Relative contributions of lattice distortion and orbital ordering to resonant x-ray scattering in manganites

We investigated the origin of the energy splitting observed in the resonant x-ray scattering (RXS) in manganites. Using thin film samples with controlled lattice parameters and orbital states at a fixed orbital filling, we estimated that the contribution of the interatomic Coulomb interaction relative to the Jahn-Teller mechanism is insignificant and at most 0.27. This indicates that RXS probes mainly Jahn-Teller distortion in manganites. Submitted to: J. Phys.: Condens. Matter Hole-doped manganites with perovskite structure, R1−xAxMnO3 (R is a trivalent rareearth ion and A is a divalent alkaline-earth ion) show a variety of phases with doping concentration x. In these compounds, double-exchange interaction has been considered most important, which closely couples spin with charge degree of freedom. However, it has been recently recognized that double-exchange alone is not enough to account for the peculiar properties of manganites. Theoretical and experimental studies have shown the importance of the orbital degree of freedom to understand the rich phase diagrams [1, 2]. The direct information of the orbital ordering has been lacking due to the dearth of proper experimental means until Murakami et al. proposed the use of resonant x-ray scattering (RXS)[3, 4]. Anisotropic charge distribution in an atom results in the anisotropy in the x-ray susceptibility near the absorption edge. This gives rise to x-ray dichroism and scattering intensity at structurally forbidden Bragg reflections Lattice distortion and orbital ordering to resonant x-ray scattering in manganites 2 for polarized x-ray [5, 6]. They exploited this technique and succeeded in detecting the resonant scattering from superlattice reflections, which has been interpreted as a signature of the antiferro-type orbital ordering. The resonance at main edge corresponds to the dipolar transition from 1s to unoccupied 4p level (Mn K-edge), and the split of the 4p levels is the origin of the anisotropy. It has been argued that the RXS reflects the 3d orbital ordering because the anisotropic 3d charge distribution causes the 4p splitting via the Coulomb repulsion [7]. However, this interpretation has been later challenged; the 4p splitting is the result of Jahn-Teller distortion rather than the 3d orbital polarization [8 12]. There has been no definitive answer to these conflicting views. In order to distinguish the two mechanisms, we have performed RXS measurements of samples with controlled lattice constant and orbital ordering at a fixed orbital filling (i.e., the average number of electrons occupying the eg orbital). An epitaxially grown film is suitable for this purpose because the epitaxial strain makes possible to artificially modify the lattice constant. Thin films in this paper were all deposited on SrTiO3 (001) substrate and their hole concentration was fixed to 0.4, i.e., 0.6 in the orbital filling. The composition of the films was R0.6Sr0.4MnO3, where R was La, La0.6Pr0.4, La0.2Pr0.8, Pr, Pr0.6Nd0.4, or Nd in the decreasing order of average ionic size with correspondingly shorter out-of-plane lattice constant (c-axis) (vide infra). The in-plane lattice constant (a-axis) was fixed to that of the substrate. Bulk crystals of identical composition are all ferromagnetic metal (FM) in the ground state [13]. Because the modulation of orbital states alters the magnetic, transport, and optical properties of thin film manganites [14 16], any deviation from FM in our film signals the change in the orbital state. The lattice constant of SrTiO3 is 3.905 Å, which is larger than those of these compounds in the bulk. Our epitaxial films were thus laterally stretched causing a split in the doubly degenerate eg orbitals into x 2 − y at lower level and 3z − r at higher level. Therefore, one probable orbital state is the x − y-type orbital order accompanied by the layer-type (A-type) antiferromagnetic (A-AF) state, typified by bulk crystals of Nd1−xSrxMnO3 [17, 18]. This is because the orbital ordering promotes inplane transport, which brings about in-plane ferromagnetic coupling by double-exchange interaction and out-of-plane antiferromagnetic coupling by superexchange interaction. As will be shown later, the magnetic and magnetotransport measurements indicate that we have indeed films ranging from FM to A-AF. RXS measurements were performed at beam-line 4C and 9C at Photon Factory, KEK, Tsukuba, employing newly-developed interference technique by Kiyama et al. [19]. We observed energy dependence of interference term from (102) reflection of La0.6Sr0.4MnO3 (LSMO), Pr0.6Sr0.4MnO3 (PSMO) and Nd0.6Sr0.4MnO3 (NSMO) films at various azimuthal angles with the photon energy near the Mn K-absorption edge. Our results show that the Jahn-Teller mechanism has dominant influence on Mn 4p splitting, which is consistent with other reports for manganite thin films [19, 20, 21]. Thin film samples were grown using pulsed laser deposition technique [22]. The thickness of the films was about 50 nm. X-ray diffraction measurements for (00l) and Lattice distortion and orbital ordering to resonant x-ray scattering in manganites 3 (114) reflection peaks confirmed that all films grew epitaxially with a (001) orientation and that the out-of-plane lattice constant systematically decreased as the A-site ion was replaced by a smaller ion as depicted in the abscissa in figure 1(b). Figure 1(a) shows the temperature dependence of the resistivity measured within the ab-plane using a common four probe method and (b) shows the magnetization at 5 K under the magnetic field of 500 Oe after field cooling. All films had metallic ground state and the insulator to metal (I-M) transition temperature (TIM) was continuously shifted to lower temperatures from the LSMO to the NSMO film. However, the magnetic property exhibited a dramatic variation with the lattice constant ratio c/a. The LSMO film had ferromagnetic transition at 325 K and the magnetization was about 3.2 μB/Mn in the ground state. As c/a is reduced, the magnetization decreased; for the NSMO film, the magnetization was only about 0.26 μB/Mn and didn’t saturate even at 50 kOe. The small spontaneous magnetization in spite of in-plane metallic conductivity signals the A-AF ordering. However one might still argue that the small magnetization and the metallic conduction are the result of the phase separation rather than the A-AF ordering: small fraction of ferromagnetic metallic region is embedded in antiferromagnetic insulator. In order to differentiate the two possibilities we measured the transport across a NSMO film. A NSMO film was deposited on 5% La-doped SrTiO3 (La-STO), which is a good conductor. By x-ray diffraction and M-T and M-H curves, we confirmed that it had the same lattice constant and magnetic properties as those of the NSMO film grown on STO. The film was etched to form two 100 × 100 μm square pads separated by a 10 μm gap using photolithography technique (see the inset of figure 2). Because the substrate is highly conductive, the resistivity was estimated as that coming from two 70 nm thin film resistors in series. We show in figure 2 the result of temperature dependence of out-of-plane resistivity of the NSMO/La-STO film measured under the magnetic field of 0 and 50 kOe respectively applied parallel to the ab-plane. The large out-of-plane resistivity could be partly due to the insulating layer formation at the interface, which contributes to the overall offset of the resistivity. However, the interfacial layer is inactive electronically in general and does not respond to the magnetic field in particular [23]. Therefore, the appearance of the out-of-plane magnetoresistance around 200 K (figure 1(b)) concomitant with the in-plane I-M transition in figure 1(a), which persists down to low temperatures, signifies the A-AF-type order inside the film. The negative magnetoresistance is brought about by the canting of the out-of-plane antiparallel spin order. This behaviour is consistent with the observations in the bulk crystals [18]. For a phase separated film, the magnetoresistance should peak around the Curie temperature. While the magnetotransport measurement showed the evidence of ferro-type orbital ordering in NSMO, the LSMO film should have more isotropic orbital distribution judged from the 3D FM behaviour. Thus we have samples with varing degree of orbital polarization and a range of c/a values, which allow us to differentiate the two mechanisms. Lattice distortion and orbital ordering to resonant x-ray scattering in manganites 4 In the previous RXS measurements used for antiferro-type orbital ordering in manganites, the incident beam is σ-polarized and only the π-polarized scattering beam is detected at a superlattice position. In the present case, however, the diffraction spots from the ferro-type orbital ordering and/or the Jahn-Teller distortion coincide with the Bragg peaks. Thus the quite large σ → σ Bragg scattering masks the σ → π scattering due to the anisotropic scattering factor of Mn atoms, the information we are after. To circumvent the difficulty, an interference technique was devised [19, 20]. The new technique is a method to extract an interference term between σ → σ scattering and σ → π scattering. Consider a geometry in which the analyzer crystal is deliberately rotated by ∆φ from the angle at which only the π -polarized beam can pass. There is a small projection of σ → σ scattering onto the analyzer which can interfere with the projection of σ → π scattering. Note that Bragg scattering from incident π-polarized x-ray (π → π scattering) is negligible because the incident x-ray is almost completely σ-polarized. The interferrence effect is analysed as follows. The atomic scattering factor of Mn atom is given by