||Synchrotron X-ray Resonant Scattering in metallic oxides
Synchrotron X-ray Resonant Scattering in metallic oxides: Charge and Orbital ordering
Joaquín García, Gloria Subías, Javier Blasco, M. G. Proietti,
M. C. Sánchez and J. Herrero-Martin
Mixed-valence transition-metal (TM) oxides exhibit many interesting properties such as superconductivity, colossal magnetoresistance and metal-insulator phase transitions. Generally, the description of the electronic state of these compounds is made on the basis of the ionic model proposed by Goodenough and it implies the spatial or temporal charge localization on the transition-metal atoms. Following this framework, the low temperature insulating phases of these oxides have generally been described as a periodic ordering of distinct ionic states in the lattice. This phenomenology, so-called charge ordering (CO) , has become nowadays a main topic in the description of TM oxides, such as manganese perovskites. Intimately related to the charge ordering, it has also been proposed the concept of orbital ordering (OO), as the orientational ordering of the d-orbitals of the transition-metal atoms in the lattice. The two archetype examples of charge and orbital ordering are Fe 3 O 4 (magnetite) and LaMnO 3 (the mother compound of magnetoresistive manganites), respectively.
The characterization of the charge-orbital-ordering (COO) phenomena is a hard and controversial task up to now. Generally, the observation of different crystallographic sites by either x-ray or neutron diffraction techniques has been considered as a proof of charge ordering. A direct way to demonstrate the onset of a long-range periodic charge arrangement is the observation of superlattice reflections by the recently developed X-ray Resonant Scattering technique in modern synchrotron radiation facilities. The appearance of a resonance at the transition-metal K absorption edge is due to the out-of-phase interference of identical (or almost) crystallographic sites because of the difference in the atomic anomalous scattering factors f. The anomalous part of the scattering factor, f'(E) + if"(E), is related to the x-ray absorption coefficient µ . For dipolar transition, resonant reflections can then originate by either the different energies of s-p excitations for atoms with different valence states (CO reflections) or by the directional splitting of the p-unoccupied states in an anisotropic local environment (Anisotropic Tensor of Susceptibility, ATS, reflections, often associated to OO reflections).
In the course of our research, we have investigated the COO phenomena carrying out X-ray Resonant Scattering experiments in two relevant systems. The first one includes Fe 3 O 4 and related spinel ferrites. The second one is Nd 0.5 Sr 0.5 MnO 3 as example for half-doped manganites. Both systems showed a metal-insulator phase transition with decreasing the temperature, the low temperature phase being described as a COO phase. We have shown that the observed resonant reflections in the two systems can be easily explained only considering the anisotropy of the local geometrical structure around the excited TM atom.
Magnetite was the first material where a CO transition was proposed to explain the insulator behaviour below T V ~ 120 K (Verwey transition). It crystallizes in the spinel cubic structure (space group Fd-3m ) at room temperature. The formula unit can be written as Fe 3+ [Fe 2+ ,Fe 3+ ]O 4 where the bracket indicates atoms located at the octahedral sites while cations outside the bracket are at the tetragonal sites. According to this formula, 2+ and 3+ Fe ions are dynamically disordered at the same crystallographic site. This dynamical transformation of Fe 2+ into Fe 3+ implies the motion of the electron to be responsible for the metallic conductivity. Then, the insulator behaviour was explained in terms of localization of the mobile electron at the octahedral sites, giving rise to a long range spatial CO pattern (Verwey model). Spinel ferrites are obtained from Fe 3 O 4 by partial substitution of the Fe ions by other divalent cations. In particular, Co 2+ locates at the octahedral site in CoFe 2 O 4 whereas Mn 2+ occupies the tetrahedral site in MnFe 2 O 4 .
X-ray resonant scattering experiments were carried out on Fe 3 O 4 [1,2], MnFe 2 O 4 and CoFe 2 O 4 single crystals, grown by floating zone method in our laboratory, at the beam-line D2AM at the ESRF ( Grenoble , France ). Symmetry forbidden (002) and (006) reflections were measured at room temperature, below T V and in the case of magnetite, above the Néel temperature (T N ) in order to check any effect associated to the onset of the ferrimagnetism. The azimuthal angle (rotation around the scattering vector Q = k' - k ) dependence and polarization analysis ( s - s ' and s - p' components for s–polarised incident bem) of the scattered intensity were also analysed.
Figure 1 compares the energy dependence of the diffracted intensity of (002) and (006) reflections at the Fe K-edge at room temperature for the three spinel ferrites. The spectra shows three main features whose origin we have determined experimentally: a pre-edge resonance (dipole-quadrupole transitions at the tetrahedral Fe ion), a main resonance at the absorption K-edge and an energy extended modulation (dipole transitions at the pseudo-octahedral metal ion). The dipolar part of the spectra has been analysed using a tensorial formalism for the anomalous scattering factor. In the local frame of the pseudo-octahedron, trigonal-distorted, the scattering tensor is diagonal with two main components, parallel and perpendicular to the trigonal axis. This analysis reproduces well the energy, azimuthal and polarization dependences. Moreover, the energy-dependent spectra at temperatures below T V or above T N in magnetite are identical to the room temperature one.
Figure 1. Energy dependence spectra of (002)
[closed symbols] and (006) [open symbols] reflections. Solid lines are
the respective fluorescence spectra. Lines are a guide for the eye and
asterisks mark spurious Renninger reflections.
All these results show: First, the atomic scattering factor is identical among the different octahedral atoms in magnetite pointing out to the lack of charge localization (temporal or spatial) in the sense of bimodal CO of ionic states. Secondly, the anisotropy of the anomalous scattering factor is mainly originated by the anisotropy of the local geometrical symmetry of the octahedral atom instead of a supposed 3d orbital ordering.
In the case of half-doped manganites, several x-ray resonant scattering studies have claimed on the observation of real COO phases. However, neither our previous XANES (X-ray Absorption Near Edge Structure) measurements on these manganites nor a proper re-examination of the x-ray resonant scattering data reported in the literature [3,4] supported this electronic localization at atomic scale.
We have recently performed a X-ray resonant scattering experiment at the beam line ID20 at the ESRF (Grenoble, France) at the Mn K-edge in a Nd 0.5 Sr 0.5 MnO 3 single-crystal , also grown by floating zone method in our laboratory. The low temperature phase of this compound has also been described as a COO phase within a checkerboard pattern of Mn 3+ (Jahn-Teller ion) and Mn 4+ ions according to the antiferromagnetic CE-type phase below T N ~170 K. We observe dipole resonance at the Mn K-edge for the low temperature superlattice (300) and (030) [assigned to CO] and forbidden (05/20) [assigned to OO] reflections. The energy, azimuthal angle and polarization dependences of these reflections have nicely been analysed using a semi-empirical structural model for the tensorial atomic scattering factors: Two non-equivalent crystallographic octahedral sites are found for the Mn atoms below T N , (1) tetragonal-distorted [described with two components in the diagonal, f 1 par and f 1 perp to the tetragonal axis] and (2) nearly-regular [the three components in the diagonal are identical, f 2 ]. Figure 2 compares the x-ray scattering data to the best-fit semi-empirical model, obtained for d anis= f 1 par- f 1 perp=1.6 eV and d chem.= f 1 - f 2 =0.7 eV, for both the supposed “CO” and “OO” reflections. Although the experiment probe the existence of two kinds of Mn atoms, we demonstrate that they cannot be identified as (1) Mn 3+ and (2) Mn 4+ ions with a d chem= f 1 - f2 =4.5 eV determined from XANES spectroscopy. Then, the “CO” reflections are naturally explained by the different local geometry of the two Mn sites and the “OO” reflections as due to the anisotropy of the tetragonal local distortion at one of the Mn sites without including any ordering of the Mn d-orbitals, i.e. Jahn-Teller effect.
Figure 2. Energy dependence spectra of (030)
and (05/20) reflections at the Mn K-edge at T=60 K (symbols) compared
to the best-fit structural model (lines) at maximum and minimum azimuthal
Summarizing, we conclude that no charge localization occurs
on the transition-metal atoms in either magnetite or the half-doped NdSr-manganite.
This result might force the scientific community to change the atomic concept
of electronic localization in mixed-valence TM oxides .
This work was partially supported by the CICyT MAT-02-0121
project and DGA.
References and Principal publications
 J. García, G. Subias, M. G. Proietti, H. Renevier,
Y. Joly, J. L. Hodeau, M. C. Sánchez and J. F. Bérar, Phys.
Rev. Lett. 85 , 578 (2000).
 J. García, G. Subias, M. G. Proietti, J. Blasco, H. Renevier, J.
L. Hodeau and Y. Joly. Phys. Rev. B 63 , 054110 (2001).
 J. García, M.C. Sánchez, J. Blasco, G. Subías and M.G.
Proietti. J. Phys.: Condens. Matter 13 , 3243 (2001). J. García,
M.C. Sánchez, G. Subías and J. Blasco. J. Phys.: Condens. Matter
13 , 3229 (2001).
 J. García and G. Subías, Phys. Rev. B 68
, 12701 (2003).
 J. Herrero-Martin, J. García, G. Subías, J. Blasco and M.
C. Sánchez. Phys. Rev. B to be published .
 J. García and G. Subías, J. Phys. Condens. Matter 16
, R145 (2004)