Charge ordering in transition metal oxides

Solid State Sciences 8 (2006) 861–867 www.elsevier.com/locate/ssscie

Charge ordering in transition metal oxides J. Paul Attfield Centre for Science at Extreme Conditions (CSEC) and School of Chemistry, University of Edinburgh, King’s Buildings, Edinburgh EH9 3JZ, UK Received 7 February 2005; accepted 13 February 2005 Available online 3 April 2006 Dedicated to Prof. C.N.R. Rao on the occasion of his 70th birthday

Abstract Long range ordering of two transition metal charge (oxidation) states occurs in many oxides. Direct structural evidence from powder neutron diffraction studies on several half-doped manganites (Pr0.5 Ca0.5 MnO3 , TbBaMn2 O6 , YBaMn2 O6 ) and magnetite (Fe3 O4 ) is reviewed. Charge ordering is accompanied by subtle distortions to low (monoclinic or triclinic) symmetry in all cases. The half-doped manganites reveal polymorphism of both charge and Mn3+ orbital ordered arrangements. The degree of charge separation estimated by bond valence sums for these and other oxides is only 20–80% of the ideal difference. The origin of this effect is not clear from present data. © 2006 Elsevier SAS. All rights reserved.

The phenomenon of charge order (CO), a long range order of different metal oxidation states in a crystal lattice, was first proposed for magnetite (Fe3 O4 ) below the 120 K Verwey transition [1,2]. CO has become important in recent years as CO stripes or other correlations may be important to the mechanism of superconductivity in cuprates [3], colossal magnetoresistances (CMR) in manganites [4], and other phenomena in oxides. However, it is only in the last decade that CO transition metal oxide structures have been experimentally determined. ‘Charge ordered’ is here taken to mean the low temperature state of a material that undergoes a symmetry-breaking charge ordering transition. Above the transition temperature TCO , a single crystallographic metal site is found, with the average charge state. Below TCO , two or more inequivalent sites are observed. Charges at the two sites may be estimated from the measured bond distances using the bond valence sum (BVS) method [5]. In the simplest usage, the valence Vn is estimated from:  Vn = exp(dn − di )/B i

summed over the bond distances di from each metal site to the coordinating oxygens. B is a global constant and dn is the bond valence parameter for the metal in an assumed oxidation state n. E-mail address: [email protected] (J.P. Attfield). 1293-2558/$ – see front matter © 2006 Elsevier SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2005.02.011

An intermediate valence state may be estimated by interpolation between the estimates obtained for the nearest integral valence states. If H and L are the higher and lower formal oxidation states, then the intermediate valence is V=

L(VH − VL ) − (H − L)VL . (VH − VL ) − (H − L)

Results from our recent work on charged ordered manganites and magnetite are summarised below, followed by a comparison with other CO structures. 1. Pr0.5 Ca0.5 MnO3 The charge ordered (CO) ground state in manganites is most easily observed in half doped materials such as La0.5 Ca0.5 MnO3 . The first model for this CO phase was proposed by Goodenough [6] after the magnetic structure had been found to be the complex CE-type, with ferromagnetic couplings along zig-zag chains [7]. The model assumed that localised Mn3+ and Mn4+ states order in alternate planes (“stripes”) as shown in Fig. 1(a). Orbital ordering (OO) results from the Jahn–Teller distortion of the high spin 3d4 Mn3+ configuration, and the resulting superexchange interactions are consistent with the observed CE-type spin structure. A powder X-ray and neutron diffraction study of La0.5 Ca0.5 MnO3 [8,9] fitted the crystal structure in a monoclinic P21 /m

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Table 1 A comparison of the refinement results for Pr0.5 Ca0.5 MnO3 at 10 K using Pnm21 or P21 /m pseudosymmetry models Model

Pnm21

Mn–O distances (Å)

Mn1a

Mn1b

Mn1a

P21 /m Mn2a

Mn2b

±b

1.985(6) 1.854(6)

1.909(7) 1.908(7)

1.977(5) 1.851(5)

1.907(3) (×2)

1.922(3) (×2)

±(1/2a + c)

2.084(12) 1.904(14) 1.858(13) 1.975(14)

2.013(10) 2.040(8) 1.852(10) (×2)

1.910(9) (×2)

±(1/2a − c)

1.899(13) 1.981(14) 1.931(13) 2.041(14)

1.931(10) 1.930(8) 1.964(10) (×2)

2.027(8) (×2)

Mean Mn–O

1.935(11) 1.953(12)

1.931(8)

1.959(6)

1.953(7)

BVS

3.72

3.73

3.46

3.51

3.50

The fitting parameters are the overall reduced-χ 2 and residuals for the X-ray (X) and neutron (N) profiles. Mn–O distances are shown for the three pairs of bonds in the given directions (see Fig. 1) followed by the mean value and the bond valence sum (BVS) for each unique Mn site.

Fig. 1. The refined charge and orbitally ordered arrangements in Pr0.5 Ca0.5 MnO3 using P21 /m or Pnm21 pseudosymmetries. The elongated Mn–O bonds at the Mn3+ sites corresponding to the d2z orbitals are shown as broken lines, and the arrows show spin directions for a CE-type arrangement as consistent as possible with the orbital orderings. The Mn site labels are shown on the P21 /m model.

√ √ symmetry 2 2ap × 2ap × 2ap superstructure with 2 displacement coordinates to describe the charge and orbital ordering modulation. The results confirmed the striped CO model. The structures of several other half doped manganites have subsequently been fitted using the same model [10–12], allowing up to 7 coordinate variables to describe the CO and OO modulations. An alternative refinement model for half-doped manganites has recently been derived from a neutron diffraction study of a single crystal of Pr0.6 Ca0.4 MnO3 [13]. (The 1 : 1 CO structure modulation is found for 0.3 < x < 0.5 in Pr1−x Cax MnO3 , 3+ at the Mn4+ sites for x = 0.5.) implying substitution of Mn√ √ This study showed that the 2 2ap × 2ap × 2ap supercell has Pm monoclinic symmetry so that the four Mn sites shown in Fig. 1 are symmetry independent. Orthorhombic Pnm21 symmetry constraints were applied—this constrains sites 1a and 2a, and sites 1b and 2b, to be equivalent. No charge difference between the a and b sites was found, consistent with a Zener polaron ordering (ZPO) model in which an electron is localised in Mn–O–Mn bridges by double exchange when the Mn spins are parallel, so the Mn sites both have an average valence of +3.5.

The striped CO and the ZPO models have recently been tested against highly resolved powder X-ray (ID31 at ESRF) and neutron (HRPD at ISIS) diffraction data collected at 10 K from a polycrystalline sample of Pr0.5 Ca0.5 MnO3 [14]. A comparison of the fitting indices, Mn–O bond lengths and Mn valences (calculated using the Bond Valence Sum method) are given in Table 1. The fitting indices show that the P21 /m and the Pnm21 models give equivalent fits to the X-ray data, but the fit to the neutron intensities (RF2 (N) residuals in Table 1) were significantly better with the P21 /m model (RF2 = 4.58%) than with Pnm21 (RF2 = 6.58%). Notably, both the refined P21 /m and the Pnm21 models give charge and orbitally ordered descriptions for Pr0.5 Ca0.5 MnO3 . In P21 /m symmetry (Fig. 1), there are three independent Mn sites; 1(a and b), 2a and 2b. The refined Mn–O distances and BVS estimates of formal charge (Table 1) show that these sites approximate to Mn4+ , Mn3+ and Mn3+ , respectively, with the latter sites showing elongation of one pair of bonds in the ac plane characteristic of OO. This is the striped picture for CO and OO [6], however, the differences between the BVS values show that the CO is only 25% of the theoretical separation of 1 charge unit. In the Pnm21 description (Fig. 1), the refinement again evidenced charge ordering of Mn4+ and Mn3+ respectively at the two independent Mn sites; (1 and 2)a and (1 and 2)b. The two sites are arranged in double rows, and so this model describes a bistriped charge ordering, in contrast to the singly striped P21 /m model. Although the Pnm21 refinement model does not provide the best fit to the data, it nevertheless describes an alternative CO and OO model, whereas in the previous single crystal study of Pr0.6 Ca0.4 MnO3 , the same pseudosymmetry did not reveal any CO or OO at the two Mn sites [13]. This discrepancy may arise from twinning in the single crystal of Pr0.6 Ca0.4 MnO3 (which was analysed assuming six twin domains), and from the additional disorder introduced by use of a 40% rather than a 50% doped manganite.

J.P. Attfield / Solid State Sciences 8 (2006) 861–867

2. RBaMn2 O6 cation ordered manganites An alternative family of half-doped AMnO3 manganites is provided by the RBaMn2 O6 series in which the R 3+ and Ba2+ cations are ordered in alternating [001] perovskite layers. Charge and orbital ordering superstructures are evidenced for R = Sm and subsequent rare earths and Y [15]. The 300 K structures of the R = Tb [16] and Y [17] materials have been determined using highly-resolved time-of-flight powder neutron diffraction data collected from the HRPD instrument at the ISIS facility, UK. 2.1. TbBaMn2 O6 The observed diffraction peak splittings showed that a structural distortion had lowered the cell symmetry from tetragonal P4/nmm to monoclinic P21 /m. Further inspection of the neutron data revealed very weak diffraction peaks (Fig. 2(a)) from a superstructure with propagation vector (0 1/2 0). A superstructure model was constructed by transforming the structure to a

Fig. 2. Part of the 90◦ bank HRPD neutron powder diffraction profiles; the labelled reflections that evidence the (0 1/2 0) AFOO superstructure of TbBaMn2 O6 at 300 K in (a) are absent for YBaMn2 O6 at 300 K (b), and for TbBaMn2 O6 at 373 K (c).

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b-doubled cell with triclinic P1 symmetry (a = 5.56044(6) Å, b = 11.12021(11) Å, c = 7.63668(6) Å, α = 89.980(4)◦ , β = 90.234(1)◦ , γ = 89.977(2)◦ ) generating four independent Mn atomic sites. Free refinement of all the atomic coordinates in the triclinic superstructure was not feasible with only six weak superstructure peaks being observed. However, it was possible to test for the possibility of orbital order in the P1 b-doubled supercell, through constrained x and y displacements of pairs of the oxygen sites around two pairs of Mn sites. The MnO6 octahedra in TbBaMn2 O6 are strongly distorted as a result of the ordering of large Ba2+ and small Tb3+ in alternate A-cation layers, which causes acentric distortions of the octahedra. The difference between the mean distances for the Mn1 and Mn2 type octahedra showed that Mn3+ /Mn4+ charge order is present. The charges estimated by the bond valence sum method are 3.67 at the Mn1 site and 3.45 at the Mn2 sites. The refined, local displacements of the oxygen atoms in the triclinic superstructure all have a magnitude of 0.035 Å, and they produce longer and shorter trans pairs of Mn–O distances around both the Mn2 sites. Hence, the Mn2 octahedral geometries are a superposition of the acentric distortions resulting from internal structural strains (fitted in the P21 /m sub-cell refinement), and the centric orbital ordering (Jahn–Teller) distortion fitted in the triclinic superstructure. The Mn site distortions thus corroborate the charge ordering inferred from the mean Mn–O distances. A-cation disordered 50% doped AMnO3 manganites such as (Pr0.5 Ca0.5 )MnO3 above show a ‘striped’ charge and orbitally ordered arrangement (Fig. 1(a)) in which ‘checkerboard’ charge ordered layers are stacked directly above each other. The structure of TbBaMn2 O6 ((Tb0,5 Ba0.5 )MnO3 ) revealed an alternative arrangement Fig. 3(a), in which the same charge and orbitally ordered layers are stacked in an alternate fashion giving a ‘rocksalt’ three dimensional charge ordering. In both structures, the Jahn–Teller distortions within each CO plane are ordered with equal numbers of orbital distortions in two perpendicular directions. This is antiferro-orbital ordering (AFOO). The comparison of TbBaMn2 O6 and La0.5 Ca0.5 MnO3 shows that the striped charge ordered arrangement is not intrinsic to half-doped AMnO3 manganites, but can be switched to the alternative rocksalt structure by internal strains imposed by A-cation order. This is the first example of charge ordering polymorphism, here within the MnO3 2.5− framework. Another notable aspect was that Mn3+ /Mn4+ ordered TbBaMn2 O6 was made through topotactic oxygen intercalation into TbBaMn2 O5 in which there is long range Mn2+ /Mn3+ ordering. Charge ordering in both a layered host and the intercalated product is unprecedented, and it is interesting to consider whether the reaction is ‘topoelectronic’, i.e., whether any charge ordering ‘memory’ effects occur at the atomic or domain scale during the oxygen intercalation. At high temperatures (>370 K), the b-doubled superstructure of TbBaMn2 O6 is lost. This signifies a change of orbital ordering as discussed in the context of the structure of YBaMn2 O6 below.

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Table 2 Mn–O distances (Å) for the two octahedra in YBaMn2 O6 Mn1–O O1(a) O1(b) O2

1.947(8) 1.993(9) 2.005(9)

1.977(8) O4(a) O4(b) O3

1.971(8) 2.039(8) 1.906(8)

Mn2–O O1(a) O1(b) O2

1.989(7) 1.981(9) 1.889(9)

1.931(8) O4(a) O4(b) O3

1.963(7) 1.866(9) 1.898(8)

The individual values are shown for trans pairs of bonds, below the mean value for each octahedron.

(a)

(b) Fig. 3. Unit cell views of (a) the AFOO TbBaMn2 O6 structure, (b) the FOO YBaMn2 O6 structure. The longest trans pairs of Mn–O bonds about the Mn3+ sites are shaded.

2.2. YBaMn2 O6 The 300 K powder neutron diffraction pattern of YBaMn2 O6 is similar to that of CO TbBaMn2 O6 [16]. However, the (h k/2 l) superstructure peaks that signify the AFOO in TbBaMn2 O6 are absent in the profile of YBaMn2 O6 at 300 K (Fig. 2(b)), and at temperatures down to 4 K. Nevertheless, additional broadenings of some reflections requires a further lowering of symmetry, from monoclinic to triclinic P1 (a = 5.51974(8), b = 5.51379(8), c = 7.60319(10) Å and α = 90.017(2), β = 90.280(1) and γ = 90.106(1)◦ ). All of the atomic coordinates were refined independently. The Mn–O distances (Table 2) showed that the MnO6 octahedra are distorted by the strains that result from the size difference between the A-cations and the difference between the mean Mn–O distances within the two octahedra confirms that Mn3+ /Mn4+ CO is present. The bond valence sums for the Mn1 and Mn2 sites are respectively 3.36 and 3.81. In the monoclinic P21 /m description of the YBaMn2 O6 structure, the O1(a and b) and the O4(a and b) sites are symme-

try equivalent, so the two trans pairs of O1–Mn–O4 distances in the xy plane are of equal length. Hence, the P21 /m symmetry cannot describe long range orbital order in this plane, although it does allow for the CO distortions. Lowering symmetry to triclinic P1 breaks the symmetry equivalence of the O1 and O4 sites. Free refinement of the atom parameters (Table 1) gives a model in which the O1(b)–Mn1–O4(b) trans pair distances are longer, by 0.05 and 0.07 Å, than those in the O1(a)–Mn1– O4(a) pair. This demonstrates that orbital ordering distortions are present at the Mn3+ site. The triclinic OO distortion has a (0 0 0) propagation vector so that all the elongated bonds are approximately parallel to the same direction, [110] (Fig. 3(b)). Hence, the 300 K structure of YBaMn2 O6 has a novel ferroorbital ordered (FOO) state, which has not been previously found in AMnO3 manganites, although AFOO is common as in the former two structures. These results show that the AFOO and FOO states are of comparable stability in the CO phase of the RBaMn2 O6 perovskites. The slightly greater disparity in size between R 3+ and Ba2+ for R = Y compared to R = Tb changes the ground state from AFOO in the latter material to FOO in the former. This is corroborated by a high temperature neutron diffraction study [18]. The CO and FOO distortions in YBaMn2 O6 persist up to a simultaneous charge and ferro-orbital ordering transition at TCO = TFOO = 498 K. However, TbBaMn2 O6 shows two transitions; the superstructure peaks that characterise the (0 1/2 0) AFOO distortion disappear at ∼370 K (see Fig. 2(c)) and the CO melts at 473 K. The 370 K transition is thus a novel antiferro- to ferro-orbital order transition within the CO regime of TbBaMn2 O6 . 3. Magnetite, Fe3 O4 The ferrimagnetism and moderate electrical conductivity (∼10−2  cm at 300 K) of magnetite arise from its inverse spinel type crystal structure. This is formally written as Fe3+ [Fe2+ Fe3+ ]O4 to show that the first (A type) Fe3+ is tetrahedrally coordinated, whereas the bracketed Fe2+ and Fe3+ ions occupy (B type) octahedrally coordinated sites. Verwey made the fundamental discovery [1] that magnetite undergoes a sharp, first order transition on cooling below ∼120 K at which the resistivity increases sharply by two orders of magnitude, and the structure distorts from cubic symmetry. This was the first report of a charge ordering transition and an orthorhombic

J.P. Attfield / Solid State Sciences 8 (2006) 861–867

superstructure model (Verwey model) with ordering of Fe2+ and Fe3+ states on the B sublattice was proposed [2]. Despite much research, no conclusive structural model of the low temperature phase emerged subsequently because of the complexity of the low temperature structure, and the difficulties caused by microtwinning at the Verwey√transition. √ The low temperature structure was shown to have a 2ac × 2ac × 2ac crystallographic supercell with space group Cc, from a neutron diffraction study of a partially de-twinned single crystal [19]. A detailed structure refinement below TV resulted from a neutron diffraction study of an almost fully de-twinned single crystal by Iizumi et al. [20]. Although large atomic displacements of Fe and O atoms were found, no charge ordered arrangement was identified in the refined structure. A recent structure refinement of Fe3 O4 at 90 K from combined synchrotron X-ray and neutron studies has provided direct evidence for charge ordering [21,22]. The orthorhombic subcell with space group Pmca (as used by Iizumi et al. [20]) gave a better fit than any other space group, and removal of any of the Pmca pseudo-symmetry elements such as the inversion centre (which results in Pmc21 symmetry) led to instabilities. The four inequivalent B sites in this model each represent an averaging over four of the 16 unique B sites in the larger Cc supercell. Two of the sites were found to have a BVS of 2.5, and the other two both have 2.7. This was the first direct crystallographic observation for CO in magnetite. The small (20%) magnitude is partly the result of the subcell used; the low valent sites may be averaged over (3Fe2+ + Fe3+ ) sites in the full Cc superstructure (with each high valent site averaged over (Fe2+ + 3Fe3+ ) subsites). This would give a charge separation of 40% in the full superstructure. NMR evidence supports the existence of 16 independent B sites consistent with this superstructure [23,24]. Based on the above refinement and subsequent resonant diffraction experiments [25] there are eight possible arrangements for the Fe2+ /Fe3+ ordering in the full superstructure, one of which is shown in Fig. 4. None of these models meets the Anderson criterion of having two Fe2+ ions per tetrahedron of four B sites [26], but this is not surprising, e.g., in light of the above observations concerning CO polymorphism in manganites. Two charge modulations parallel to c are apparent in all the possible solutions. The average charge density has a [001]c modulation. Band structure calculations [27] of the cubic phase show nesting on the Fermi surface at the [001]c (X) point, corresponding to an instability in the states of the ‘extra’ (minority spin) t2g electrons. The small [001]c deformations open up a gap in the energy spectrum (estimated to be 150 meV from photoemission studies [28]) leading to the observed loss of conductivity at the Verwey transition. This is essentially a charge density wave (CDW) mechanism, but with strong electron-lattice coupling that leads to a commensurate CDW as electrons are localised at atomic sites, corresponding to the chemical picture of charge ordering. A frozen [001]c charge density wave model is also supported by NMR measurements 24 and the observed critical scattering above TV strongly supports such a mechanism [29]. The nodal planes in the [001]c wave forces a second [0 0 1/2]c

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Fig. 4. One of eight possible models for charge ordering in the C-centred superstructure of Fe3 O4 (black/white circles = Fe2+ /Fe3+ ).

modulation of the phase of the charge, which is also seen in diffuse scattering measurements [30]. 4. Discussion All of the above four oxides show 1 : 1 charge ordering in a simple lattice. In principle, the charge ordering could result in cubic (for Pr0.5 Ca0.5 MnO3 and Fe3 O4 ) or tetragonal (for RBaMn2 O6 ) superstructures, but the observed superstructures are actually monoclinic or triclinic. This demonstrates the need for highly-resolved diffraction data to determine correct CO structures; the lattice distortions in RBaMn2 O6 are close to the resolution limit of modern powder diffractometers. The large degree of symmetry breaking at the CO transition results from the superposition of several distortions that may be of incompatible symmetry; octahedral tilting and rotations in the perovskite materials, breathing type distortions from the two charge states, and orbital ordering. The combination of several distortions enables different charge or orbital ordering states to be observed by changing the counter-cations in the lattice. This is demonstrated by the halfdoped manganites which show a polymorphism of both charge order (striped and rocksalt CO) and orbital order (AFOO and OO states). The local strain (s) imposed upon the MnO3 3.5− network by the A site cations may be written: s = s(UVW) + ds, where s(UVW) represents the average strain of (UVW) periodicity, and ds are the local size variations that result from

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mixing A-cations of different radii, characterised by the size variance σ 2 . The striped CO phase of Pr0.5 Ca0.5 MnO3 is stabilised by a large s(0 0 0) strain (i.e., no long range A-cation order and a small perovskite tolerance factor) and small ds. Rocksalt CO is favoured by the s(0 0 1/2) strain that results from R/Ba cation order, and increasing the magnitude of s(0 0 1/2) (equivalent to the difference between R 3+ and Ba2+ radii) switches the orbital ordering from AFOO in TbBaMn2 O6 to FOO in YBaMn2 O6 . The results of the above studies are compared with other charge ordered transition metal oxide structures in Table 3. This table shows all of the types of transition metal oxides that undergo a charge ordering transition and for which a low structure determination has been reported [31–38]. (Additional refinements with other rare earth cations have been reported for several types, but only one representative example is shown here for brevity.) Almost all of the structure determinations have resulted from powder neutron diffraction experiments, because of the sensitivity of neutrons to oxygen positions, and the difficulties (for single crystal methods) of twinning in many materials below TCO . However, the most complex structure, revealing CO over 8 independent V-sites in NaV2 O5 , was analysed using synchrotron diffraction data from a twinned crystal [31]. Physical or computational methods for overcoming crystal twinning will be needed to determine complex CO structures such as the full Fe3 O4 arrangement. The degree of charge ordering observed via BVS’s in transition metal oxides that have undergone symmetry-breaking CO transitions is always much reduced from ideal values. It is difficult to discern physical trends in %CO from the present data (Table 3), for example Mn3+ /Mn4+ order gives the smallest and largest %CO values. The smallest values in manganites are

from refinements in which pseudosymmetry constraints were applied, suggesting that such constraints tend to underestimate the structural %CO. No general correlation of %CO with TCO is evident. There is also no apparent relationship between the %CO and magnetic ordering transitions or interactions, for example 40% Fe2+ /Fe3+ CO is observed both in Fe3 O4 (which orders ferromagnetically above TCO ) and TbBaFe2 O5 (antiferromagnetic below TCO ). No correlations with average oxidation state or the structural frustration of CO are seen, although these might also be expected. Most of the materials in Table 3 show 20–60% CO, and none show a full 100% CO. Experimental difficulties in resolving the CO structures may partly account for this reduction, but its consistency suggests an underlying physical cause. This could be a microstructural effect, e.g., antiphase domains in which the charge states are reversed. However, this would be expected to show some variation with temperature and from sample to sample, which is not evident from comparative studies, e.g., of the series of RNiO3 perovskites (R = Ho, Y, Er, Lu) [39]. An electronic cause for the reduction may be strong mixing between the ideal ground state and excited states in which the cation charges are exchanged, due to the pseudo-symmetry equivalence of the sites. Whatever the reason for the reduced charge separation, it is apparent that the transition metal cations are adopting one of two states rather than arbitrary non-integral valences (which could vary continuously over some range as found in classic charge-density wave materials). This is most strongly evidenced by the study of the eight independent V-sites in NaV2 O5 [31] in which four BVS’s cluster around one value 4.2. (the V4+ state) and the other four cluster around 4.8 (V5+ ). Charge ordering in transition metal oxides has been postulated and indirectly evidenced for over 60 years. In the last decade, firm structural evidence for CO has emerged from many

Table 3 Summary of charge ordering (CO) properties for semivalent transition metal oxides Material

Space group

T CO (K)

V1

V2

%COa

T M (K)

Magnetic interaction

Method

Ref.

α  -NaV4+ V5+ O5 (PrCa)[Mn3+ Mn4+ ]O6 TbBa[Mn3+ Mn4+ ]O6 YBa[Mn3+ Mn4+ ]O6 Na0.25 Mn0.75 [Mn3+ Mn4+ ]O6 (LaSr2 )Mn2 O7 Li[Mn3.1+ 10/9 Mn4+ 8/9 ]O4 Fe[Fe2.25+ Fe2.75+ ]O4 TbBa[Fe2+ Fe3+ ]O5 Ca2 [Fe3+ Fe5+ ]O6 YBa[Co2+ Co3+ ]O5 Y2 [Ni2+ Ni4+ ]O6

A112 P21 /m P1c P1 I2/m Bbmmc Fddd P2/cc Pmma P21 /n Pmma P21 /n

34 230 473 498 176 210 290 122 282 290 220 582

4.24b 3.48b 3.45b 3.36 3.28 3.67 3.20 2.51b 2.37 3.48 2.02 2.62

4.84b 3.73 3.67b 3.81 3.92 3.87 3.96 2.72b 2.76 4.58 2.69 3.17

59 24 22 44 62 19 84 40 38 55 71 28

34 150 200 200 125 170 66 868 450 115 330 145

AF AF, F AF, Fd AF, Fd AF, F AF, F AF, F F AF AF, F AF AF, F

CS PN + PS PN PN PN CN PN PN + PS PN PN PN PN

[31] [14] [16] [17] [32] [33] [34] [21] [35] [36] [37] [38]

For each material, the idealised CO formula for the refinement model is given, followed by the space group of the CO structure. V1 and V2 are the lower and higher bond valence sums calculated from experimental bond distances, from which the normalised %CO is calculated. The spin ordering transition TM and the types of interaction between spins at the CO sites (AF/F = Antiferro-/Ferro-magnetic) are also shown. The experimental method is summarised as C/P = single crystal/powder diffraction; N/S = neutron/synchrotron radiation. a %CO = 100 · (V − V ) · (F + F )/(V + V ) · (F − F ), where F ’s are the formal valences in the higher (H ) and lower (L) states, e.g., F = 4, F = 5 H L H L L H 2 1 2 1 for the first material. b Averaged over two or more symmetry-independent sites. c Additional symmetry constraints applied. d Full magnetic structure not yet reported, but the magnetic superstructures are consistent with complex CE-type magnetism, as in the other cubic-type manganites.

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diffraction studies. However, we are still at an early stage of understanding the phenomenon and magnitude of charge ordering. Electron-lattice coupling seems to dominate over electron– electron repulsions, enabling CO states to be switched or tuned by internal lattice effects and external fields. Charge ordering lies behind many important conducting phenomena such as superconductivity and CMR in oxides, and new CO materials may lead to the discovery of new electronic phenomena. Acknowledgements I thank the co-authors of the experimental studies reviewed above, the beam-line scientists at ESRF and ISIS for assistance with data collection, and EPSRC for the provision of beam time and other support. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]

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