Orbital ordering inLa0.5Sr1.5MnO4studied by model Hartree-Fock calculation

Abstract

We have investigated orbital ordering in the half-doped manganite La0.5Sr1.5MnO4, which displays spin, charge and orbital ordering, by means of unrestricted Hartree-Fock calculations on the multiband p-d model. From recent experiment, it has become clear that La0.5Sr1.5MnO4 exhibits a crosstype (z 2 − x 2 /y 2 − z 2 ) orbital ordering rather than the widely believed rod-type (3x 2 − r 2 /3y 2 − r 2 ) orbital ordering. The calculation reveals that cross-type (z 2 − x 2 /y 2 − z 2 ) orbital ordering results from an effect of in-plane distortion as well as from the relatively long out-of-plane Mn-O distance. For the "Mn 4+ " site, it is shown that the elongation along the c-axis of the MnO6 octahedra leads to an anisotropic charge distribution rather than the isotropic one.PACS numbers: 71.30.+h, 71.27.+a, 71.20.Ps Perovskite-type transition-metal oxides have attracted much attention due to their wide variety of magnetic, electrical and structural properties. In particular, manganites are extensively studied because of their rich physical properties such as colossal magnetoresistance (CMR) and spin, charge and orbital ordering [1]. Historically, their electronic states have been understood in terms of a double-exchange (DE) mechanism with localized t 2g electrons and itinerant e g electrons [2,3]. Also, it has been recognized that the e g orbitals are strongly hybridized with the oxygen p orbitals, and participate in the cooperative Jahn-Teller (JT) distortion of the MnO 6 octahedra [4,5]. The degeneracy of the e g level is lifted by the JT distortion and the resulting orbital polarization at the Mn 3+ sites can be accompanied by certain types of antiferromagnetic (AFM) spin ordering. Half-doped manganites such as La 0.5 Ca 0.5 MnO 3 and La 0.5 Sr 1.5 MnO 4 exhibit a so-called CE-type AFM ordering, as shown in Fig. 1. The magnetic moments of Mn on a zigzag chain are coupled ferromagnetically, whereas the neighboring chains are coupled antiferromagnetically. The charge and orbital ordering in the single-layered perovskite La 0.5 Sr 1.5 MnO 4 and three-dimensional perovskite Nd 0.5 Sr 0.5 MnO 3 were investigated using resonant x-ray diffraction and an alternating Mn 3+ /Mn 4+ pattern were observed directly [6,7]. Mizokawa and Fujimori [8] showed that JT distortion consistent with orbital ordering plays an important role in stabilizing the CE-type AFM state by means of unrestricted Hartree-Fock calculations. The orbital ordering of the e g electrons had been thought of as a rod-type (3x 2 −r 2 /3y 2 −r 2 ) orbital ordering, as shown in Fig. 1(a). More recently, however, from the studies of liner dichroism in the Mn 2p-edge x-ray absorption [9] and resonant soft x-ray scattering at the Mn 2p edge [10] of the La 0.5 Sr 1.5 MnO 4 , where T CO ≃ 217 K and T N ≃ 110 K [11], it was demonstrated that e g electrons exhibit predominantly cross-type (z 2 − x 2 /y 2 − z 2 ) orbital ordering as shown in Fig. 1(b).In order to understand the underlying mechanism of the cross-type orbital ordering, we have studied orbital orderin...

Doping dependence of spin and orbital correlations in layered manganites

“…the electron density at bridge sites increases) without greatly affecting the type of the OO (not shown). Here we would like to emphasize that our findings concerning the nature of spin and OO, as well as rather weak charge order, agree with the recent Hartree-Fock calculations on the multiband d-p model, 58 indicating that the local Coulomb interactions and superexchange suffice already to stabilize the CE phase. There is no doubt, however, that the oxygens distortions also contribute to the stability of this phase, 46,58 and would expand the regions of the CE phase in the phase diagrams shown in the next Section.…”

“…Here we would like to emphasize that our findings concerning the nature of spin and OO, as well as rather weak charge order, agree with the recent Hartree-Fock calculations on the multiband d-p model, 58 indicating that the local Coulomb interactions and superexchange suffice already to stabilize the CE phase. There is no doubt, however, that the oxygens distortions also contribute to the stability of this phase, 46,58 and would expand the regions of the CE phase in the phase diagrams shown in the next Section. At the same time realistic oxygens distortions would also modify somewhat the type of occupied orbitals, but the essential features of the orbital order in the CE phase, see Fig.…”

“…Therefore, the charge order with alternating Mn 3+ and Mn 4+ ions has been challenged, and intermediate valence picture with only small density variations has been suggested both in experimental 55 and in theoretical studies. 24,56,57,58 In this Section we would like to address as well the recent controversy concerning the type of the OO in the CE phase. We analyzed the orbital occupation in the 3x 2 − r 2 and 3y 2 − r 2 orbitals for various values of the crystal field splitting E z ≥ 0 (Fig.…”

Search for the Photo-Induced Hidden Phase in Inorganic and Organic Systems

“…A model calculation for a ground state shows a 0.3% increase in the ratio of d 3z 2 −r 2 /(d 3x 2 −r 2 or d 3y 2 −r 2 ) under 0.8 mJ/cm 2 excitation based on the observed structural changes [18,19]. Combining all the observations, Fig.…”

Orbital ordering in La0.5Sr1.5MnO4: Density functional and exact

“…4,5 The rod-type orbital order is in agreement with the x-ray scattering measurements as well as an earlier theoretical study, but is different from the cross-type order suggested in Refs. 8,9. Exact diagonalization and tight-binding model studies allowed us to examine the interplay between the various energy terms and revealed the reason for the particular orbital order.…”