. F.; Ramirez, A. P.; Schiffer, P. Phys. ReV. B 2000, 62, 13876. (87) Vasiliu-Doloc, L.; Osborn, R.; Rosenkranz, S.; Mesot, J.; Mitchell, J. F.; Sinha, S. K.; Seeck, O. H.; Lynn, J. W.; Islam, Z. Int. J. Mod. Phys. B 2000, 14, 3711. (88) Potter, C. D.; Swiatek, M.; Bader, S. D.; Argyriou, D. N.; Mitchell, J. F.; Miller, D. J.; Hinks, D. G.; Jorgensen, J. D. Phys. ReV. B 1998, 57, 72. (89) Campbell, B. J.; Osborn, R.; Argyriou, D.; Vasiliu-Doloc, L.; Mitchell, J. F.; Sinha, S. K.; Ruett, U.; Ling, C. D.; Islam, Z.; Lynn, J. W. Phys. ReV. B, in press. (90) Booth, C. H.; Bridges, F.; Kwei, G.; Lawrence, J. M.; Cornelius, A. L.; Neumeier, J. J. Phys. ReV. B 1998, 57, 10440. (91) Caignaert, V.; Suard, E.; Maignan, A.; Simon, C.; Raveau, B. J. Magn. Magn. Mater. 1996, 153, L260. (92) Louca, D.; Egami, T. J. Appl. Phys. 1997, 81, 5484. (93) Louca, D.; Kwei, G. H.; Mitchell, J. F. Phys. ReV. Lett. 1998, 80, 3811. (94) Kimura, T.; Tomioka, Y.; Kumai, R.; Okimoto, Y.; Tokura, Y. Phys. ReV. Lett. 1999, 83, 3940. (95) Kimura, T.; Kumai, R.; Okimoto, Y.; Tomioka, Y.; Tokura, Y. Phys. ReV. B 2000, 62, 15021.

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