Orbital structure and magnetic ordering in layered manganites: Universal correlation and its mechanism

Since the discovery of the colossal magnetoresistance (CMR), studies of manganites with cubic perovskite structure have been renewed theoretically and experimentally. Competition and cooperation between spin, charge and orbital degrees of freedom as well as lattice cause the dramatic changes of transport and magnetic properties. Manganites with bilayered structure A2−2xB1+2xMn2O7, where A and B are trivalent and divalent cations, respectively, are another class of CMR materials [1,2]. Since an extremely large MR is observed near the transition from paramagnetic (PM) insulator to ferromagnetic (FM) metal, it has been considered that several concepts proposed in the cubic compounds are applicable to the bilayered ones. In cubic manganites, one of the key factors dominating the magnetic orderings is the tolerance factor [3]; a bending of a Mn-O-Mn bond decreases the hopping integral of carriers. As a result, the ferromagnetic transition temperature Tc decreases in the double exchange (DE) scenario. However, in bilayered manganites, the Mn-O-Mn bond angle is almost unchanged with changing cations and carrier concentration, as shown later, in spite of a wide variety of the magnetic structures. Various key factors dominating the magnetic ordering, which are not included in the DE model, were experimentally suggested, e.g. the antiferromagnetic (AFM) superexchange (SE) interaction [4], the local lattice distortion [5–8], the charge and orbital degrees of freedom and their orderings [9,10] and so on. However, systematics in their correlations for a variety of compounds and their mechanisms still remain to be clarified. In this letter, we study the correlation between magnetic ordering and orbital structure in bilayered manganites. The two eg orbitals, i.e. the 3d3z2−r2 and 3dx2−y2 orbitals in a Mn 3+ ion split in the crystalline field of the bilayered structure and one of them is occupied by an electron. It is known that the occupied orbital controls the anisotropy of the magnetic interaction as well as its strength. The level separation between the orbitals is calculated in the ionic model for a large number of the compounds. We find a universal correlation between the relative stability of the orbitals and the magnetic transition temperatures as well as the magnetic structures. A mechanism of the correlation is investigated based on the theoretical model with the eg orbitals under strong