Orbital ordering in the layered manganites
The interaction between the long range correlations of electrons and the encompassing crystal structure is a key aspect of solid state physics. This thesis studies the long range interactions of the 3D orbitals in the single and bilayered manganites. Orbital ordering and the omnipresent Jahu-Teller distortions appear at low temperatures ill these samples, accompanied by a real-space charge order. The results display different aspects of these long range order phenomena ill Lao.5Sr1.5nO4, Nd1_xSr1+xMn04 where 0.66 >x >0.8, and La2_2x:Sr1+2xMn207where 0.5 > x > 0.7 using different techniques of x-ray diffraction. High energy x-ray diffraction is optimised to detect structural aspects ill materials, and as Audi is sensitive to the Jalm-Teller distortions. Resonant scattering at the Mil к edge is used to study both the structural and the more specific charge and orbital ordering. Finally, soft x-ray resonant diffraction at the Mn L edge is used as a specialised technique for looking at the magnetic and orbital ordering. A small crystal field distortion irt always observed to be present ill the orbitally ordered materials, however the size of the distortion is very large in the single layer Lao.5Sr1.5MnO4aud very small ill the bilayer LaSr2Mn207. Despite this, orbital ordering is observed in both materials. Combining experimental data with theoretical models, suggests that integer charge ordering occurs oil the MnO6 octahedra in both materials within the orbitally ordered regime.