Perovskite-type transition metal oxides (TMOs) show many fascinating phenomena, such as high- T c superconductivity in cuprates and colossal magnetoresistance in manganites. 3 d TMOs have been extensively studied since their rather narrow d band can induce a Mott instability. Valence d orbitals of a transition metal ion in an octahedral crystal field are split into the t 2g and e g levels, where the d xy , d yz and d zx orbitals are lower in energy than the d 3z 2 -r 2 and d x 2 -y 2 . When the d orbitals are partially and selectively occupied (e.g., by Jahn-Teller effect), the orbital angular momentum of the transition metal ion is totally quenched because the orbitals that are stabilized by the Jahn-Teller distortion are expressed using real wave functions. With increasing period number of an element, the spatial extent of d orbitals tends to increase, and therefore, their bandwidth is expected to be broad. Indeed, Sr 2 RhO 4 (4 d 5 ) is a fairly good metal compared with Sr 2 CoO 4 (3 d 5 ). Sr 2 IrO 4 (5 d 5 ) is a magnetic insulator [1], whereas it would have a t 2g 5 low-spin state and become a metal with a partially filled wide t 2g band. Recently, it has been predicted that the strong spin-orbit coupling recovers the orbital motion of 5 d electrons; the resultant spin-orbit integrated states form two narrow bands, so that even a small on-site Coulomb repulsion opens a Mott gap [2]. To confirm the realization of a spin-orbit coupling induced Mott insulator, we have conducted resonant X-ray magnetic scattering (RXMS) experiments at beamlines BL19LXU and BL29XU . We used highly brilliant SR with a photon energy corresponding to Ir L -edge (2 p - 5 d ) to explore unconventional electronic states. A selection rule of RXMS identifies a 5 d state as a complex spin-orbit integrated state and not as a crystal field state [3]. Figure 1 shows RXMS spectra of the magnetic reflection (1 0 22) at the Ir L edge. The reflection intensity at the L 2 edge is less than 1% of that at the L 3 edge, which is a direct consequence of a selection rule for RXMS. Figure 2 illustrates 5 d level splitting by a crystal field and a spin-orbit coupling. RXMS at the L 2 edge becomes forbidden for the spin-orbit integrated state, whereas equal resonant intensities are expected at the L 2 and L 3 edges for the crystal field state. The spin-orbit integrated state well explains the experimentally obtained RXMS spectra. The magnetic structure of Sr 2 IrO 4 remained undetermined, because Ir is a strong neutron absorber. Using the enhancement at the L 3 edge, we have tried to determine the magnetic structure of Sr 2 IrO 4 . The crystal structure is of the K 2 NiF 4 type and shown in Fig. 3(a). Our RXMS results revealed that the magnetic structure is canted antiferromagnetic (see Fig. 3(b)). In zero field, magnetic reflections are observed at (1 0 4 n +2), (0 1 4 n ) and (0 0 odd ) as shown in Figs. 3(c)-3(e). By representational analysis with the extinction rule for magnetic reflections, a symmetrically allowed possible magnetic structure is considerably restricted to two candidates. One is compatible with metamagnetism of Sr 2 IrO 4 and the other is not, so that the magnetic structure is uniquely specified. The application of a magnetic field induces metamagnetic transition and rearrangement of magnetic moments. The determined magnetic structure also well explains the appearance of a net magnetic moment in the metamagnetic state and an accompanying change in the extinction rule for magnetic reflections [3]. The experimental establishment of the spin-orbit integrated states of valence electrons is a first step for developing a new research field of relativistic materials. For materials characterized by a spin-orbit coupling, RXMS is an ideal method to probe the phase of the outer electron wave function. Our study opens up a new exclusive feature of X-ray magnetic scattering. 54 Electronic and Magnetic Structures of Spin-Orbit Coupling Induced Mott Insulator Sr 2 IrO 4 Materials Science : Structure 1.0 0.8 0.6 0.4 0.2 0.0 Intensity (arb. unit) 11.25 11.20 11.15 Photon Energy (keV) (1 0 22) Magnetic reflection (1 0 22) Magnetic reflection (1 0 22) Magnetic reflection 12.90 12.85 12.80 // // Sr 2 IrO 4 10 K L 2 (2 p 1/2 → 5 d ) L 3 (2 p 3/2 → 5 d ) Fig. 1. RXMS spectra of the magnetic reflection (1 0 22) at the L edge. 55 Fig. 3. Crystal and magnetic structures of Sr 2 IrO 4 . (a) Crystal structure of Sr 2 IrO 4 (space group I 4 1 /acd). The blue, red and purple spheres represent Ir, O and Sr, respectively. (b) Magnetic structure of Sr 2 IrO 4 in zero magnetic moment. Arrows represent J eff = 1/2 moments. (c) Scan profile along the (1 0 L ) direction at 10 K in zero magnetic field. (d) Scan profile along the (0 1 L ) direction at 10 K in zero magnetic field. (e) Scan profile along the (0 0 L ) direction at 10 K in zero magnetic field. References [1] G. Cao et al .: Phys. Rev. B 57 (1998) R11039. [2] B. J. Kim et al .: Phys. Rev. Lett. 101 (2008) 076402. [3] B. J. Kim, H. Ohsumi, T. Komesu, S. Sakai, T. Morita, H. Takagi and T. Arima: Science 323 (2009) 1329. Hiroyuki Ohsumi a, *, Taka-hisa Arima a,b and Hidenori Takagi c,d a SPring-8 / RIKEN b Institute of Multidisciplinary Research for Advanced Materials, Tohoku University c Department of Advanced Materials Science, The University of Tokyo d RIKEN Advanced Science Institute (Wako) *E-mail: ohsumi@spring8.or.jp 2 p 1/2 2 p 3/2 Spin-orbit integrated state ( J eff = 1/2) resonance only at L 3 1:1 intensity ratio at L 3 and L 2 Crystal field state valence (5 d t 2 g ) L 3 √ 1 3 √ 1 3 √ √ 2 3 – √ √ 2 3 √ √ 2 3 √ √ 2 3 √ 1 3 – √ 1 3 √ √ 2 3 √ √ 2 3 √ 1 3 √ 1 3 √ 1 3 √ √ 2 3 √ √ 2 3 – √ 1 3 + + + + + L 2 L 3 L 2 Fig. 2. 5 d level splitting diagram of (left) a tetragonal crystal field and (right) the spin-orbit coupling. Equal resonant intensities are expected at the L 2 and L 3 edges for the crystal field state. For the spin-orbit integrated state ( J eff =1/2), RXMS at the L 2 edge becomes forbidden. Wave functions of 5 d electrons are depicted with their orbital form and spin. Red and blue correspond to up and down spins, respectively. 19 18 17 16 L (r.l.u) Intensity (arb. units) 24 23 22 21 20 19 18 24 23 22 21 20 19 18 (0 1 L ), T=10 K (1 0 L ), T=10 K (c) (a) (b) (d) (0 0 L ), T=10 K (e) c o a 1 a 2
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