electronic phase separation and other novel phenomena and properties exhibited by mixed-valent...

January 2008, published 13, doi: 10.1098/rsta.2007.2140366 2008 Phil. Trans. R. Soc. A

Vijay B Shenoy and C.N.R Rao materialsmixed-valent rare-earth manganites and relatedphenomena and properties exhibited by Electronic phase separation and other novel

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Electronic phase separation and other novelphenomena and properties exhibited bymixed-valent rare-earth manganites

and related materials

BY VIJAY B. SHENOY1

AND C. N. R. RAO2,*

1Centre for Condensed Matter Theory, Department of Physics,Indian Institute of Science, Bangalore 560 012, India

2Chemistry and Physics of Materials Unit and CSIR Centre of Excellencein Chemistry, Jawaharlal Nehru Centre for Advanced Scientific Research,

Jakkur Post, Bangalore 560 064, India

Transition metal oxides, such as the mixed-valent rare-earth manganites Ln(1Kx)AxMnO3

(Ln, rare-earth ion, and A, alkaline-earth ion), show a variety of electronic orders withspatially correlated charge, spin and orbital arrangements, which in turn give rise to manyfascinating phenomena and properties. These materials are also electronically inhomo-geneous, i.e. they contain disjoint spatial regions with different electronic orders. Not onlydo we observe signatures of such electronic phase separation in a variety of properties, butwe can also observe the different ‘phases’ visually through different types of imaging. Wediscuss various experiments pertaining to electronic orders and electronic inhomogeneitiesin the manganites and present a discussion of theoretical approaches to their understanding.It is noteworthy that the mixed-valent rare-earth cobaltates of the type Ln(1Kx)AxCoO3 alsoexhibit electronic inhomogeneities just as the manganites.

Keywords: rare-earth cobaltates; rare-earth manganites; electronic phase separation;charge-ordering

On

*A

1. Introduction

Transition metal oxides such as rare-earth manganites, cuprates and cobaltatesexhibit a plethora of properties and phenomena (Imada et al. 1998; Rao 2000) thathave stimulated sustained investigations by materials chemistry and physicscommunities. Many of the fascinating properties of these oxides arise from the factthat the transition metal ions can exhibit mixed valence with strongly correlatedelectrons giving rise to many ‘electronic orders’. By electronic orders, we meanspatially correlated arrangement of charge, spin, orbital and/or phase (as in asuperconductor). In addition, there is overwhelming evidence that these oxideswith high chemical homogeneity can show spatially inhomogeneous structures,i.e. regions showing different electronic orders (Mathur & Littlewood 2003;

Phil. Trans. R. Soc. A (2008) 366, 63–82

doi:10.1098/rsta.2007.2140

Published online 7 September 2007

e contribution of 15 to a Discussion Meeting Issue ‘Mixed valency’.

uthor for correspondence ([email protected]).

63 This journal is q 2007 The Royal Society


300

200

100

0.1 0.3 0.5 0.7 0.9X

COAFMI

CA

F

PMI

FMI

FMM

CO

CA

F

T(K

) COI

TCO

TC

(a)

250

150

50

0.1 0.3 0.5 0.7 0.9

PMI

FMI

TC

TCO

TN

CO

CO

AFM

I

X

(b)

Figure 1. Phase diagram of (a) La1KxCaxMnO3 and (b) Pr1KxCaxMnO3 (adapted from Raoet al. (2004)).

V. B. Shenoy and C. N. R. Rao64


Rao et al. 2004; Dagotto 2005; Shenoy et al. 2006).While many issues pertaining tothese oxides have been understood, their science has many puzzles and challengesin addition to the promise of applications. The development of new oxide materialsvia the methods of materials chemistry with controlled electronic orders, and theirtheoretical understanding, therefore, continue to be at the forefront of research incondensed matter science.

In this article, we discuss spin, charge and orbital orders in transition metaloxides, in particular, in the rare-earth manganites which have become famoussince 1993 owing to the phenomenon of colossal magnetoresistance (CMR)exhibited by them (Rao & Raveau 1998). We also touch upon the issue ofelectronic inhomogeneities; we discuss the signatures of the presence of suchinhomogeneities and theoretical approaches to understand the same.

2. Electronic orders in rare-earth manganites

Rare-earth manganites of the type Ln(1Kx)AxMnO3 (Ln, rare-earth ion, and A,alkaline-earth ion) which crystallize in the perovskite structure were investigatedseveral years ago by Wollan & Koehler (1955), but it was the discovery of CMRthat stimulated their resurgence (Rao & Raveau 1998; Dagotto et al. 2001;Salamon & Jaime 2001; Tokura 2006). In the parent undoped compoundLaMnO3, the manganese ions exist in a C3 state, while the doped system such asLa(1Kx)CaxMnO3 contains (nominally) a fraction (1Kx) of Mn3C and x of Mn4C

ions. This mixed-valent character of Mn underlies the rich phase diagrams(figure 1) exhibited by the manganites. A study of the phase diagram reveals alarge number of electronic orders present in these systems. In what follows, wediscuss some of these electronic orders.

LaMnO3 exhibits spin, orbital and lattice orders. The spin order is that of anA-type antiferromagnet (figure 2). This is accompanied by the orbital order,which couples strongly with the lattice distortion due to the Jahn–Teller (JT)effect, giving rise to the lattice distortion pattern shown in figure 2. Interestingly,the JT distortion pattern loses long-range order at approximately 750 K. Thistransition is also associated with a symmetry change of the crystal from an

Phil. Trans. R. Soc. A (2008)


(a)

(b)

(c)

5A

ab

c

Figure 2. (a) A-type antiferromagnetic spin order, (b) Jahn–Teller distortion pattern and(c) orbital ordering in LaMnO3 (after Rao (2000)).

65Electronic phase separation


orthorhombic structure at lower temperatures (due to the cooperative JTdistortion) to a cubic structure at higher temperatures. At low temperatures, thecombination of orbital ordering and JT distortion leads to an effectiveferromagnetic (FM) exchange interaction between the spins on the plane, anda strong antiferromagnetic (AFM) exchange between spins between the planes,resulting in an A-type AFM arrangement of the spins. Other undopedmanganites such as NdMnO3 also show a similar electronic order.

Doping of manganites with alkaline-earth ions such as Ca2C and Sr2C results ina fraction of the manganese ions occurring in the C4 state, giving rise a newelectronic order, charge order, wherein theC3 andC4 charges of the Mn ions arearranged in a periodic fashion (figure 3). Charge order is known to occur in othermetal oxides as well, Fe3O4 being a well-known example (Rao 2000). The charge-ordered state is found predominantly in manganites with small Ln and A ions.Further, charge order disappears at high temperatures. Thus, in Pr0.7Ca0.3MnO3,charge order appears only below 230 K. Interestingly, Pr0.7Ca0.3MnO3 also showsAFM order below 170 K, where both antiferromagnetism and charge ordercoexist. At low temperatures, this manganite is electrically insulating. In contrast,La0.7Ca0.3MnO3 does not show charge order, although it enters a FM metallicphase below a Curie temperature of 230 K, showing a PM insulating behaviourabove this temperature. In the Sr-based La0.7Sr0.3MnO3, the high-temperaturePM phase is metallic. Note that the average radius of the A-site cations, hrAi, islarger in these two manganites than in Pr0.7Ca0.3MnO3. CMR is observed atrelatively moderate fields in La0.7Ca0.3MnO3. Another important aspect of thedoped manganites is that, when the size of the A-site cation (or the eg bandwidth)is large enough, electrons of the Mn3C hop to Mn4C by the double-exchange (DE)mechanism. The DE mechanism plays a crucial role in the occurrence of



ab

Mn3+ (3y2–r2)

Mn3+ (3x2–r2)Mn3+ (3x2–y2)

Mn4+ Mn4+(a) (b)

Figure 3. Ordering of charge, spin and orbital in dopedmanganites. (a) CE-type order, the dashed lineshows the unit cell and (b) A-type order. In both figures, circles correspond toMn4C (after Rao (2000)).



metallicity and ferromagnetism in these materials. The phenomenon of CMR isexplained by invoking the DE mechanism along with certain competinginteractions involving phonons. Charge ordering is exactly the opposite of DE,since it localizes electrons creating an AFM insulating state.

Half-doped manganites show many interesting electronic orders. For example,Nd0.5Sr0.5MnO3, which is a FM metal at high temperatures, shows a transition toa charge-ordered AFM state at approximately 150 K. The charge-orderingtemperature is usually somewhat higher than the magnetic-ordering temperature(TCOTTN). Interestingly, the charge order can be ‘melted’ by a small magneticfield (Kuwahara et al. 1995). At low temperature, the charge-ordered state isassociated with a CE-type AFM order (figure 3), orbital order and a regularpattern of JT distortions. The magnetic order consists of ab planes stacked alongthe c-axis (figure 3) with an AFM coupling between spins on neighbouringplanes. This may be contrasted with A-type order (figure 2). Note that there isno charge ordering in an A-type antiferromagnet unlike in a CE-typeantiferromagnet. Usually, orbital and spin orders that are not accompanied bycharge order show A-type antiferromagnetism.

The presence of charge and orbital orders can be observed experimentally by astudy of the structures of themanganites. For example, the charge-ordered structureof Nd0.5Sr0.5MnO3 consists of distorted oxygen octahedra (figure 4) containingzigzag chains with alternate long and shortMn–O bonds. The bond lengths are 1.921and 2.021 A along h110i and 1.881 and 2.020 A along hK110i (figure 4). Theemergence of a charge gap is also indicated by vacuum tunnelling measurements(Biswas et al. 1997). Intriguingly, the low-temperature gap (approx. 250 meV) ismuch larger than TCOw12 meV. Moreover, a magnetic field of 6 T (approx.1.2 meV) can destroy the charge-ordered state. A consequence of this is the largemagnetostrictive effect arising from the magnetic field-induced structural transitionthat accompanies the AFM charge-ordered insulator to FM-metal transition.

An interesting fundamental question that arises is, what controls the differentelectronic orders? At the level of the chemistry of the constituents, the meanA-site cation radius hrAi is expected to play an important role. This arises from the



Nd/Ca O Mn3+ Mn4+Mn3+

(a) (b)

Figure 4. (a) Structure of charge-ordered Nd0.5Sr0.5MnO3 in the ab plane at 10 K. Mn4C ions arelocated at (1/2, 0, 0) and Mn3C are located at (0, 1/2, 0). The structure contains zigzag chains withalternate long and short Mn–O bonds (see text). (b) The same structure as given in (a), shown inpolyhedral representation ((a) after Vogt et al. (1996) and (b) after Woodward et al. (1999)).



fact that the bandwidth of the eg electrons of Mn ions is affected by the size of theA-site cation, i.e. increasing hrAi is equivalent to increasing the hydrostaticpressure, which increases the Mn–O–Mn bond angle and consequently thebandwidth. Detailed studies of the effect of hrAi on the electronic order have beenreported by Woodward et al. (1998). Systems with very large hrAi tend to be FMandmetallic, with aCurie temperatureTc that increaseswith hrAi. Charge orderingis also strongly affected by hrAi, with a smaller hrAi stabilizing charge-ordered phaseat low temperatures. It is evident that the tuning of hrAi via chemical meansprovides an important means of controlling the phase of the manganite.

3. Electronic inhomogeneities in rare-earth manganites

As noted in §1, there is strong experimental evidence to indicate that manycorrelated oxides are electronically inhomogeneous (figure 5). Nowhere is itmanifested better than the rare-earth manganites. Thus, these materials of highchemical homogeneity consist of different spatial regions with different electronicorder (Mathur & Littlewood 2003; Rao et al. 2004; Dagotto 2005; Shenoy et al.2006), a phenomenon that has come to be known as ‘phase separation’. Theseregions can be static or dynamic and can be tuned by the application of externalstimuli like a magnetic field. Moreover, the size scale of these inhomogeneities canvary from nanometres to as large as micrometres. The presence of electronicinhomogeneities raises many intriguing questions. What is the microscopic originof these inhomogeneities?Why do they possess such a large range of length-scales?More importantly, are they responsible for the CMR and such responses exhibitedby the manganites and related oxide materials? Indeed, there are suggestions inthe literature that these features observed in correlated oxides indicate that they



(a) (b)

(c) (d )

Figure 5. Schematic of electronic phase separation. Shaded portions indicate FM metallic regions;the unshaded portions correspond to AFM insulating regions. (a) FM metallic puddles in aninsulating AFM background, (b) metallic regions with insulating droplets, (c) charged stripes and(d ) phase separation on the mesoscopic scale.



are ‘electronically soft’ providing the possibility of spatial tuning of electronicproperties, not unlike the liquid crystalline materials (Mathur & Littlewood 2003;Dagotto 2005; Milward et al. 2005). In this section, we discuss the phase separationphenomena especially in the rare-earth manganites. Following a description of theexperimental signatures of electronic inhomogeneities, we discuss the theoreticalideas put forth to understand this phenomenon in §3a.

(a ) Signatures of electronic inhomogeneities

Investigations employing a variety of experimental probes indicate the presenceof electronic inhomogeneities. When the length-scale of the inhomogeneities is large(a few hundred nanometres), structural and magnetic information from the X-rayand neutron diffraction patterns show clear signatures. Specialized local probes suchas NMR and Mossbauer spectroscopies can be used to probe inhomogeneities at asmaller length-scale. Thermodynamic (e.g. magnetization) and transport measure-ments also indicate the presence of inhomogeneities. Direct observational evidenceprovided by images employing transmission electron microscopy, scanning probemicroscopy and photoemission micro-spectroscopy makes for a convincing case forthe presence of the electronic inhomogeneities.

The pioneering work on manganites by Wollan & Koehler (1955) revealed thepresence of electronic inhomogeneities. They observed both FM and AFM peaksin the magnetic structure of La1KxCaxMnO3 obtained from neutron scattering.They concluded that there is the simultaneous presence of ferromagnetism andantiferromagnetism in this material. A more recent neutron diffraction study isthat of Woodward et al. (1999) on Nd0.5Sr0.5MnO3. This material first becomesFM at 250 K, partially transforming to an A-type AFM phase at approximately220 K, followed by a transformation of a substantial fraction to a CE-type AFMphase at approximately 150 K. The CE-type AFM (abbreviated as CO-CEAF)phase has a simultaneous ordering of spins, orbitals and charge in a complexspatial arrangement as shown in figure 3. It is evident from the studies ofWoodward et al. (1999) that the three phases coexist at low temperatures.The size scale of the inhomogeneities is at least in the mesoscopic range



100

80

60

40

20

0 100 200 300

phas

e fr

actio

n (%

)

temperature (K)

60(i) (iii)

(iv)(ii)

50

40

30

20

10

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100

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40

20

0

4.03.53.02.52.01.51.00.5

04.03.53.02.52.01.51.00.5

0

phas

e fr

actio

n (%

)ph

ase

frac

tion

(%)

mag

netic

mom

ent (

m B)

mag

netic

mom

ent (

m B)

magnetic phases magnetic phases

H = 0TT = 125K

H = 6T

T = 125K

H = 6TT = 125K

H = 0TT = 125K

FM(Imma)

FM(Imma)

FM(Imma)

FM(Imma)CO-CEAF

(P2r/m) CO-CEAF(P2r/m)A-AF

(Imma)

A-AF(Imma)

A-AF(Imma)

A-AF(Imma)

Mn+3

Mn+4

(a) (b)

Figure 6. (a) Volume fraction of phases as a function of temperature in Nd0.5Sr0.5MnO3. Opendiamonds, open circles and open squares represent ferromagnet (FM), antiferromagnet (A-type,A-AF) and antiferromagnet (CE-type, CO-CEAF), respectively. (b) Phase fractions at 125 K atdifferent magnetic fields (i) 0 T and (ii) 6 T; (iii) and (iv) show the magnetic moment in each of thephases ((a) after Woodward et al. (1999) and (b) after Ritter et al. (2000)).



(a few hundred nanometres or more), since they are large enough to producewell-defined reflections in neutron and X-ray diffraction patterns. The variationof the volume fraction of the three phases with temperature is shown in figure 6a.This phase diagram has an unusual feature with the three phases existing at the150 K transition and below. The effect of the volume fractions of the electronicinhomogeneities due to an external magnetic field was studied by Ritter et al.(2000). The results shown in figure 6b demonstrate the evolution of theinhomogeneities where the FM fraction grows at the expense of the AFM regionsin the presence of the applied magnetic field. Note the growth of one phase at thecost of another in figure 6. Clearly, the phase separation observed here is of anon-trivial type, in contrast to a situation where the sample is not phase-purecontaining multiple phases that are both structurally and chemically distinct.Another interesting example (Radaelli et al. 2001) of phase separation is inPr0.7Ca0.3MnO3, which shows the presence of two distinct phases below thecharge-ordering transition at 80 K. A charge-ordered AFM phase and a charge-delocalized phase have been observed by neutron diffraction.

Signatures of electronic inhomogeneities may be inferred from magnetic andelectron transport measurements as well. Sudheendra & Rao (2003) studied theseproperties of (La1KxLnx)0.7Ca0.3MnO3, where LnZNd, Gd or Y. The lanthanideelementwas varied to control the averageA-site cation radius hrAi. In the case of theLa compound (xZ0.0) with the largest value of hrAi, a clear FM transition with asaturationmagnetization of 3mB is observed (figure 7a) up to a critical Nd doping ofx%xcz0.5. At higher values of Nd doping (xOxc), there is a monotonic increase ofthemagnetizationwith decrease in temperature, although themagnetization neverattains the maximum value of 3mB. Interestingly, reducing the value of hrAi by Gd(intermediate value of hrAi) or Y (smallest value of hrAi) substitution decreases thexc, i.e. the critical doping value x above which the sharp FM transition vanishes,



mB

(fo

rmul

a un

it)m

B (

form

ula

unit)

mB

(fo

rmul

a un

it)2

1

0

3

2

1

0

3

2

1

0

0 50 100 150 200 250 300

x = 0.5x = 0.6

x = 0.7

x = 0.26

x = 0.4

x = 0.5

x = 0.6x = 0.7 x = 0.8

x = 0.2

x = 0.0

x = 0.8

x = 0.6

x = 0.7

x = 0.8

x = 0.9

x = 0.3

x = 0.4

x = 0.4

x = 0.2

x = 0.2

x = 0.0

x = 0.0

T (K)

3

x = 0.5

(i)

(ii)

(iii)

(a)

Figure 7. (a) Temperature dependence of the effective magnetic moment per formula unit in(La1KxLnx)0.7Ca0.3MnO3. (b) Temperature dependence of the resistivity in (La1KxLnx)0.7Ca0.3MnO3.The insets show the ‘resistivity hysteresis’ upon warming of the sample. In graphs in (a) and (b), (i), (ii)and (iii) correspond to LnZNd, Gd and Y, respectively. (c) Variation of (i) magnetization and(ii) resistivity as with temperature. The data shown are in Ln0.7KxLn

0

xA0.3KyAy

0MnO3 with mean

radius of the A-site cation are fixed at 1.216 A. The different curves show results for different s2 ((a,b)after Sudheendra & Rao (2003) and (c) after Kundu et al. (2005b)).



reduces with the mean A-site cation radius hrAi. Moreover, the FM transitiontemperatureTc for x!xc increases with hrAi as expected. The precipitous reductionof the saturation magnetization at xTxc is a signature of electronic and magneticinhomogeneities induced by the A-site cation disorder. Transport measurementsalso show the signature of electronic inhomogeneities. In figure 7b, we show thevariation of resistivity with temperature to demonstrate that all the threesubstitutions of manganites with LnZNd, Gd and Y exhibit a metal–insulatortransition for x!xc. The insets in figure 7b show the resistivity hysteresis across the



104

102

10

10–2

10–2

10–2

106

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104

102

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0 50 100 150 200 250 300 350

x = 0.7

x = 0.7

x = 0.6

x = 0.5x = 0.4

x = 0.3

x = 0.1

x = 0.0

x = 0.8

x = 0.9x = 0.8

x = 0.5

x = 0.4x = 0.2

x = 0.0

0 50 100 150T (K)

T (K)

200 250 300

103

102

101

1010–1

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102

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1010–1

1.0

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0 50 100 150 200 250 300

T (K)0 50 100 150 200 250 300

0

x = 0.0

x = 0.26

x = 0.4

x = 0.5

x = 0.7 x = 0.9

x = 0.1x = 0.2

r (Ω

cm

)r

(Ω c

m)

r (Ω

cm

)

T (K)

(i)

(ii)

(iii)

(b)

Figure 7. (Continued.)



transition. The insulator–metal transition temperature decreases linearly ondoping and increases nearly linearly with hrAi. Electronic phase separation in suchmanganites generally occurs when hrAi is relatively small (!1.18 A) and isfavoured by size disorder arising from the size mismatch between the A-sitecations. This disorder is quantified (Rodrıguez-Martınez & Attfield 2001) by theparameter s2Z

Pixir

2i KhrAi2, where xi is the fractional A-site occupancy of

species i with radius ri. A study of several series of manganites with fixed hrAi andvarying s2 shows that, as s2 is lowered, the phase-separated system transforms to aFMmetallic state. It has been demonstrated recently (Kundu et al. 2005b) that in aseries of manganites of the type Ln0:7KxLn

0xA0:3KyA

0yMnO3, where hrAi always

remains large (thereby avoiding effects due to bandwidth), a decrease in s2

transforms the insulating non-magnetic state to a FM metallic state (figure 7c).The above examples,while being indicative of the existence ofmultiple electronic

and magnetic phases within a single apparently structurally and chemically purephase, do not provide direct evidence with regard to the length-scale of the



40

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0

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103

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10–1

10–3

0 50 100 150 200 250 300 350

H = 500 Oe

0.0010.0080.0090.0130.0210.028

r (Ω

cm

)M

(em

u g–1

)

T (K)

s2(Α2)

<rA> = 1.216A

(i)

(ii)

(c)

Figure 7. (Continued.)



inhomogeneities.While diffraction provides evidence of electronic phase separationon a mesoscale, NMR spectroscopy has revealed the possibility of phase separationat nanoscopic scales (Kuhns et al. 2003).

(b ) Visual evidence for electronic phase separation

We now turn to the experimental work that shows direct visual evidence ofelectronic inhomogeneities, thereby allowing one to probe the length-scale of theinhomogeneity. One of the earliest reports of the direct evidence of electronic patternsinmanganiteswas in the hole-doped side of (La,Ca)MnO3.Mori et al. (1998) observedcharged stripes in thin films of La1KxCaxMnO3 with 0.5%x%0.75 by high-resolutionlattice images obtained by transmission electron microscopy. The spatial structureconsisted of paired JT distorted oxygen octahedra surrounding the Mn3C ions,separated by stripes of Mn4CO6 octahedra. The spacing of the stripes, usually 5–10lattice spacings,was foundtobegovernedbythedoping.Theelectronic inhomogeneityin this casewas of a nanoscopic length-scale. Further evidence of nanoscopic electronicinhomogeneity inmanganiteswas obtainedbya scanning tunnellingmicroscopy studyof Bi1KxCaxMnO3 (xz0.75) by Renner et al. (2002). They found nanoscopic charge-ordered and metallic domains which correlated with the structural distortions.

The first direct evidence of mesoscale inhomogeneities in manganites wasprovided by Uehara et al. (1999), who observed electronic inhomogeneities inLa0.0625KyPryCa0.375MnO3 by transmission electron microscopy. This workdemonstrated the coexistence of charge-ordered (insulating) regions with





interspersed FM metallic domains with a typical size of approximately 0.2 mm,bringing these features of inhomogeneity up to the mesoscopic scale. The authorssuggested a possible mechanism for the colossal magnetoresistive response arisingfrom such an electronic and magnetic inhomogeneity. The spin alignment of each ofthe FM metallic domains is random and the spin-polarized conduction electron ofone domain cannot hop effectively via other domains due to the absence of availableelectronic states with the correct spin configuration on other randomly orientedmagnetic domains. On application of amagnetic field, the spins of differentmagneticdomains align, enabling an unhindered hopping of electrons, thereby resulting in adrastic reduction of the resistance, known as the colossal negative magnetoresis-tance. This study suggested that such a mesoscopic phase separation is essential forcolossal responses. Approximately at the same time, Fath et al. (1999) used scanningtunnelling spectroscopy to study metal–insulator transitions in La0.7Ca0.3MnO3 andfound evidence of electronic inhomogeneities with a mesoscopic scale ofapproximately 0.2 mm, below the FM transition temperature, with FM metallicdomains interspersed in insulating regions, just as in the work by Uehara et al.(1999). Most interestingly, the domains evolved as a function of the appliedmagnetic field, with the volume fraction of the magnetic (metallic) domainsincreasing at the cost of the non-magnetic (insulating) parts, closely accompanyingthe decrease in the resistivity with the magnetic field. This scenario contrasts withthe spatially static phase separation scenario suggested by Uehara et al. (1999).Amagnetic force microscope study of La0.33Pr0.34Ca0.33MnO3 by Zhang et al. (2002)has indicated that magnetic domains of mesoscopic scale evolved with temperatureshowing magnetic hysteresis coinciding with the resistivity hysteresis. Thisobservation again suggested that mesoscale inhomogeneities are possibly crucialfor colossal responses in magnetoresistance. Loudon et al. (2002) have studiedLa0.5Ca0.5MnO3 using transmission electron microscopy and electron holographyand foundmesoscopicdomains ofFMregions interspersed in insulating regions.Theyalso found evidence that some of the FM regions were charge ordered. A possibleinterpretation of the result is that the mesoscopic FM region is itself inhomogeneousat the nanoscale with coexisting metallic and charge-ordered regions.

A final example ofmesoscale electronic inhomogeneities is from the experiments ofSarma et al. (2004), who used photoemission spectromicroscopy which has theadvantage of spatially resolving the local metallic/non-metallic nature andsimultaneously determining the local chemical composition with a resolution ofapproximately 0.5 mm.Using this technique, they studied La0.25Pr0.375Ca0.375MnO3.The key finding was that the material showed very large (10!5 mm2) domains ofinsulating regions interspersed in a metallic background. These regions evolved onincreasing temperature, with the metallic regions undergoing a metal-to-insulatortransition at higher temperatures. On cooling the sample back to low temperatures,the insulating regions appeared essentially at the same locations, indicating, for thefirst time, a memory effect associated with the electronic inhomogeneities.

4. Electronic phase separation in rare-earth cobaltates

Electronic phase separation in rare-earth cobaltates of the type Ln1KxAxCoO3

has come to the fore in the last 2 years. La0.5Sr0.5CoO3 and other members ofthis family were once considered to be itinerant electron ferromagnets



12

10

8

6

4

2

00.1 0.2 0.3

X

0.4 0.5

FM/P

M r

atio

FM/P

M r

atio

12108642070 120 170

temperature (K)220

x = 0.5

Figure 8. Variation of the ratio of the FM to PM species with composition in La(1Kx)SrxCoO3 (filledsquares, Mossbauer data at 78 K from Bhide et al. (1975); filled diamonds, NMR data at 1.9 K fromKuhns et al. (2003); inset shows the temperature variation of the FM/PM ratio in La0.5Sr0.5CoO3

from the Mossbauer data).



showing metallic behaviour, but it was recognized later that the FM orderingwas not long range (Rao et al. 1977; Senaris Rodrıguez & Goodenough 1995).It is now established that La0.5Sr0.5CoO3 exhibits a glassy magnetic behaviour(Wu et al. 2005). Recent studies of the magnetic and electrical properties ofseveral members of the Ln1KxAxCoO3 family have revealed that they areelectronically phase-separated (Burley et al. 2004; Kundu et al. 2005a; Wuet al. 2005). The phase separation is favoured by small hrAi as well as sizedisorder (Kundu et al. 2006). Measurements of magnetic relaxation andmemory effects have shown that glassy behaviour is common among thecobaltates (Kundu et al. 2005a, 2006). Studies employing local probes such asNMR and Mossbauer spectroscopy have provided direct evidence for differentdistinct species involving large magnetic/metallic clusters and small non-magnetic clusters (Bhide et al. 1975; Kuhns et al. 2003). Thus, the NMR andMossbauer studies of La(1Kx)SrxCoO3 show distinct signals corresponding toFM and PM species. Cobalt Mossbauer spectra show a signal due to the CMspecies, but are always accompanied by a signal due to the PM species evenat low temperatures (T!Tc). In figure 8, we show the variation of the FM toPM ratio with composition in La(1Kx)SrxCoO3. In the inset, the variation ofthe FM to PM ratio of La0.5Sr0.5CoO3 with temperature is shown (Kunduet al. 2007). Cobalt NMR studies of a cobaltate with small hrAi has shownthe presence of two distinct signals varying in intensity with temperature(Kundu et al. 2007).

5. Theoretical approaches

We now turn to a discussion of theoretical ideas that have been proposed toexplain the origin of the electronic inhomogeneities, with specific focus onmanganites. The simplest possible description of manganites at a microscopic level





involves the Mn d-orbitals and the lattice distortion of the oxygen octahedronsurrounding the Mn ion (Dagotto 2003). The octahedral crystal field splitsthe degeneracy of the five Mn d-orbitals into three degenerate t2g orbitals and

two degenerate eg orbitals. In the doped manganites, both Mn3C and Mn4C

configurations are present; both have three electrons in the t2g orbitals, and Mn3C

has, in addition, a lone electron in one of the eg orbitals. The spins of the t2gelectrons are aligned parallel due to strong Hund coupling, and it is only theresulting ‘core spins’ (SZ3/2) of the t2g electrons that affect the low-energyphysics of manganites. Thus, the relevant degrees of freedom at each manganesesite are: an average of (1Kx) electrons per site populating the two eg orbitals, thet2g core spins and lattice (phonon) degrees of freedom corresponding to thedistortion of the oxygen octahedra surrounding the manganese ion. The egelectrons hop from a Mn site to neighbouring Mn sites with an amplitude t(approx. 0.2 eV). The spin of the eg electron has a strong FM Hund coupling JH(approx. 2.0 eV) with the local t2g core spin. Another important energy scale is theon-site Mott–Hubbard repulsion U (approx. 5.0 eV) which forbids doubleoccupancy of the local eg sector. Neighbouring t2g spins interact with each othervia an AFM superexchange coupling JSE (approx. 0.02 eV). Finally, the energygained by the JT distortion of the oxygen octahedron is given by EJT (approx.0.5 eV). Competition between these different interactions, leading to a variety ofstates very close in energy, is responsible for the complex phase diagram ofmanganites with many electronic orders, and their extreme sensitivity to externalperturbations such as temperature, magnetic field and strain (Sarma et al. 1995;Satpathy et al. 1996; Millis 1998; Ramakrishnan et al. 2003; Cepas et al. 2006).

Owing to the difficulties of dealing with all the degrees of freedom andcompeting interactions mentioned above, much of the early work aimed atunderstanding colossal responses and electronic inhomogeneities in manganiteshas been based on simplified models which neglect one or more of them. Aprominent example is the work of Dagotto and coworkers (Dagotto 2003), whostudied simple magnetic Hamiltonians with competing phases that are separatedby a first-order transition. Based on these studies, they suggested that the systemis prone to macroscopic phase separation, which is frustrated by disorder leadingto the electronic inhomogeneities at various scales, the magnitude of the disorderdetermining the scale. From the real-space structure obtained from simulations,they constructed a random resistor network to explain the colossal responses by amechanism similar to the one proposed by Fath et al. (1999), again suggestingthat the phase separation is key to colossal responses. Other simplified modelshave been studied, and alternate scenarios have been proposed. There are alsosuggestions that manganites close to half doping are near a multicritical pointwith competing phases affected by disorder (Motome et al. 2003; Tokura 2006).Ahn et al. (2004) consider a model Hamiltonian including electron–phononinteraction, and long-range elastic coupling between local lattice distortions.They present a scenario for mesoscopic/microscopic inhomogeneities and suggestthat these are responsible for the colossal responses.

We now turn to a recent study of electronic inhomogeneities in manganites(Shenoy et al. 2007), which attempts to take into account all the degrees offreedom and their interactions based on the [b model (Ramakrishnan et al. 2003,2004; Krishnamurthy 2005).





(a ) The [b model for manganites

The [b model (Pai et al. 2003; Ramakrishnan et al. 2004) uses the idea that,under the conditions prevailing in doped manganites, the electrons populatingthe doubly degenerate eg states centred at the Mn sites spontaneously reorganizethemselves into two types of coexisting electron fluids. One is obtained bypopulating essentially site-localized states labelled [ which are polaronic, withstrong local JT distortions of the oxygen octahedra, an energy gain EJT andexponentially reduced intersite hopping. The other, labelled b, is a fluid ofbroadband, non-polaronic electrons, with no associated lattice distortions andundiminished hopping amplitudes. There is a strong local repulsion between thetwo fluids, as double occupancy on a site costs an extra Coulomb of energy U.The spins of [b and b are enslaved to the Mn-t2g spins on site due to the large FMHund’s coupling JH. In the simplest picture, assuming all the t2g spins and the egspins to be aligned parallel, the [ and b electrons can be regarded as spinless,leading to the Falicov–Kimball (Freericks & Zlatic 2003) like [b Hamiltonian

H[ b ZKEJT

X

i

n[ iKtX

hijiðb†i bj Ch:c:ÞCU

X

i

n[ inbi: ð5:1Þ

Here, [ †i and b†i create [ polarons and b electrons, respectively, at the sites i of a cubic

Mn lattice, and n[ i h[ †i [ i and nbi hb†i bi are the corresponding number operators.

(b ) The extended [b model and the effects of long-range Coulomb interactions

This model assumes that theMn ions occupy the sites of a cubic lattice (taken tobe of unit lattice parameters), while the dopant A ions occupy an x fraction of the‘body centre’ sites of each unit cube formed by the Mn ions. Since the aim is tostudy the effect of long-range Coulomb interactions on phase separation, we makefurther simplifying assumptions. It is assumed that the t2g core spins are alignedferromagnetically and that JH/N; this effectively projects out [ or b electron spinopposite to that of the t2g core spins—we obtain an effectively spinless model. Theabove considerations lead us to the following extended [b Hamiltonian

H ZH[ bCHC and HC ZX

i

Fiqi CV0

2

X

isj

qiqjrij

: ð5:2Þ

Here [ †i and b†i create [ and b electrons, respectively, at site i, and n[ i h[ †i [ iand nbi hb†i bi are the corresponding number operators. In terms of the hole

operator (h†i h[ i which removes an [ polaron at site i ), the electron charge

operator qi hh†i hiKb†i bi and has the average value x per site owing to overall

charge neutrality. The Coulomb term HC has two parts; the charge at site i hasenergy qiFi , where Fi is the electrostatic potential there due to A2C ions, and theinteraction between the charges at sites i and j leads to an energy V0((qiqj)/rij). Inwhat follows, we take the short-range Coulomb correlation U to be large (N).

We now discuss the results of full-scale numerical simulations of theHamiltonian (5.2) on finite three-dimensional periodic lattices, allowing for arandom distribution of the A ions following Shenoy et al. (2007). Here, all theenergy scales are normalized by the bare intersite hopping amplitude t. Systems aslarge as 20!20!20 have been considered. The numerical determination of thegroundstate of (5.2) requires further simplifying approximations. The mostimportant approximation is the Hartree approximation, i.e. the charge operator qi



V0= 0.1, EJT = 2.0, x = 0.3(a) (b)

V0 = 0.1, EJT = 2.0, x = 0.4

V0 = 0.0EJT = 2.0x = 0.3

Figure 9. Real-space electronic distribution obtained from simulations on a 163 cube. Magenta(darkest) denotes hole clumps with occupied b electrons, white (lightest) denotes hole clumps withno b electrons, cyan (2nd lightest) denote singleton holes, and light blue (2nd darkest) representsregions with [ polarons. (a) Isolated clumps with occupied b-electrons (b-electron puddles). (b)Larger doping; percolating clumps. Inset: ‘macroscopic phase separation’ absence of long-rangeCoulomb interaction (V0Z0.0) (after Shenoy et al. (2007)).



is replaced by its expectation value in the groundstate hqiiZh†i hiK hb†i bii. Since we

have assumed that U/N, the b electrons do not hop to sites where an [ polaron ispresent. This leads to the segregation of the two types of electron into disjointclusters. In a cluster of hole sites (which has at least two nearest neighbour holesites), which we call a ‘clump’, the b electron states are determined by solving thequantum kinetic energy Hamiltonian exactly. This is a new generalization of thecommon Coulomb glass simulation (Baranovskii et al. 1979; Davies et al. 1984;Vojta & Schreiber 2001), which includes the quantum mechanically obtained bstates within their clump or puddle. The electrostatic energy is calculatedaccurately using the Ewald technique and fast Fourier transform routines.

In the absence of the long-range Coulomb interaction (V0Z0), this procedureleads to the macroscopically phase-separated state (see inset of figure 9). Theholes aggregate to one side of the simulation box and a fraction of the electronsoccupying the [ states is promoted to the b states in the one large hole clump—with their concentrations determined by the equality of the chemical potential inthe two regions (i.e. the highest occupied b level equals KEJT). This phaseseparation is due to the strong Coulomb repulsion between the two types ofelectron fluids and is in agreement with known results on the Falicov–Kimballmodel (Freericks et al. 2002; Freericks & Zlatic 2003).

Long-range Coulomb interaction ‘frustrates’ phase separation, i.e. macroscopicphase separation costs prohibitive energy in the presence of long-range Coulombinteractions. The precise nature of the resulting groundstate electronic configurationdepends on the JT energy EJT and the doping level x. There are two critical dopinglevels xc1 and xc2 for any given JT energy EJT.When the doping level is less than xc1,i.e. x!xc1, no b states are occupied—the holes (and hence also the [ polarons) forma Coulomb glass (Efros & Shklovskii 1975). When the doping exceeds xc1, some of





the hole clumps are occupied and the groundstate consists of isolated b-electronpuddles dispersed in a polaronic background (figure 9). There is a second criticaldoping level xc2 (see Shenoy et al. 2007); when xTxc2 the occupied b-electron puddlespercolate and the system attains metallicity (figure 9).

The size scale of the electronic inhomogeneity is nanometric. However, itsdependenceonV0 differs fundamentally fromtheanalytical results of the samemodel,which assumed a homogeneous distribution (jellium) of the dopant A ions. For themore realistic, random distribution of the A ions, the size of the electronicinhomogeneity is almost independent of the long-range Coulomb parameter V0, inthat even an extremely smallV0 produces clump sizes that are of the size scale of a fewlattice spacings.Thedependenceof the average sizeof the electronic inhomogeneity isthus due to the long-range Coulomb interaction which along with the randomdistribution of A ions acts as a ‘singular perturbation’ that frustrates macroscopicphase separation. However, the sizes and the distribution of the clumps aredetermined by the random distribution of the A ions, and thus we conclude thatdoped manganites (and similarly, possibly many other correlated oxides) arenecessarily and intrinsically electronically inhomogeneous, on a nanometric scale.

The results of the extended [b model with realistic energy parameters presentedhere provide several new insights into the complex electronic inhomogeneities seen incorrelated oxides, and in particular the low-bandwidth manganites with a large FMregion in their phase diagram. These arguments may be sharply contrasted withearlier work. In particular, this work suggests that the nanoscale inhomogeneities inmanganites arise not out of ‘phase competition’-induced phase separation frustratedby disorder as argued from the studies of model spin Hamiltonians (Dagotto 2003),but from short-range Coulomb correlation-induced phase separation frustrated bylong-range Coulomb interaction, similar to what has been suggested in cuprates(Emery et al. 1990; Emery&Kivelson 1993).Most importantly, nanoscale electronicinhomogeneities are present in both the insulating and metallic phases of dopedmanganites. As is evident from figure 9, each of these constitute a singlethermodynamic phase that is homogeneous atmesoscales.One has ametal–insulatortransition between two such nanoscopically inhomogeneous phases at xc2 as afunction of doping. These observations are in agreement with experiments. Indeed,the electron holography results of Loudon et al. (2002) show that even the ferro-metallic regions have interspersed in them charge-ordered insulating regions whichcan be interpreted as the cluster of [ states.

6. Concluding remarks

A number of competing energy scales are operative in mixed-valent correlatedoxides giving rise to a large number of electronic orders. In the Ln(1Kx)AxMnO3

manganites, a variety of spin, charge and orbital (and associated lattice order) isfound. The emergence of these orders can be understood based on a simpleparametrization, i.e. the mean A-site cation radius which controls the bandwidthof the eg electrons. An intriguing aspect of these materials is that smallperturbations can drive a transition from one type of electronic order to another,as is evident from the effect of a small magnetic field on the charge-ordered state.

In addition to the large number of electronic orders, it is found experimentallythat there is coexistence of different electronic orders in disjoint spatial regions,





i.e. these materials are electronically inhomogeneous showing signatures inthermodynamic and transport properties and can be seen directly in severalexperimental probes. These inhomogeneities can be of varied scales (nm to mm)and can be static or dynamic. Although the phenomenon has been called phaseseparation, it is clear that the regions of distinct electronic order may notnecessarily be ‘thermodynamic phases’, particularly in the case where they are ofnanometric scale. Indeed, the theoretical model discussed in the paper shows thata single ‘phase’ of the manganite itself is inhomogeneous on a nanometric scale.

Although, we have focused onmanganites and cobaltates, electronic inhomogene-ities are important in many other oxides. In the high Tc cuprate La2CuO4Kd, theelectronic phase separation is caused by compositional variations with super-conducting clusters of La2CuO3.06 and AFM clusters of La2CuO3.01 (Sigmund &Muller 1994). Even in the cuprates that possess chemical homogeneity on amesoscale, it has been suggested that the unusual variation of zero-temperaturesuperfluid density with the superconducting transition temperature is due to thepossible coexistence of AFM and superconducting domains (Broun et al. 2005).Neutron-scatteringmeasurements suggest thepresenceof charge stripes (Tranquadaet al. 2004), while scanning probe microscopy indicates a spatially inhomogeneoussuperconducting gap (McElroy et al. 2005).

Theoretical understanding of the phenomenon of electronic inhomogeneities isstill incomplete. Although a large body of previous work based on modelHamiltonians and phenomenological models exists, the microscopic mechanismsand the length-scales that arise in these systems remain poorly understood. Themicroscopically motivated theoretical model that we have discussed here clearlyindicates that these materials are electronically inhomogeneous at nanoscales due tostrong correlation physics. Naturally, the question of the origin of mesoscaleinhomogeneities remains. There are several scenarios that could explain the origin ofthemesoscale patterns. There is a possibility that, sincemanyof the transitions are offirst order, many of the inhomogeneities are due to an ‘incomplete transition’, i.e.they aremetastable states.The secondpossibility is thepresence of long-range elasticstrain fields which are unscreened. Indeed, it is well known that pressure (strain) candrive transitions in the manganites (Soh et al. 2002; Postorino et al. 2003). The keyquestion is whether strain effects are extrinsic (caused by defects, etc.) or intrinsic,i.e. the system reorganizes spontaneously into domains (much like a martensite).

The need for further exploration of electronic orders and inhomogeneities inoxides is evident. Experiments need to be designed so as to isolate long-rangestrain effects, with theoretical efforts towards building coarse-grained models tounderstand the mesoscale physics. This issue is particularly important forexploiting the electronic softness of these materials for applications.

V.B.S. gratefully acknowledges illuminating discussions and collaborative work with H. R.Krishnamurthy and T. V. Ramakrishnan.

References

Ahn, K. H., Lookman, T. & Bishop, A. R. 2004 Strain-induced metal–insulator phase coexistencein perovskite manganites. Nature 428, 401–404. (doi:10.1038/nature02364)

Baranovskii, S. D., Efros, A. L., Gelmont, B. L. & Shklovskii, B. I. 1979 Coulomb gap in disorderedsystems: computer simulation. J. Phys. C: Solid State Phys. 12, 1023–1034. (doi:10.1088/0022-3719/12/6/015)


http://dx.doi.org/doi:10.1038/nature02364

http://dx.doi.org/doi:10.1088/0022-3719/12/6/015





Bhide, V. G., Rajoria, D. S., Rao, C. N. R., Rama Rao, G. & Jadhao, V. G. 1975 Itinerant-electron

ferromagnetism in La1KxSrxCoO3: mossbauer study. Phys. Rev. B 12, 2832–2843. (doi:10.1103/PhysRevB.12.2832)

Biswas, A., Raychaudhuri, A. K., Mahendiran, R., Guha, A., Mahesh, R. & Rao, C. N. R. 1997Direct measurement of the charge ordering gap in Nd0.5Sr0.5MnO3 using vacuum tunnelling.

J. Phys. Condens. Matter 9, L355–L360. (doi:10.1088/0953-8984/9/24/002)Broun, D. M., Turner, P. J., Huttema, W. A., Ozcan, S., Morgan, B., Liang, R., Hardy, W. N. &

Bonn, D. A. 2005 In-plane superfluid density of highly underdoped YBa2Cu3O6Cx.arxiv.org:cond-mat/0509223.

Burley, J. C., Mitchell, J. F. & Short, S. 2004 Competing electronic ground states inLa1KxCaxCoO3. Phys. Rev. B 69, 054401. (doi:10.1103/PhysRevB.69.054401)

Cepas, O., Krishnamurthy, H. R. & Ramakrishnan, T. V. 2006 Instabilities and insulator–metal

transitions in half-doped manganites induced by magnetic-field and doping. Phys. Rev. B 73,035218. (doi:10.1103/PhysRevB.73.035218)

Dagotto,E. 2003Nanoscale phase separationand colossalmagnetoresistance. Berlin,Germany: Springer.Dagotto, E. 2005 Complexity in strongly correlated electronic systems. Science 309, 257–362.

(doi:10.1126/science.1107559)Dagotto, E., Hotta, T. & Moreo, A. 2001 Colossal magnetoresistant materials: the key role of phase

separation. Phys. Rep. 344, 1–153. (doi:10.1016/S0370-1573(00)00121-6)Davies, J. H., Lee, P. A. & Rice, T. M. 1984 Properties of the electron glass. Phys. Rev. B 29,

4260–4271. (doi:10.1103/PhysRevB.29.4260)Efros, A. L. & Shklovskii, B. I. 1975 Coulomb gap and low-temperature conductivity of disordered

systems. J. Phys. C: Solid State Phys. 8, L49–L51. (doi:10.1088/0022-3719/8/4/003)Emery, V. J. & Kivelson, S. A. 1993 Frustrated electronic phase separation and high-temperature

superconductors. Physica C 209, 597–621. (doi:10.1016/0921-4534(93)90581-A)Emery, V. J., Kivelson, S. A. & Lin, H. Q. 1990 Phase-separation in the t–J model. Phys. Rev. Lett.

64, 475–478. (doi:10.1103/PhysRevLett.64.475)Fath, M., Freisem, S., Menovsky, A. A., Tomioka, Y., Aarts, J. & Mydosh, J. A. 1999 Spatially

inhomogeneous metal–insulator transition in doped manganites. Science 285, 1540–1542.(doi:10.1126/science.285.5433.1540)

Freericks, J. K. & Zlatic, V. 2003 Exact dynamical mean field theory of the Falicov–Kimballmodel. Rev. Mod. Phys. 75, 1333–1382. (doi:10.1103/RevModPhys.75.1333)

Freericks, J. K., Leib, E. H. & Ueltschi, D. 2002 Phase separation due to quantum mechanicalcorrelations. Phys. Rev. Lett. 88, 106401. (doi:10.1103/PhysRevLett.88.106401)

Imada, M., Fujimori, A. & Tokura, Y. 1998 Metal–insulator transitions. Rev. Mod. Phys. 70,

1039–1263. (doi:10.1103/RevModPhys.70.1039)Krishnamurthy, H. R. 2005 A new theory of dopedmanganites exhibiting colossal magnetoresistance.

Pramana 64, 1063–1074. (Invited talk published in the Proc. 22nd IUPAP Int. Conf. on StatisticalPhysics (eds S. Dattagupta, H. R. Krishnmurthy, R. Pandit, T. V. Ramakrishanan & D. Sen).)

Kuhns, P. L., Hoch, M. J. R., Moulton, W. G., Reyes, A. P., Wu, J. & Leighton, C. 2003 Magneticphase separation in La1KxSrxCoO3 by 59Co nuclear magnetic resonance. Phys. Rev. Lett. 91,

127202. (doi:10.1103/PhysRevLett.91.127202)Kundu, A. K., Nordblad, P. & Rao, C. N. R. 2005a Nonequilibrium magnetic properties of single-

crystalline La0.7Ca0.3CoO3. Phys. Rev. B 72, 144423. (doi:10.1103/PhysRevB.72.144423)Kundu, A. K., Seikh, M. M., Ramesha, K. & Rao, C. N. R. 2005b Novel effects of size

disorder on the electronic and magnetic properties of rare earth manganates of the typeLa0.7KxLnxBa0.3Mn0.3 (LnZPr, Nd, Gd or Dy) with large average radius of the A-site cations.

J. Phys. Condens. Matter 17, 4171–4180. (doi:10.1088/0953-8984/17/26/015)Kundu, A. K., Nordblad, P. & Rao, C. N. R. 2006 Spin-glass behavior in Pr0.7Ca0.3CoO3 and

Nd0.7Ca0.3CoO3. J. Solid State Chem. 179, 923–927. (doi:10.1016/j.jssc.2005.12.014)Kundu, A., Sarkar, R., Pahari, B., Ghoshray, A. & Rao, C. N. R. 2007 A comparative study of the

magnetic properties and phase separation behavior of the rare earth cobaltates, Ln0.5Sr0.5CoO3

(Ln=rare earth). J. Solid State Chem. 180, 1318–1324. (doi:10.1016/j.jssc.2007.02.003)


http://dx.doi.org/doi:10.1103/PhysRevB.12.2832





http://dx.doi.org/doi:10.1126/science.1107559

http://dx.doi.org/doi:10.1016/S0370-1573(00)00121-6



http://dx.doi.org/doi:10.1016/0921-4534(93)90581-A

http://dx.doi.org/doi:10.1103/PhysRevLett.64.475

http://dx.doi.org/doi:10.1126/science.285.5433.1540

http://dx.doi.org/doi:10.1103/RevModPhys.75.1333






http://dx.doi.org/doi:10.1016/j.jssc.2005.12.014

http://dx.doi.org/doi:10.1016/j.jssc.2007.02.003




Kuwahara, H., Tomioka, Y., Asamitsu, A., Moritomo, Y. & Tokura, Y. 1995 A first-order phase

transition induced by a magnetic field. Science 270, 961–963. (doi:10.1126/science.270.5238.961)

Loudon, J. C., Mathur, N. D. & Midgley, P. A. 2002 Charge-ordered ferromagnetic phase in

La0.5Ca0.5MnO3. Nature 420, 797–800. (doi:10.1038/nature01299)

Mathur, N. D. & Littlewood, P. B. 2003 Mesoscopic texture in manganites. Phys. Today 56, 25–30.

(doi:10.1063/1.1554133)

McElroy, K., Lee, J., Slezak, J. A., Lee, D.-H., Eisaki, H., Uchida, S. & Davis, J. 2005 Atomic-scale

sources and mechanism of nanoscale electronic disorder in Bi2Sr2CaCu2O8Cd. Science 309,

1048–1052. (doi:10.1126/science.1113095)

Millis, A. J. 1998 Colossal magnetoresistance manganites: a laboratory for electron–phonon

physics. Phil. Trans. R. Soc. A 356, 1473–1480. (doi:10.1098/rsta.1998.0230)

Milward, G. C., Calderon, M. J. & Littlewood, P. B. 2005 Coexisting charge modulation and

ferromagnetism produces long period phases in manganites: new example of electronic soft

matter. Nature 433, 607–610. (doi:10.1038/nature03300)

Mori, S., Chen, C. H. & Cheong, S.-W. 1998 Pairing of charge-ordered stripes in (La, Ca)MnO3.

Nature 392, 473–476. (doi:10.1038/33105)

Motome, Y., Furukawa, N. & Nagaosa, N. 2003 Competing orders and disorder-induced insulator to

metal transition in manganites. Phys. Rev. Lett. 91, 167204. (doi:10.1103/PhysRevLett.91.167204)

Pai, G. V., Hassan, S. R., Krishnamurthy, H. R. & Ramakrishnan, T. V. 2003 Zero-temperature

insulator–metal transition in doped manganites. Europhys. Lett. 64, 696–702. (doi:10.1209/epl/

i2003-00282-0)

Postorino, P., Congeduti, A., Dore, P., Sacchetti, A., Gorelli, F., Ulivi, L., Kumar, A. & Sarma,

D. D. 2003 Pressure tuning of electron–phonon coupling: the insulator to metal transition in

manganites. Phys. Rev. Lett. 91, 175501. (doi:10.1103/PhysRevLett.91.175501)

Radaelli, P. G., Ibberson, R. M., Argyriou, D. N., Casalta, H., Andersen, K. H., Cheong, S.-W. &

Mitchell, J. F. 2001 Mesoscopic and microscopic phase segregation in manganese perovskites.

Phys. Rev. B 63, 172419. (doi:10.1103/PhysRevB.63.172419)

Ramakrishnan, T. V., Krishnamurthy, H. R., Hassan, S. R. & Pai, G. V. 2003 Theory of

manganites exhibiting colossal magnetoresistance. arxiv.org:cond-mat/0308396.

Ramakrishnan, T. V., Krishnamurthy, H. R., Hassan, S. R. & Pai, G. V. 2004 Theory of insulator

metal transition and colossal magnetoresistance in doped manganites. Phys. Rev. Lett. 92,

157203. (doi:10.1103/PhysRevLett.92.157203)

Rao, C.N.R. 2000 Charge, spin, and orbital ordering in the perovskitemanganates, Ln(1Kx)A(x)MnO(3)

(LnZrare earth, AZCa or Sr). J. Phys. Chem. B 104, 5877–5889. (doi:10.1021/jp0004866)

Rao, C. N. R. & Raveau, B. (eds) 1998 Colossal magnetoresistance, charge ordering and related

properties of manganese oxides. Singapore: World Scientific.

Rao, C. N. R., Parkash, O., Bahadur, D., Ganguly, P. & Nagabhushana, S. 1977 Itinerant electron

ferromagnetism in SR2C-doped rare-earth, CA2C-doped rare-earth, and BA2C-doped rare-

earth orthocobaltites (LN1Kx(3C)Mx(2C)CoO3). J. Solid State Chem. 22, 353–360. (doi:10.1016/

0022-4596(77)90011-1)

Rao, C. N. R., Kundu, A. K., Seikh, M. M. & Sudheendra, L. 2004 Electronic phase separation in

transition metal oxides. Dalton Trans. 3003–3011.

Renner, C., Aeppli, G., Kim, B. G., Soh, Y.-A. & Cheong, S.-W. 2002 Atomic-scale images of

charge ordering in a mixed-valence manganite. Nature 416, 518–521. (doi:10.1038/416518a)

Ritter, C., Mahendiran, R., Ibarra,M. R., Morellon, L., Maignan, A., Raveau, B. & Rao, C. N. R. 2000

Direct evidence of phase segregation and magnetic-field-induced structural transition in Nd0.5Sr0.5-MnO3 by neutron diffraction. Phys. Rev. B 61, R9229–R9232. (doi:10.1103/PhysRevB.61.R9229)

Rodrıguez-Martınez, L. M. & Attfield, J. P. 2001 Disorder-induced orbital ordering in

L0.7M0.3MnO3 perovskites. Phys. Rev. B 63, 024424. (doi:10.1103/PhysRevB.63.024424)

Salamon, M. B. & Jaime, M. 2001 The physics of manganites: structure and transport. Rev. Mod.

Phys. 73, 583–628. (doi:10.1103/RevModPhys.73.583)


http://dx.doi.org/doi:10.1126/science.270.5238.961


http://dx.doi.org/doi:10.1063/1.1554133


http://dx.doi.org/doi:10.1098/rsta.1998.0230


http://dx.doi.org/doi:10.1038/33105


http://dx.doi.org/doi:10.1209/epl/i2003-00282-0

http://dx.doi.org/doi:10.1209/epl/i2003-00282-0




http://dx.doi.org/doi:10.1021/jp0004866

http://dx.doi.org/doi:10.1016/0022-4596(77)90011-1

http://dx.doi.org/doi:10.1016/0022-4596(77)90011-1

http://dx.doi.org/doi:10.1038/416518a

http://dx.doi.org/doi:10.1103/PhysRevB.61.R9229






Sarma, D. D., Shanthi, N., Barman, S. R., Hamada, N., Sawada, H. & Terakura, K. 1995 Bandtheory for ground-state properties and excitation spectra of perovskite LaMO3 (MZMn, Fe, Co,Ni). Phys. Rev. Lett. 75, 1126–1129. (doi:10.1103/PhysRevLett.75.1126)

Sarma, D. D. et al. 2004 Direct observation of large electronic domains with memory effect in dopedmanganites. Phys. Rev. Lett. 93, 097202. (doi:10.1103/PhysRevLett.93.097202)

Satpathy, S., Popovic, Z. S. & Vukajlovic, F. R. 1996 Electronic structure of the perovskite oxides:La1KxCaxMnO3. Phys. Rev. Lett. 76, 960–963. (doi:10.1103/PhysRevLett.76.960)

Senaris Rodrıguez, M. A. & Goodenough, J. B. 1995 Magnetic and transport properties of the systemLa1KxSrxCoO3Kd (0!x%0.50). J. Solid State Chem. 118, 323–336. (doi:10.1006/jssc.1995.1351)

Shenoy, V. B., Sarma, D. D. & Rao, C. N. R. 2006 Electronic phase separation in correlated oxides:the phenomenon, its present status and future prospects. Chemphyschem 7, 2053–2059. (doi:10.1002/cphc.200600188)

Shenoy, V. B., Gupta, T., Krishnamurthy, H. R. & Ramakrishnan, T. V. 2007 Coulombinteractions and nanoscale electronic inhomogeneities in manganites. Phys. Rev. Lett. 98,097201. (doi:10.1103/PhysRevLett.98.097201)

Sigmund, E. & Muller, K. A. (eds) 1994. Phase separation in cuprate superconductors. Heidelberg,Germany: Springer.

Soh, Y.-A., Evans, P., Cai, Z., Lai, B., Kim, C.-Y., Aeppli, G., Mathur, N., Blamire, M. & Isaacs,E. 2002 Local mapping of strain at grain boundaries in colossal magnetoresistive films usingx-ray microdiffraction. J. Appl. Phys. 91, 7742–7744. (doi:10.1063/1.1455609)

Sudheendra, L. & Rao, C. N. R. 2003 Electronic phase separation in the rare-earth manganates(La1KxLnx)0.7Ca0.3MnO3 (LnZNd, Gd and Y). J. Phys. Condens. Matter 15, 3029–3040.(doi:10.1088/0953-8984/15/19/306)

Tokura, Y. 2006 Critical features of colossal magnetoresistive manganites. Rep. Prog. Phys. 69,797–851. (doi:10.1088/0034-4885/69/3/R06)

Tranquada, J. M., Woo, H., Perring, T. G., Goka, H., Gu, G. D., Xu, G., Fujita, M. & Yamada, K.2004 Quantum magnetic excitations from stripes in copper oxide superconductors. Nature 429,534–538. (doi:10.1038/nature02574)

Uehara,M.,Mori, S., Chen, C.H.&Cheong, S.W. 1999 Percolative phase separation underlies colossalmagnetoresistance in mixed-valent manganites. Nature 399, 560–563. (doi:10.1038/21142)

Vogt, T., Cheetham, A. K., Mahendiran, R., Raychaudhuri, A. K., Mahesh, R. & Rao, C. N. R.1996 Structural changes and related effects due to charge ordering in Nd0.5Ca0.5MnO3. Phys.Rev. B 54, 15 303–15 306. (doi:10.1103/PhysRevB.54.15303)

Vojta, T. & Schreiber, M. 2001 Localization and conductance in the quantum Coulomb glass.Philos. Mag. B 81, 1117–1129.

Wollan, E. O. & Koehler, W. C. 1955 Neutron diffraction study of the magnetic properties of theseries of perovskite-type compounds [La(1Kx), Cax]MnO3. Phys. Rev. 100, 545–563. (doi:10.1103/PhysRev.100.545)

Woodward, P. M., Vogt, T., Cox, D. E., Arulraj, A., Rao, C. N. R., Karen, P. & Cheetham, A. K.1998 The influence of cation size on the structural features of Ln1/2A1/2MnO3 perovskites atroom temperature. Chem. Mater. 10, 3652–3665. (doi:10.1021/cm980397u)

Woodward, P. M., Cox, D. E., Vogt, T., Rao, C. N. R. & Cheetham, A. K. 1999 Effect ofcompositional fluctuations on the phase transitions in (Nd1/2Sr1/2)MnO3. Chem. Mater. 11,3528–3538. (doi:10.1021/cm990281d)

Wu, J., Lynn, J. W., Glinka, C. J., Burley, J., Zheng, H., Mitchell, J. F. & Leighton, C. 2005Intergranular giant magnetoresistance in a spontaneously phase separated perovskite oxide.Phys. Rev. Lett. 94, 037201. (doi:10.1103/PhysRevLett.94.037201)

Zhang, L., Israel, C., Biswas, A., Greene, R. L. & de Lozanne, A. 2002 Direct observation ofpercolation in a manganite thin film. Science 298, 805–807. (doi:10.1126/science.1077346)





http://dx.doi.org/doi:10.1006/jssc.1995.1351

http://dx.doi.org/doi:10.1002/cphc.200600188

http://dx.doi.org/doi:10.1002/cphc.200600188


http://dx.doi.org/doi:10.1063/1.1455609


http://dx.doi.org/doi:10.1088/0034-4885/69/3/R06


http://dx.doi.org/doi:10.1038/21142


http://dx.doi.org/doi:10.1103/PhysRev.100.545

http://dx.doi.org/doi:10.1103/PhysRev.100.545

http://dx.doi.org/doi:10.1021/cm980397u

http://dx.doi.org/doi:10.1021/cm990281d




electronic phase separation and other novel phenomena and properties exhibited by mixed-valent...

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