VOLUME 80, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 2 MARCH 1998 Direct Observation of Charge and Orbital Ordering in La0.5Sr1.5MnO4 Y. Murakami,1 H. Kawada,1 H. Kawata,1 M. Tanaka,1 T. Arima,2 Y. Moritomo,3 and Y. Tokura4,5 1Photon Factory, Institute of Materials Structure Science, High Energy Accelerator Research Organization, Tsukuba 305-0801, Japan 2Institute of Materials Science, University of Tsukuba, Tsukuba 305-0006, Japan 3Center for Integrated Research in Science and Engineering (CIRSE), Nagoya University, Nagoya 464-0814, Japan 4Department of Applied Physics, University of Tokyo, Tokyo 113-0033, Japan 5Joint Research Center for Atom Technology (JRCAT), Tsukuba 305-0046, Japan (Received 16 September 1997) Charge ordering and orbital ordering in La0.5Sr1.5MnO4 have been investigated by using synchrotron x-ray diffraction. The alternating pattern of Mn31 Mn41 in real space is observed directly by making use of their anomalous dispersion. The first clear evidence of the orbital ordering of eg electrons on Mn31 is also presented based on the measurements of ATS (anisotropy of the tensor of susceptibility) reflection near the Mn K-absorption edge. The present observations indicate that the charge ordering and orbital ordering occur simultaneously at a transition temperature higher than that of the spin ordering. [S0031-9007(98)05409-X] PACS numbers: 71.45.Lr, 61.10.­i, 71.90.+q Recently, it has been recognized that the charge, spin, occur simultaneously, and then the spin ordering occurs and orbital degrees of freedom play important roles in at a lower temperature. the electric and magnetic properties of the transition-metal The synchrotron x-ray diffraction measurements were oxides. Especially, in perovskite-type manganites, the dis- performed at beam line-4C at the Photon Factory, KEK, covery of a wide variety of magnetic-field-induced phe- Tsukuba. The incident beam is monochromatized by a nomena, such as a colossal magnetoresistance [1] and a Si(111) double crystal and focused by a bent cylindrical magnetostructural transition [2], has stimulated much ac- mirror. X rays with an energy near the manganese K- tivity in this field. Meanwhile, in a system with a smaller absorption-edge EA were used, and the energy resolution one-electron bandwidth, a charge-ordering (CO) transition was about 2 eV. The energy was calibrated by using the has been observed, in which the doped carriers are ordered absorption edge of a manganese metal foil. Single crys- in real space [3]. A typical example is a layered-perovskite tals of La0.5Sr1.5MnO4 were grown by the floating-zone system La0.5Sr1.5MnO4 in which the average manganese method. The (110) plane was polished with diamond paste valence is Mn3.51. Moritomo et al. [4] and Bao et al. [5] to a flat surface. The sample size was approximately have studied the CO transition of this system by measure- 1.5 3 1.0 3 2.0 mm, and the FWHM mosaic was about ments of resistivity, magnetic susceptibility, and electron 0.5±. The crystal was mounted in a closed cycle 4He re- diffraction. Sternlieb et al. [6] have also presented clear frigerator on a six-axis diffractometer. nuclear and magnetic neutron diffraction spectra below the The proposed CO model by Sternlieb et al. is included CO temperature TCO 217 K and the Neel temperature in Fig. 1. The resulting CO unit cell has dimensions p p TN 110 K , respectively. However, it was difficult to 2 a 3 2 a 3 c relative to the room-temperature struc- directly observe an alternating Mn31 Mn41 pattern, be- ture with the crystal space group I4 mmm, and a cause superlattice peaks of CO in neutron and electron 3.86 Å, c 12.44 Å. We have directly confirmed this diffraction measurements include the intensity arising from Mn31 Mn41 pattern through the use of the anomalous the distortion of crystalline lattice, as a result of oxygen dispersion of Mn31 and Mn41, as follows. The atomic- displacement, etc. scattering factor near EA is generally represented by In this Letter we present the first direct evidence of an alternating Mn31 Mn41 pattern of La f E f0 1 f0 E 1 if00 E , (1) 0.5Sr1.5MnO4 by using the anomalous dispersion of the scattering factor depending on the x-ray energy E , where f0, f0, and f00 are for Mn31 and Mn41 in synchrotron x-ray diffraction the Thomson scattering factor and the real and imaginary measurements. Below the TCO there is one eg electron on parts of anomalous scattering factor, respectively. Since the Mn31 site and no eg electron on the Mn41 site. The EA of Mn41 will be slightly different from that of Mn31, eg electron on Mn31 has an orbital degree of freedom, that we can expect an anomaly of the peak intensity of the CO is, 3z2 2 r2 - and x2 2 y2 -type orbital. The orbital- superlattice near EA, which is attributed to the anomalous ordering (OO) configuration of the eg electrons on Mn31 scattering term. Such an anomaly of the superlattice peak is clearly demonstrated for the first time by making use 3 2, 3 2, 0 was observed near EA, as exemplified for the of the anisotropy of the tensor of susceptibility (ATS) case at T 29.6 K in Fig. 2. In order to analyze the en- reflection technique. It is found that the CO and OO ergy dependence in terms of the CO model, we obtained 1932 0031-9007 98 80(9) 1932(4)$15.00 © 1998 The American Physical Society VOLUME 80, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 2 MARCH 1998 tor F h 2, h 2, 0 at odd h, is given by F h 2, h 2, 0 ~ f031 2 f041 1 i f0031 2 f0041 1 C , (2) where C is independent of the energy, contributed by f31 0 2 f41 0 plus the term from the oxygen distortion which is due to the CO. The solid curve in Fig. 2 shows the calculated energy dependence for the 3 2, 3 2, 0 superlattice after absorption correction, which agrees with the experimental data very well. This is direct evidence that the alternating Mn31 Mn41 pattern is formed in the CO state at a sufficiently low temperature T 29.6 K ø TCO . Namely, this CO state is not a small modulation of the manganese valence, but represents an integer charge of valence from site to site. In order to probe the possible OO configuration of eg electrons on the Mn31 site, we adopt the model shown in Fig. 1. This assumption is based on the spin ordering FIG. 1. Schematic view of the charge, spin, and orbital ordering in a layered perovskite manganite, La configuration observed by neutron diffraction [6]; the spins 0.5Sr1.5MnO4. The stacking vector along the c axis is shown in the figure. should be parallel in the direction of extension of the orbitals as a result of the double-exchange mechanism [8]. p p The unit cell of this OO model is 2 a 3 2 2 a 3 c, the anomalous dispersion terms for Mn31 and Mn41, that as shown by thick solid lines in Fig. 1. We used the is, f031, f041, f0031, and f0041. The f0031 and f0041 could ATS reflection technique in order to observe such a OO. be directly obtained from the room-temperature absorp- ATS reflection means that "forbidden" reflections may, tion spectra of LaSrMnO4 Mn31 and La0.5Sr1.5MnO4 in fact, be observed due to the anisotropy of the x-ray Mn31 1 Mn41 , which is shown in Fig. 3. The en- susceptibility of atoms, that is, the atomic-scattering factor ergy difference between the EA's of Mn31 and Mn41 was f , which is attributed to the asphericity of the atomic about 4 eV. The f031 and f041 can be transformed by the electron density [9]. This anisotropy is so small in the Kramers-Kronig transformation of the f0031 and f0041, re- x-ray region that in conventional x-ray diffraction theories spectively, in which Cromer and Liberman's calculation f is treated as a scalar. Near E was applied to estimate the region outside the absorption A, however, the ATS measurements [7]. The f0 E obtained by this procedure is also shown in Fig. 3. Making use of these f0 E and f00 E , we can calculate the energy dependence of the structure factor of the CO superlattice. The structure fac- FIG. 2. Energy dependence of the charge-ordering superlat- tice reflection 3 2, 3 2, 0 near the manganese K-absorption edge at T 29.6 K. The solid curve is a calculated one based FIG. 3. Energy dependence of the anomalous scattering factor on f0 E and f00 E of Mn31 and Mn41. f0 and f00 of Mn31 and Mn41. 1933 VOLUME 80, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 2 MARCH 1998 reflections become measurable, since the effect of the muthal angle. The detailed procedure of the calculation is anisotropy is dramatically enhanced at resonance [10]. the same as described in Ref. [11]. The calculation indi- Since the f of Mn31 1 in Fig. 1 is not equivalent to that cates that the intensity has a 180± period in the azimuthal of Mn31 2 due to the anisotropy of the eg electron wave angle and that the polarization is rotated in the scattering function in the OO state, an ATS reflection is expected process (s0 ! p; see the inset of Fig. 5). In Fig. 5, we to occur. Figure 4 shows the energy dependence of the show the experimentally obtained azimuthal-angle depen- integrated intensity of the 3 4, 3 4, 0 reflection, which dence of the superlattice intensity of 5 4, 5 4, 0 reflection reflects a superlattice of OO. We successfully observed a normalized by the fundamental reflection 1, 1, 0 . The azi- striking enhancement of the reflection at E 6.552 keV. muthal angle w 0± corresponds to the configuration in It seems likely that this resonant diffraction results from which the sum of the wave vectors of the incident and dif- electric dipole transitions, because the resonant energy is fracted beams k0 1 k is parallel to the a axis. The solid about 5 eV higher than the EA of Mn31. The dipole curve was calculated by Eq. (4), which fit well the experi- transitions would correspond to the 1s core levels to the mental data with only a scaling factor for the intensity axis. 4p band, which is hybridized with the polarized 3d band. This is the first firm evidence of OO in this system. At In order to confirm that this reflection is indeed an ATS this stage, however, we could not uniquely determine the reflection arising from the OO, we measured the angular OO pattern because we can deduce the same calculated dependence around the scattering vector (azimuthal scan) results assuming the 3y2 2 r2 - and 3x2 2 r2 -type or- of this reflection. For a normal charge reflection, the bital instead of the y2 2 z2 - and z2 2 x2 -type orbital intensity is independent on the azimuthal angle, but an for Mn31 1 and Mn31 2 in Fig. 1, respectively. In order ATS reflection shows a characteristic oscillation. The to determine the orbital uniquely, we may need the careful atomic-scattering tensors of Mn31 1 and Mn31 2 take measurements of the other orbital superlattice. the following form, respectively, assuming the y2 2 z2 - Figure 6 shows the temperature dependence of the and z2 2 x2 -type orbital based on the xyz coordinates normalized intensity of superlattices 1 2, 1 2, 0 and shown in Fig. 1: 5 4, 5 4, 0 at E 6.552 keV, w 110±, which rep- 0 1 0 1 resent the order parameters of CO and OO, respectively. fk 0 0 f 0 0 Thus, the CO and OO occur concomitantly (and perhaps f B C B C 1 @ 0 f 0 A, f2 @ 0 fk 0 A . cooperatively) at a higher critical temperature T 0 0 f 0 0 f 210 K than that of spin ordering T 110 K [6]. (3) This result indicates that the spin ordering configura- tion is ruled by the OO configuration. Earlier electron Thus, the crystal-structure factor is also calculated as a diffraction studies by Moritomo et al. reported evidence tensor. Taking into account the transformation introduced of 1 4, 1 4, 0 and 3 4, 3 4, 0 structural scattering at by the azimuthal scan, we calculated the azimuthal angle T 110 K [4]. Bao et al. also observed these reflections dependence of the OO superlattice intensity; I u, w ~ fk 2 f 2 cos2 u sin2 w , (4) in the configuration shown in the inset of Fig. 5, where u is the Bragg angle of the OO superlattice and w the azi- FIG. 5. Azimuthal-angle dependence of the intensity of the OO superlattice reflection 5 4, 5 4, 0 normalized by the fundamental reflection 1, 1, 0 at E 6.552 keV, T 29.6 K. FIG. 4. Energy dependence of the orbital-ordering superlattice The solid curve is the calculated intensity of Eq. (4). Inset: reflection 3 4, 3 4, 0 near the manganese K-absorption edge Schematic view of the experimental configuration and definition at T 29.6 K. of the polarization directions. 1934 VOLUME 80, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 2 MARCH 1998 K. Chabara, T. Ohno, M. 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