61 Among 4 d electron systems, Ca 2-x Sr x RuO 4 has especially attracted attention because of its rich and novel ground states such as in Mott transition [1-3]. Since Ca 2-x Sr x RuO 4 has four 4 d electrons in the t 2g orbitals, the significance of orbital degree of freedom is invoked. Nevertheless, few works have been carried out on orbital ordering in 4 d electron system so far. The anisotropic tensor of an X-ray susceptibility signal is enhanced near an absorption edge. However, conventional resonant X-ray scattering (RXS) measurement is not useful for the observation of a ferro-type orbital state, in which charges are distributed with the same local symmetry at each Ru ion site. This is because it is difficult to extract the signal for a ferro-type orbital state at Γ points, which is accompanied with large magnitude of a fundamental reflection by Thomson scattering. However, the RXS interference technique can offer unique access to observing the ferro-type orbital state, in which the signal of the ferro-type orbital state is magnified by the interference with a fundamental signal. In the present study, it is revealed that the observation of orbital states by a resonant X-ray scattering interference technique is significant for understanding the rich phase diagram of Ca 2-x Srx RuO 4 [4]. Figure 1(a) shows the resonant X-ray scattering configuration at beamline BL46XU . ψ is an azimuthal angle, which is the angle around scattering vector Q , while ϕ A indicates the detector angle. The X-ray absorption of Ru is observed around 22.15 keV in Fig. 1(b). Figure 1(c) shows the energy profiles at Q = (0 2 6) with polarization angles of ϕ A = 98 º (dotted thick line) and 82 º (thin line) at ψ = 270 º at 305 K. The interference term for ferro-type orbital ordering is obtained by subtracting the intensity at ϕ A = 82 º from that at ϕ A = 98 º : for ϕ A = 90 º ± ∆ ϕ ( ∆ ϕ = 8 º ), I (90 º + ∆ ϕ ) - I (90 º - ∆ ϕ ) α 2 Re [F σσ F σ π ] sin 2 2 θ A sin 2 ∆ ϕ , in which F σσ and F σ π denote the scattering factors for the σ → σ and σ → π scattering processes, respectively, and 2 θ A is the scattering angle in the analyzer crystal. F σπ has information on the asphericity of 4 d charge distribution, while F σσ corresponds to a fundamental signal. Noticeable point is that F σπ is enhanced by F σσ . Therefore, a small signal for a ferro-type ordering is detectable. The resonant signal for ferro- type orbital ordering in Fig. 1(c) appears near the K absorption edge. Near the K absorption edge, an atomic scattering factor is represented by a tensor and the RXS signal has an azimuthal angle dependence. Ferro-type Orbital State in Mott Transition System Ca2-x Sr x RuO 4 Revealed by Resonant X-ray Scattering Interference Technique Fig. 1. (a) Schematic picture of resonant X-ray scattering configuration. (b) Incident energy dependence of X-ray fluorescence in Ca 2 RuO 4 . (c) Energy scans at 305 K for ϕ A = 98 º (dotted thick line) and ϕ A = 82 º (thin line) at azimuthal angle ψ = 270 º at Q = (0 2 6). The bottom thick line is obtained by subtracting the energy spectrum at ϕ A = 82 º from that at ϕ A = 98 º , which corresponds to the interference term. (b) (c) (a) Analyzer Crystal Detector c * Q Sample 0 22.10 Ca 2 RuO 4 Intensity (arb. units) Energy (keV) Intensity (arb. units) 22.15 22.20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 2 4 6 8 10 62 In order to further verify that the observed resonant signal corresponds to the orbital ordering in Ca 2 RuO 4 , the azimuthal angle dependence has been observed. The magnitude of the signal at the main edge peak at 305 K exhibits the characteristic oscillation with the 360 º period (Fig. 2). F σπ mainly contributes to the ψ dependence of the interference signal. The observed ψ dependence shows the minimum and maximum at around ψ = 90 º and 270 º , respectively, while the intensity approaches zero at ψ = 0 º and 180 º . These features are well explained by the analysis for a ferro-type d xy ordering, as shown in Fig. 2. In addition, we analyzed the ψ -dependence of the resonant signal at Q = (0 2 14), which is also consistent with the behavior of the d xy orbital. Figure 3 shows the temperature dependence of the RXS signal. Above 200 K, the magnitude gradually decreases and then disappears near a metal-insulator transition ( T MI ~ 357 K). Note that the RXS signal is observed at room temperature. Braden et al. showed that at around 300 K, the apical bond length RuO(2) is almost equal to the averaged equatorial bond length RuO(1) [5]. Therefore, the Jahn-Teller distortion is unreasonable for the main origin of the orbital ordering in Ca 2 RuO 4 . As discussed in ref. [6], it is possible that a two-dimensional crystal field as well as a superexchange interaction play a significant role in stabilizing the ferro-type orbital ordering, in addition to the Jahn-Teller effect of a RuO 6 octahedron. M. Kubota a, *, Y. Murakami b,c and M. Mizumaki c a Photon Factory, IMSS, KEK b Department of Physics, Tohoku University c SPring-8 / JASRI *E-mail: masato.kubota@kek.jp References [1] Y. Maeno et al. : Nature 372 (1994) 532. [2] S. Nakatsuji et al. : J. Phys. Soc. Jpn. 66 (1997) 1868. [3] S. Nakatsuji and Y. Maeno: Phys. Rev. Lett. 84 (2000) 2666. [4] M. Kubota, Y. Murakami, M. Mizumaki, H. Ohsumi, N. Ikeda, S. Nakatsuji, H. Fukazawa and Y. Maeno: Phys. Rev. Lett. 95 (2005) 026401. [5] M. Braden et al. : Phys. Rev. B 58 (1998) 847. [6] Fang et al. : Phys. Rev. B 69 (2004) 045116. Fig. 2. Azimuthal angle dependences of interference term for main edge peak at 305 K and 6 K at Q = (0 2 6). – 3 – 2 – 1 0 1 2 3 6 K 305 K 0 90 180 360 270 Ca 2 RuO 4 Intensity (arb. units) Azimuthal Angle (degree) Q = (0 2 6) Fig. 3. Temperature dependence of interference term at Q = (0 2 6) with ψ = 270 º in Ca 2 RuO 4 . 0 0.05 0.10 0.15 0.20 0.25 0.30 0 50 100 150 200 250 300 350 Ca 2 RuO 4 Intensity (arb. units) Temperature ( K ) Q = (0 2 6)
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