Nature of Orbital Ordering in La_0.5Sr_1.5MnO_4 is Studied by Soft X-ray Linear Dichroism

We have investigated orbital ordering in the half-doped manganite La$_{0.5}$Sr$_{1.5}$MnO$_4$, 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 La$_{0.5}$Sr$_{1.5}$MnO$_4$ exhibits a cross-type $(z^2-x^2/y^2-z^2)$ orbital ordering rather than the widely believed rod-type $(3x^2-r^2/3y^2-r^2)$ orbital ordering. The calculation reveals that cross-...

Resonant soft x-ray diffraction has been used to probe the temperature dependent orbital and magnetic structure of $\mathrm{LaSr_{2}Mn_{2}O_7}$. Previous crystallographic studies have shown that this material has almost no MnO$_{6}$ oxygen displacement due to Jahn-Teller distortions at low temperatures. Within the low-temperature A-type antiferromagnetic phase, we found strong intensity at the $({1/4},{1/4},0)$ orbital and $LaSr_{2}Mn_{2}O_7$ magnetic reflections. This shows ...

We have analyzed the experimental evidence of charge and orbital ordering in La0.5Sr1.5MnO4 using first principles band structure calculations. Our results suggest the presence of two types of Mn sites in the system. One of the Mn sites behaves like an Mn(3+) ion, favoring a Jahn-Teller distortion of the surrounding oxygen atoms, while the distortion around the other is not a simple breathing mode kind. Band structure effects are found to dominate the experimental spectrum fo...

We report resonant x-ray scattering data of the orbital and magnetic ordering at low temperatures at the Mn $L_{\rm 2,3}$ edges in \lsmo. The orderings display complex energy features close to the Mn absorption edges. Systematic modeling with atomic multiplet crystal field calculations was used to extract meaningful information regarding the interplay of spin, orbital and Jahn-Teller order. These calculations provide a good general agreement with the observed energy dependenc...

Using first principle band structure calculations, we critically examine results of resonant x-ray scattering experiments which is believed to directly probe charge and orbital ordering. Considering the specific case of La0.5Sr1.5MnO4, we show that this technique actually probes most directly and sensitively small structural distortions in the system. Such distortions, often difficult to detect with more conventional techniques, invariably accompany and usually cause the orbi...

We report the first direct resonant soft x-ray scattering observations of orbital ordering. We have studied the low temperature phase of La$_{0.5}$Sr$_{1.5}$MnO$_4$, a compound that displays charge and orbital ordering. Previous claims of orbital ordering in such materials have relied on observations at the Manganese $K$ edge. These claims have been questioned in several theoretical studies. Instead we have employed resonant soft x-ray scattering at the manganese $L_{III}$ an...

The standard way to find the orbital occupation of Jahn-Teller (JT) ions is to use structural data, with the assumption of a one-to-one correspondence between the orbital occupation and the associated JT distortion, e.g. in O6 octahedron. We show, however, that this approach in principle does not work for layered systems. Specifically, using the layered manganite La0.5Sr1.5MnO4 as an example, we found from our x-ray absorption measurements and theoretical calculations, that t...

Temperature dependences of a magnetic and an orbital Bragg reflection at the Mn L2 and L3 edges of La0.5Sr1.5MnO4 have been collected. The temperature evolution of the orbital reflection depend strongly on the x-ray energy and reflects the different order parameteres for orbitals and Jahn-Teller distortions. The gradual increase of the orbital order parameter indicates that the orbital order and not the Jahn-Teller distortion drives the metal-insulator transition. Correspondi...

We have explored spin, charge and orbitally ordered states in La1-xSrxMnO3 (0 < x < 1/2) using model Hartree-Fock calculations on d-p-type lattice models. At x=1/8, several charge and orbitally modulated states are found to be stable and almost degenerate in energy with a homogeneous ferromagnetic state. The present calculation indicates that a ferromagnetic state with a charge modulation along the c-axis which is consistent with the experiment by Yamada et al. might be respo...

We report on first principles Self-Interaction Corrected LSD (SIC-LSD) calculations of electronic structure of LaMnO$_{3}$ in the cubic phase. We found a strong tendency to localisation of the Mn $e_{g}$ electron and to orbital ordering. We found the ground state to be orbitally ordered with a staggered order of $x^{2}-z^{2}$ and $y^{2}-z^{2}$ orbits in one plane and this order is repeated along the third direction. The difference in energy with a solution consisting of the o...