Resonant xray scattering in 3dtransitionmetal oxides: Anisotropy and charge orderings
ABSTRACT The structural, magnetic and electronic properties of transition metal oxides reflect in atomic charge, spin and orbital degrees of freedom. Resonant xray scattering (RXS) allows us to perform an accurate investigation of all these electronic degrees. RXS combines highQ resolution xray diffraction with the properties of the resonance providing information similar to that obtained by atomic spectroscopy (element selectivity and a large enhancement of scattering amplitude for this particular element and sensitivity to the symmetry of the electronic levels through the multipole electric transitions). Since electronic states are coupled to the local symmetry, RXS reveals the occurrence of symmetry breaking effects such as lattice distortions, onset of electronic orbital ordering or ordering of electronic charge distributions. We shall discuss the strength of RXS at the K absorption edge of 3d transitionmetal oxides by describing various applications in the observation of local anisotropy and charge disproportionation. Examples of these resonant effects are (I) charge ordering transitions in manganites, Fe3O4 and ferrites and (II) forbidden reflections and anisotropy in Mn3+ perovskites, spinel ferrites and cobalt oxides. In all the studied cases, the electronic (charge and/or anisotropy) orderings are determined by the structural distortions.

Article: Statistical distribution of the electric field driven switching of the Verwey state in Fe3O4
[Show abstract] [Hide abstract]
ABSTRACT: The insulating state of magnetite (Fe$_{3}$O$_{4}$) can be disrupted by a sufficiently large dc electric field. Pulsed measurements are used to examine the kinetics of this transition. Histograms of the switching voltage show a transition width that broadens as temperature is decreased, consistent with trends seen in other systems involving "unpinning" in the presence of disorder. The switching distributions are also modified by an external magnetic field on a scale comparable to that required to reorient the magnetization.New Journal of Physics 01/2012; 14(1). · 4.06 Impact Factor  SourceAvailable from: digital.csic.es[Show abstract] [Hide abstract]
ABSTRACT: Here the correlation between the chemical shift in Xray absorption spectroscopy, the geometrical structure and the formal valence state of the Mn atom in mixedvalence manganites are discussed. It is shown that this empirical correlation can be reliably used to determine the formal valence of Mn, using either Xray absorption spectroscopy or resonant Xray scattering techniques. The difficulties in obtaining a reliable comparison between experimental XANES spectra and theoretical simulations on an absolute energy scale are revealed. It is concluded that the contributions from the electronic occupation and the local structure to the XANES spectra cannot be separated either experimentally or theoretically. In this way the geometrical and electronic structure of the Mn atom in mixedvalence manganites cannot be described as a bimodal distribution of the formal integer Mn(3+) and Mn(4+) valence states corresponding to the undoped references.Journal of Synchrotron Radiation 05/2010; 17(3):38692. · 2.19 Impact Factor  SourceAvailable from: Javier Blasco[Show abstract] [Hide abstract]
ABSTRACT: The semiconductorinsulator phase transition of the singlelayer manganite La0.5Sr1.5MnO4 has been studied by means of highresolution synchrotron xray powder diffraction and resonant xray scattering at the Mn K edge. We conclude that a concomitant structural transition from tetragonal I4/mmm to orthorhombic Cmcm phases drives this electronic transition. A detailed symmetrymode analysis reveals that condensation of three soft modes― Δ2(B2u), X1 +(B2u) and X1 +(A)―acting on the oxygen atoms accounts for the structural transformation. The Δ2 mode leads to a pseudo JahnTeller distortion (in the orthorhombic bc plane only) on one Mn site (Mn1), whereas the two X1 + modes produce an overall contraction of the other Mn site (Mn2) and expansion of the Mn1 one. The X1 + modes are responsible for the tetragonal superlattice (1/2,1/2,0)type reflections in agreement with a checkerboard ordering of two different Mn sites. A strong enhancement of the scattered intensity has been observed for these superlattice reflections close to the Mn K edge, which could be ascribed to some degree of charge disproportion between the two Mn sites of about 0.15 electrons. We also found that the local geometrical anisotropy of the Mn1 atoms and its ordering originated by the condensed Δ2 mode alone perfectly explains the resonant scattering of forbidden (1/4,1/4,0)type reflections without invoking any orbital ordering.Physical review. B, Condensed matter 02/2011; 83(18). · 3.77 Impact Factor
Page 1
Resonant xray scattering in 3dtransitionmetal oxides:
Anisotropy and charge orderings
G. Subías1, J. García1, J. Blasco1, J. HerreroMartín2 and M. C. Sánchez1
1 Instituto de Ciencia de Materiales de Aragón, Departamento de Física de la
Materia Condensada, CSICUniversidad de Zaragoza, 50009Zaragoza, Spain
2 European Synchrotron Radiation Facility, 38043GrenobleCedex, France
Email: gloria@unizar.es
Abstract. The structural, magnetic and electronic properties of transition metal oxides
reflect in atomic charge, spin and orbital degrees of freedom. Resonant xray scattering
(RXS) allows us to perform an accurate investigation of all these electronic degrees.
RXS combines highQ resolution xray diffraction with the properties of the resonance
providing information similar to that obtained by atomic spectroscopy (element
selectivity and a large enhancement of scattering amplitude for this particular element
and sensitivity to the symmetry of the electronic levels through the multipole electric
transitions). Since electronic states are coupled to the local symmetry, RXS reveals the
occurrence of symmetry breaking effects such as lattice distortions, onset of electronic
orbital ordering or ordering of electronic charge distributions. We shall discuss the
strength of RXS at the K absorption edge of 3d transitionmetal oxides by describing
various applications in the observation of local anisotropy and charge
disproportionation. Examples of these resonant effects are (I) charge ordering
transitions in manganites, Fe3O4 and ferrites and (II) forbidden reflections and
anisotropy in Mn3+ perovskites, spinel ferrites and cobalt oxides. In all the studied cases,
the electronic (charge and/or anisotropy) orderings are determined by the structural
distortions.
1. Introduction
The discovery of new electronic properties, including highTC superconductivity, colossal
magnetoresistance and multiferroic modifications, in transitionmetal oxides has fuelled a
resurgence of interest in atomic charge, spin and orbital degrees of freedom in systems of highly
correlated electrons. Xray spectroscopy techniques are highly sensitive to these electron
degrees of freedom. However, they probe shortdistance correlations only. In contrast, xray
diffraction reveal longrange ordered static correlations. Resonant xray scattering (RXS)
combines absorption and diffraction as they have in common the xray atomic scattering factor
(ASF), f, which is usually written as: f = f0 + f ’+ if ” [1]. It contains an energy independent part,
f0, corresponding to the classical Thomson scattering and two energydependent terms, f ‘ and f
“, also known as the anomalous ASF. RXS occurs when the xray energy is tuned near the
absorption edge of an atom in the crystal. In this case, the anomalous ASF strongly depends on
the photon energy, which manifests in marked variations of the scattered intensity. This
dependence of the scattered intensity appears in any Bragg reflection when crossing the
absorption edge of a constituent atom.
The study of the energydependent modulation of the diffraction intensity of intense Bragg
peaks is the scope of the diffraction anomalous fine structure technique (DAFS) [2,3]. This
technique allows the determination of the local structural information around the anomalous
atom that is chemical and valence specific similar to that of Extended Xray Absorption Fine
Page 2
Structure (EXAFS). The advantage of DAFS is that it is spatially and siteselective. Our interest
here is focused on the study of either weakallowed or forbidden reflections that appear in a
phase transition. In the first case, the anomalous scattering contribution is comparable to the
Thomson one and the peculiar characteristics of RXS can be studied. The intensity of weak
superlattice reflections can be due to either a structural modulation, contributing to the structure
factor as a Thomson term or because the anomalous ASF of atoms, now in different
crystallographic sites, differ in some energy range. Normally, these differences are larger for
photon energies close to an absorption edge, showing an enhancement (or strong decrease) of
the scattered intensity just around the absorption threshold. In the case of symmetry forbidden
reflections, only the resonant term is present. Since RXS involves virtual transitions of core
electrons into empty states above the Fermi level, the excited electron is sensitive to any
anisotropy around the anomalous atom so that the anomalous ASF has a tensorial character.
Thus, a reflection can be observed on resonance if any of the components of the structure factor
tensor is different from zero. In the case of weak superlattice reflections, the resonant atoms
occupy different crystallographic sites and have different local structures. Thus, the anomalous
ASF are different at energies close to the absorption edge and the scattered intensity shows a
resonance reflecting the differences of the ASF between these nonequivalent atoms. RXS
intensity is then observed coming from the difference between the diagonal terms of the ASF. In
this case, there is a Thomson contribution and the analysis of the spectral shape must include it.
On the other hand, resonances observed in forbidden reflections are related to atoms that occupy
equivalent crystallographic sites. Symmetry elements with translation components (screw axes
and glide planes) of the crystal space group transform an atom into another equivalent in the
lattice, but with a differently oriented atomic surrounding. This makes that some of the off
diagonal terms change sign after these symmetry operations, giving rise to structure factor
tensors that contain nonvanishing offdiagonal terms. Templeton & Templeton [4] first noticed
such reflections that show a local polarization anisotropy of the xray susceptibility and they are
now known as ATS reflections. We note that ATS reflections have strong polarization and
azimuth dependences.
The vector potential of the electromagnetic field in the matterradiation interaction term can
be developed in a multipolar expansion in such a way that the symmetry of the excited levels
can be chosen. Thus, we can speak on dipolardipolar transitions, dipolarquadrupolar
transitions, etc. Consequently, resonant methods are also sensitive to the symmetry of the
electronic shells, which compose the intermediate states. For electric dipoledipole (E1E1)
transitions the wave vectors ki and kf of the incident and scattered xrays do not enter the
scattering amplitude. The strength of the xray resonances associated with electric quadrupole
quadrupole (E2E2) and electric dipolequadrupole transitions (E1E2) are less intense than for
E1E1 process but must content the ki and kf dependence. A complete polarization and azimuthal
analysis of the RXS experiment is needed to assign the multipolar origin of the RXS signal.
In this contribution, after a recall of the RXS amplitude, we will discuss several examples
that correlate with the charge and orbital ordering concepts. We restrict to the metal K edges
and mainly to the dipolardipolar channel, which describes most of the phenomenology. Two
types of reflections are observed. The first one originates from the different anomalous
scattering factors of nonequivalent atoms in the crystal. The occurrence of this type of
resonance is correlated to the energy shift of the absorption edge (chemical shift) and it has been
considered as a proof of charge ordering (CO). The second one arises from the anisotropy of the
anomalous scattering factor of an atom at crystallographic equivalent sites. These ATS
reflections have been assigned to orbital ordering (OO). However, the first type of reflections
can also exhibit anisotropic behaviour. In all the studied cases, we conclude two main results: (i)
the charge segregation is much smaller than one electron and consequently, it would be better
described as a charge modulation and (ii) the anisotropy is present in the pempty density of
states and it seems not to be correlated with a real dorbital ordering.
2. Resonant xray scattering tensor
In RXS, the global process of photon absorption, virtual photoelectron excitation and photon re
emission, is coherent through the crystal, giving rise to the usual Bragg diffraction condition
Page 3
)(
"'
0
ifff
e
j
F
jjj
j
RQi
++
∑
=
⋅r
r
(1)
where Rj
r
is the position of the jth scattering atom in the unit cell,
r
f
k
if
kkQ
rr
r
−=
is the
scattering vector (
is the Thomson scattering part of the atomic scattering factor. The resonant part,
is given by the expression [5]
and are the wave vectors of the incident and scattered beams) and
,
i
k
r
j
f0
"'
iff +
∑
n
Γ
2
−−−
〉 〉〈〈
ψ
−
=+
n
gn
g
i
nn
f
ggn
e
2
iEE
O
ˆ
O
ˆ
EE
m
f
i
f
)(
)(
1
ω
h
*3
"'
ω
h
ψψψ
h
(2)
In this expression, ω
h
is the photon energy, is the electron mass,
E
n
Γ are the energy and inverse
ψ . The interaction of the electromagnetic radiation
Oˆ
ˆf
O
e
m
g
ψ describes the
initial and final electronic state with energy and and
g
E
n
lifetime of the intermediate excited states
n
with matter is expressed by the operators
operators up to the electric quadrupole term, we have [6]:
ˆ
(
O
and . By multipole expansion of these
i
*
)
2
1
1 (
r
)()()
r k i
fififi
r
r
r
r
⋅−⋅= ε
(3)
Here rr is the electron position measured from the absorbing atom and
polarization of the incident(scattered) beam. Correspondingly, we get that there are three
contributions to the resonant scattering factor: dipoledipole (dd), dipolequadrupole (dq) and
quadrupolequadrupole (qq).
Using the Cartesian reference coordinate system defined in figure 1 for the photon
polarization and wave vector, we can develop the scalar product of equation (3) and the resonant
scattering amplitude of equation (2) can be written in the form:
−
=+
ω
)(
EE
gn
h
is the
)( fi
εr
⎥⎦
⎤
⎢⎣
⎡∑
α
∑
αβγ
∑
+−−
∑
n
Γ
2
−−−
β
,
αβγδ
αβγδ
Q
δγβαβαγγαβγ
I
γβααββα
εεεεεε
ω
h
****
3
2
"'
4
1
)(
2
)(
1
kkIkk
i
D
i
EE
m
f
i
f
ififfiifif
n
gn
e
h
(4)
where α, β, γ, δ are indexes that vary independently over the three Cartesian directions x, y, z,
and the transition matrix elements ,
contributions are characterized by the following Cartesian tensors of second, third and fourth
rank, respectively:
∑〈
=
n
ψψ
α αβγ
and associated to dd, dq and qq
αβ
D
αβγ
I
αβγδ
Q
〉〉〈
∑〈
n
=
〉〉〈
∑〈
n
=
〉〉〈
gnng
gnng
gnng
rrrrQ
rrrI
rrD
ψψψψ
ψ
γ
ψ
ψψψψ
δγβααβγδ
β
βα αβ
(5)
Page 4
Figure 1. Scheme of a general
RXS experiment
scattering plane)
(vertical
It is important to determine the symmetry properties of the D, I and Q tensors [7] that depend
on two factors: (i) the transformation properties of a space group itself and (ii) the local
symmetry of the resonant atoms position. Referring to nonmagnetic samples, the structure
factor tensor is a second rank symmetric tensor (parityeven) with six independent components
in the dd approximation. This number reduces upon taking into account the local site symmetry
of the atom. The qq term is also symmetrical under the inversion symmetry, whereas the dq
contribution is only antisymmetrical. As a result, if an atom sits in an inversion centre, the I
tensor must be zero and the dipolequadrupole transition is only allowed for atoms breaking the
inversion symmetry.
In the following we shall describe some significant RXS experiments following the two
types of resonant reflections, weakallowed and forbidden. In the first case, we shall relate them
to the charge modulation, intimately joined to the transition metalligand bond distances and in
the second case we shall relate them to the anisotropy of the geometrical local structure around
the resonant atoms. Since the charge is a timereversal invariant quantity, we shall deal either
with pure electric dd and qq transitions that are even under parity or with parityodd electric dq
transitions. Timereversal odd events that are related to the magnetic properties of the system
will be not considered.
3. Resonant effects due to different crystallographic sites (charge) ordering
Understanding the charge state in the high and low temperature phases of mixed valence
transitionmetal oxides is of fundamental interest in the context of metalinsulator transitions
that are assumed to be driven by CO. The sensitivity of RXS to the CO relies on the fact the
energy values of the absorption edge for the two different valence states of the transitionmetal
atom are slightly different (known as chemical shift). If longrange order of these valence states
exists, superlattice reflections due to the contrast between the atomic scattering factors of the
two valence states will exhibit a resonance enhancement. The point is that CO is intimately
correlated with the associated crystal distortions coming from the structural transitions that
accompanied the metalinsulator ones. Thus, a question arises whether the electronic CO is the
cause or the effect of the lattice distortions.
The concept of CO in solids was first applied by E. J. W. Verwey to the metal to insulator
transition that occurs in magnetite (Fe3O4) at Tv ∼ 120 K, now known as the Verwey transition
[8]. Above Tv, Fe3O4 has the inverse spinel cubic AB2O4 structure, where A and B are the
tetrahedral and octahedral Fe sites, respectively. Verwey originally proposed that the hopping of
valence electrons on the octahedral Bsite sublattice is responsible for metallic conductivity. In
the insulating phase, spatial localization of the valence electrons on these Bsites gives rise to an
ordered pattern of Fe3+ and Fe2+ ions in successive [001] planes (cubic notation). The Bsite
sublattice, shown in the inset of figure 2, can be regarded as a diamond lattice of tetrahedra of
nearestneighbour Fe atoms sharing alternate corners. This simple model was implying the
observation of (0,k,l) reflections with k+l=4n+2 in the low temperature phase. These reflections
Page 5
are forbidden above Tv because of the diamond glide plane of the spinel structure. The first RXS
experiments in magnetite showed that (002) and (006) reflections belonging to this type of cubic
forbidden reflections originates from the local structural anisotropy of the Fe atoms at the B
sites that have a trigonal point symmetry (3m) [911]. These works discarded the Verwey’s CO
model but they did not guarantee the lack of CO with other periodicities of the cubic unit cell.
In order to investigate other possible CO periodicities, we need to start from the low
temperature crystallographic structure. The symmetry lowering
16 nonequivalent Fe sites at tetrahedral and octahedral positions, respectively; each one can
have its own local atomic charge. However, the exact structure is not yet perfectly known [12
14]. A good approach to the real structure consists of a
aaa
22/2/
××≈
, ac being the cubic cell parameter [12,14]. Complexity is greatly
reduced because there are only 6 nonequivalent Fe atoms, two in tetrahedral sites (A1 and A2)
and four in octahedral sites (B1, B2, B3 and B4). It can be noticed that atomic displacements in
this low temperature structure result in two main types of superlattice reflections, which are
indexed in the cubic notation: (I) (h,k,l) reflections such that h+k=even resulting form the loss of
the translation that give rise to charge modulations with wave vector
fcc
halfinteger (h,k,l+1/2) reflections arising from the doubling of the cell along the c axis that
corresponds to charge modulation with
q
/ 1 , 0 , 0 (
=
possible charge segregation over the octahedral atoms along the c axis given by the sensitivity
of the RXS technique in a highly stoichiometric single crystal of Fe3O4 (TV=123.5 K) [15].
Figure 2 (left panel) shows the energy dependence of the intensities for some characteristic
Bragg and forbidden reflections at the Fe Kedge and at 60 K compared to the fluorescence
spectrum. Experimental data have been corrected for absorption.
CcmFd
→
3
generates 8 and
cell with lattice parameters
cP /2
ccc
cq
) 1 , 0 , 0 (
=
r
and (II)
c
) 2
r
. We examine now the limit for the
7,107,117,12
Energy (keV)
7,137,14 7,15
0
20
40
60
80
100
(0 0 7/2)σπ
(0 0 1)σσ
(1 1 0)σσ
(4 4 3/2)σσ
x 10
3
Intensity (arb. units)
0
0.2
0.4
0.6
0.8
1
1.2
116118120122124126128
(4,0,1/2)
(0,0,7/2)
(0,0,1)
I (T) / I (115 K)
T (K)
Figure 2. The left panel shows some of the experimental RXS spectra around the Fe Kedge in
Fe3O4, corrected for absorption. The right panel shows the temperature dependence of the
integrated intensities, on and offresonance, normalized to the lowtemperature value.
(a) Energy scans of the permitted (0,0,1) and (1,1,0) reflections show three resonant peaks, a
first one at the Fe K threshold (7118 eV) and the other two around 71247129 eV, which
corresponds to the white line in the fluorescence spectrum. The observed strong resonant effect
is a consequence of electronic and structural differences among the Fe atoms at B1 and B2
octahedral sites. This can be parameterised in terms of valence as a charge segregation δ=0.23e.
This result confirms the lack of ionic CO in terms of Fe2+ and Fe3+ ions, in agreement with
previous RXS [1618] and synchrotron powder diffraction [14] studies.
Page 6
(b) Resonant intensity is only observed in the σ−π’ channel for the (0,0,7/2) reflection,
indicating that this is a forbidden reflection in the low temperature phase. The energy scan
shows a threepeak structured resonance nearly at the same energies as the (0,0,1) and (1,1,0)
reflections. In this case, the electronic anisotropy comes from interference among equivalent
crystallographic sites. Six different sites are present for the Fe atoms so up to six different terms
could contribute to the resonant signal [19]. The superlattice (4,4,3/2) corresponds to the same
periodicity along c as the forbidden (0,0,l/2) reflections. However, it displays hardly any
resonant effect opposite to what is expected to occur at those very weak reflections. Therefore,
we can conclude that no charge segregation exists with (0,0,1/2) periodicity and the ATS
(0,0,l/2) reflections have its origin in the loss of octahedral and tetrahedral symmetry originated
by the structural phase transition.
In order to establish the correlation between the lattice distortion and the charge segregation
and anisotropy orderings, we have measured the temperature dependence of the intensity of the
following superlattice reflections: (4,0,1/2) offresonance (E=7.1 keV) and (0,0,1) and (0,0,7/2)
on resonance (E=7.125 keV), which is reported in figure 2 (right panel). The resonant and non
resonant signals simultaneously disappear at Tv (±0.5 K) and the intensity of all these reflections
is zero at temperatures above 125 K. This result shows that RXS in Fe3O4 comes from the
ordering of local distortions at the structural transition, which leads to an ordered formal charge
segregation and electronic anisotropy at the Fe atoms [15].
We will comment now on the halfdoped manganites such as Nd0.5Sr0.5MnO3 and
Bi0.5Sr0.5MnO3. It was proposed the ordering of an alternating pattern of Mn3+ and Mn4+ ions
was predicted leading to the onset of superlattice reflections doubling the b axis of the
orthorhombic Pbnm (Ibmm) cell [20]. The observed modulation wave vectors are (0,k,0) and
(0,k/2,0) with k odd for the ordering of charge and orbital degrees of freedom, respectively. The
occurrence of orbital order (OO) is also predicted independently from the CO because Mn3+ are
JahnTeller distorted ions. We have measured the energy dependence of the intensity at the Mn
K edge at Q=(0,3,0) and Q=(0,5/2,0) for both, Nd:Sr [21] and Bi:Sr [22] single crystals. Figure
3 summarizes the results obtained.
6,54 6,556,56 6,57
0,0
0,4
0,8
1,2
1,6
2,0
Intensity (arb. units)
E (keV)
Bi0.5Sr0.5MnO3
Nd0.5Sr0.5MnO3
6,546,556,566,57
0,0
0,2
0,4
0,6
0,8
1,0
1,2
Bi0.5Sr0.5MnO3
Nd0.5Sr0.5MnO3
Intensity (arb. units)
E (keV)
Figure 3. The left panel shows the normalized intensity for the nonrotated polarization channel
at the (0,3,0) peak associated to CO whereas the right panel shows the rotated polarization
channel at the (0,5/2,0) peak associated to OO in Nd0.5Sr0.5MnO3 and Bi0.5Sr0.5MnO3.
Nonresonant intensity can be observed away from the Kedge of Mn and a broad resonance
is found at the absorption edge at (0,3,0) reflections in the nonrotated (σσ’) channel. On the
other hand, a strong Gaussianshaped resonance is observed at energies close to the Kedge of
Mn at (0,5/2,0) reflections only in the rotated (σπ’) channel, which identifies these halfinteger
reflections as structurally forbidden ones. The variation with azimuth of these resonances shows
a characteristic oscillation with π periodicity. We note that in this case, the two kinds of
Page 7
behaviour mixed since the marked different anisotropy of the two types of atoms. The resonant
scattering at either (0,k,0) or (0,k/2,0) reflections does not depend on the
arises from E1 (1s→ np) transition. The temperature dependence of the resonant intensities
shows that the two types of reflections disappear at the metalinsulator phase transition.
The complete analysis of the energy lineshape and the azimuth and polarization dependence
of the resonant intensities is carried out using a semiempirical structural model [23]. The
checkerboard arrangement of two types of crystal Mn sites gives an excellent agreement with
the experimental data. These two sites differ in their local geometric structure: one site is
anisotropic (tetragonal distorted oxygen octahedron) and the other site is isotropic (nearly
undistorted oxygen octahedron). Estimates of the valence modulation between the two Mn
atoms are slightly variable depending on the manganite but all fall below the ideal charge
segregation of ±0.5e. As shown in [21] and [22], ±0.08 for Nd0.5Sr0.5MnO3 and ±0.07 for
Bi0.5Sr0.5MnO3, respectively.
CO for x different from 0.5 is in general not well defined. We have also explored further the
Bi1xSrxMnO3 system toward the Mn3+rich side, that is for x=0.37 [24]. Superlattice reflections
of (0,k,0) and (0,k/2,0) types with k odd were observed at the Mn Kedge. This is to be
compared with the observation of the Kedge resonances in Bi0.5Sr0.5MnO3. Figure 4 shows an
example of the resonant enhancement as observed at (0,3,0) and (0,7/2,0) reflections in
Bi0.63Sr0.37MnO3.
4 1.5
(0,3,0)
Intensity (arb. units)
wave vector and it
k
1.5
2
2.5
3
3.5
0
0.5
1
6.53 6.546.55
E (keV)
6.56 6.576.58
Intensity σσ'
Intensity σπ'
x 200
0
60 30 0
0.2
0.4
0.6
0.8
1
1.2
30 60 90 120 150 180
ϕ (º)
E=6552.6 eV
σσ'
6540655065606570
0,0
0,2
0,4
0,6
0,8
1,0
6040 20 0 20 40 60 80 100120140160180
ϕ (deg)
0,0
0,2
0,4
0,6
0,8
1,0
E=6551.6 eV
Intensity (arb. units)
(0, 7/2 ,0)
Intensity (arb. units)
E (keV)
Figure 4. RXS results in Bi0.63Sr0.37MnO3 at the Mn Kedge. (a) Polarization analysis of the
(0,3,0) reflection as a function of photon energy. (b) energy dependence of the forbidden
(0,7/2,0) reflection for the σπ’ channel. The insets show the respective azimuthal angle
dependence on resonance.
The energy dependence of the intensity for both, weakallowed (0,k,0) and forbidden
(0,k/2,0) reflections is identical to that observed in the halfdoped bismuth manganite (figure 3).
The dependencies of the resonant intensities with azimuthal angle reveals identical twofold
symmetry too. We note that the σσ’ intensity of the (0,3,0) peak approaches the nonresonant
intensity at the minimum opposite to the constant evolution expected for a pure CO reflection.
These results indicate that the checkerboard ordering of two types of Mn atoms in terms of the
local structure in the ab plane in a ratio 1:1 is strongly stable and extends to doping
concentrations x<0.5. Intermediate valence states lower than +3.5 are deduced for
Bi0.63Sr0.37MnO3, where the charge disproportion is found to be ±0.07.
The last example is provided by La0.33Sr0.67FeO3, which shows a charge modulation that is
commensurate with the carrier concentration (n=1x) and corresponds to a wave vector
q=(2π/ap) (1/3,1/3,1/3), being ap the primitive cubic lattice parameter. Ordered layers of Fe3+
and Fe5+ ions in a sequence of …Fe3+Fe3+Fe5+… along the cubic [111] direction were originally
Page 8
proposed to explain the metalparamagnetic to insulatorantiferromagnetic transition at 200 K
[25]. We have investigated this threefold CO using the RXS technique [26]. Superlattice
(h/3,h/3,h/3) reflections in the pseudocubic cell notation were observed in the nonrotated σσ’
polarization channel for h=2, 4 and 5. These reflections are forbidden in both cubic (Pm3m)
and rombohedral (R3c) symmetries. However, they exhibit a resonant behavior at energies
close to the Fe K edge on top of a nonresonant signal, as shown in figure 5.
7,107,117,127,137,147,15
0
5
10
15
20
25
30
35
40
45
50
55
60
906030
Azimuthal angle (°)
0306090
0
1
2
3
(4/3,4/3,4/3)
σσ'
Integr. Intens. (a.u.)
(5/3,5/3,5/3)
(2/3,2/3,2/3)
(4/3,4/3,4/3)
Intensity (electron units)
E (keV)
Figure
scans of the σσ’
intensity
(h/3,h/3,h/3)
reflections measured
at 10 K and corrected
for absorption. The
inset shows
dependence of the
resonant
(7129.5 eV) on the
azimuth angle
(4/3,4/3,4/3)
reflection.
5.
Energy
for the
no
intensity
for
The nonresonant intensities are explained due to a periodic structural modulation of both Fe
and Sr(La)O3 atomic planes along the cubic [111] direction. To account for the strong variation
in the Thomson scattering among the different satellite reflections, the Fe and Sr(La)O3 atomic
planes must move in opposite senses, keeping the inversion symmetry of the supercell. These
shifts differentiate two crystallographic sites for the Fe atoms and produce an ordered sequence
of two compressed and one expanded FeO6 octahedra. The compressed octahedron is
asymmetric with three short and three long FeO bonds whereas the expanded one is regular.
Concerning the local charges of the two types of Fe cations, the chemical shift between the
expanded and compressed Fe atoms was found to be 0.7±0.1 eV. This is to be compared to the
energy shift of 1.26 eV between Fe3+ and Fe4+ [27]. Assuming a linear relationship between
energy shift of the K absorption edge and local charge, we determined that the amount of charge
segregation is 0.6e. Since the resonant intensity is constant as a function of the azimuth angle
over a range of 180 º, as shown in the inset of figure 5, the Fe atoms have not a local anisotropy
in this case. This result indicates the presence of a pure charge density wave ordering in the
mixedvalent perovskite La0.33Sr0.67FeO3.
4. Resonant effects due to anisotropy (orbital) ordering
The direct observation of OO is a difficult task because it is accompanied by other effects such
as lattice distortions and charge segregations. The study of the RXS and the anisotropic
character of the xray scattering were developed in crystallography more than 20 years ago [4].
In particular, Dmitrienko [28,29] developed a general theoretical treatment of the “forbidden”
ATS reflections, deriving new extinction rules valid near the absorption edge. In the
microscopic point of view, these ATS reflections are due to the presence of the absorbing atom
in an anisotropic chemical environment, which brings about the orientation of unoccupied
electronic levels.
The experimental application of RXS to the study of OO started in 1998, when Murakami
and coworkers [30] investigated the CO and OO in La0.5Sr1.5MnO4 at the Mn Kedge. It was
Page 9
concluded the successful observation of OO of the
type orbital) on Mn
angular dependence around the scattering vector of the intensity (azimuthal dependence)
confirms that they result from the anisotropic character of the anomalous part of the atomic
scattering factor. However, it was later demonstrated that the JahnTeller distortion of the
oxygen octahedra surrounding the Mn atoms is sufficient to reproduce the experimental results
at the K edge without invoking any contribution of the 3dOO [31].After this first observation,
RXS is widely used to study the orbital degree of freedom in several manganites [3236] and
other transitionmetal oxides [3740]. In particular, the following experiments provide key
information for the mechanism of RXS and OO.
(1) The parent compound of colossal magnetoresistive manganites, LaMnO3, was expected
to show an alternating ordering of and
780 K due to the greatly distorted MnO
[41]. The observation of resonance in the σπ’ scattered intensity of the (3,0,0) forbidden
reflection at the Mn Kedge was initially interpreted as a direct probe of this OO [32].
Moreover, the increase of the resonant signal with decreasing temperature as TN was
approached from above was interpreted as a direct correlation of the magnetic order with OO.
Recently, we have revisited the RXS at the Mn Kedge of LaMnO3, both experimentally and
theoretically [36]. We have observed two independent forbidden reflections, (0,3,0) [or,
equivalently (3,0,0)] and (0,0,3), which are related to two different nonzero offdiagonal
elements of the secondrank atomic scattering factor tensor. The different energy dependence of
the RXS spectra for the two types of forbidden reflections has been explained within the
multiple scattering theory in terms of longrange ordered structural distortions around Mn atoms
using a cluster that includes up to 63 atoms beyond the first oxygen neighbors [42], as
demonstrated in figure 6(a). Since no change in either the intensity or its azimuthal dependence
was observed when crossing TN at 140 K (see figure 6(b)), these forbidden reflections are
ascribed as ATS reflections in agreement with a structural origin and opposite to the OO
interpretation.
2.1
1.2
absorption, theory
(030), theory
(003), theory
electrons ( and 
g e
)3 (
22
rz −
)(
22
yx −
3+ sites by detecting the (2n+1/4,2n+1/4,0) forbidden reflections. The
orbitals in the ab plane below
)3 (
22
rx −
)3 (
22
ry −
6 octahedron and the Atype antiferromagnetic order
0
6.54
0.5
1.1
1.6
6.556.56
E (keV)
6.576.58
Intensity (arb. units)
(003)(030)
0
5
10
15
20
25
0.0
1.2
0.4
0.8
absorption, theory
(030), theory
(003), theory
0
5
10
15
20
25
0.0
0.4
0.8
(030)
(003)
EE0 (eV)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
050100150200 250300
(003)
(030)
Intensity (arb. units)
Temperature (K)
TN
0
180160140120100 80 60 40 20 0
Azim uth angle (degree)
0.2
0.4
0.6
0.8
1
1.2
Calculation
(030)
(003)
Intensity (arb. units)
Figure 6. (a) Experimental (circles) RXS of the (0,3,0) and (0,0,3) forbidden reflections in
LaMnO3. The inset shows the MXAN calculations done using the 63atoms cluster (upper panel)
and the 6atoms cluster (lower panel). (b) Temperature dependence of the integrated intensity of
the (0,3,0) and (0,0,3) reflections on resonance, normalized for comparison. The inset shows the
respective azimuthal angle dependence on resonance.
(2) Another example of the excitement of forbidden reflections on a cubic crystal structure
that deserves discussion are the (0,0,l) (l=4n+2) reflections in Fe3O4. Once the Verwey model of
Page 10
CO was discarded, these reflections offer the possibility to study RXS excited by a dqtransition
which is only allowed on the tetrahedral site whereas the octahedral site allows, on the contrary,
only for dd and qq transitions. Two distinct resonant lines are observed in the RXS spectra of
(0,0,2) and (0,0,6) forbidden reflections in Fe3O4 at the preedge and at the main edge energies
of the Fe Kedge [10]. The comparison of the energy and azimuthal dependence of these
reflections at the Fe and Co K edges in Fe3O4, CoFe2O4 and MnFe2O4 spinels is reported in
figure 7 [38]. No preedge resonance is observed either at the Fe Kedge in MnFe2O4 or at the
Co Kedge in CoFe2O4, whereas the mainedge resonance is observed at the Fe Kedge in both,
CoFe2O4 and MnFe2O4, and at the Co Kedge in CoFe2O4.
7,107,117,12
Energy (KeV)
7,13 7,14 7,15
0
1
2
3
4
0
0.2
0.4
0.6
0.8
1
1.2
7.77.727.74
Intensity (arb. units)
E (keV)
CoFe2O4
Co Kedge
CoFe2O4
MnFe2O4
Fe3O4
Fe Kedge
Intensity (arb. units)
Figure 7. Energy scans of the (0,0,2)
(closed symbols) and (0,0,6) (open
symbols) forbidden reflections at the Fe K
edge in the spinel ferrites. The inset
compares the Co Kedge RXS of the
(0,0,2) and (0,0,6) reflections in CoFe2O4.
These results confirm that the prepeak resonance originates from dq transitions at the
tetrahedral Fe atoms and the mainedge resonance is due to the anisotropy of the trigonal (
point symmetry of octahedral B sites of the spinel structure. The azimuthal dependence
corroborates the dd character of the mainedge resonance, which does not depend on either the
type or the formal valency of the transitionmetal atom that occupies the octahedral site. We
note here that we have observed anisotropic RXS, mainly of a structural origin, in a system
where the local atom environment is nearly isotropic since there is not a significant distortion of
the ligand configuration [43].
(3) Recently, the correlation of OO and magnetic ordering has been studied on layered cobalt
oxides, RBaCo2O5.5 with R=rareearth [39,40]. Resonances have been observed at the Co K
edge for (0,k,0) reflections with k odd in TbBaCo2O5.5 whereas (h,0,0) reflections with h odd
were not detected either on or off resonance in any phase transition [39]. The cusp of the
resonant scattering is either up –(0,3,0) and (0,7,0) or down –(0,1,0) and (0,5,0) depending on
the k value. This behavior arises from displacements of the Tb and Ba ions from the ideal
tetragonal positions while the occurrence of RXS and its azimuthal dependence comes form the
presence of two different environments for Co atoms (octhedron and pyramid), ordered along
the b axis. Therefore, resonant (0,k,0) reflections with k odd corresponds to ATS reflections and
no further contribution due to OO has been deduced from this experiment [40]. On the other
hand, superlattice (1,0,l) with l even reflections were reported occurring at the metalinsulator
transition in GdBaCo2O5.5x [40]. RXS was observed at these reflections, which is sensitive to
the difference in anisotropy of adjacent Co pyramids and/or Co octahedral and it has been
associated to the presence of OO.
)
Page 11
5. Conclusions
RXS has demonstrated its potential to solve old and new problems on strong correlated
transitionmetal oxides. The results on the low temperature insulating phase of magnetite has re
opened the discussion on the origin of the Verwey transition. The classical CO model has been
overcome and many recent theoretical papers gives a more realistic interpretation without
invoking to ionic ordering. In general, all these RXS results discard the description of mixed
valence transitionmetal oxides as a bimodal distribution of integer valence states and the so
called CO phase implies the segregation in different crsytallographic sites whose electronic
differences are mainly determined by the structural distortions. These structural distortions
induces a different charge density on different crystallographic sites and in some cases, an
electronic anisotropy by lowering the local symmetry. Finally, RXS has been also fundamental
to determine the type of ordering in many cases, such as Bi0.67Sr0.33MnO3 and La0.33Sr0.67FeO3.
Acknowledgement
The authors thank financial support from the Spanish MICINN (FIS0803951 project) and DGA
(Camrads). We also acknowledge ESRF for granting beam time and technical support.
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