Ordered states of Manganite and Dynamical mean-field theory

Pure LaMnO3 is an insulator. But, when doped with appropriate amount of doubly valenced impurities, it becomes a conductor retaining the ferromagnetism. Notion of double exchange has been devised to explain this phenomena. Along with this ferromagnetic conductivity, manganites show a variety of physical properties. Some of spin, charge, and orbital orderings are illustrated. Neutron scattering and electron diffraction is useful tool investigate the spin and charge ordered state of manganites. Also, resonance X-ray scattering can give a direct evidence of orbital orderings. Some aspect of Dynamical mean field theory is presented. In some sense, it has a analogue to classical mean-field theory. But it retinas the local fluctuation. This formalism is applied to the colossal magneto-resistance of manganite. Manganite Manganese compounds of AMnO3 (A = La,Ca,Ba,Sr,Pb,Nd,Pr) have a perovskite structure. Depending of composition of A ions, manganites show a variety of electrical and magnetic properties, including magnetic, charge, orbital orderings, and metal-insulator transition. If A is all trivalent ions such as La, all of manganese ions are Mn. If A is all divalent ions such Sr, all of manganese ions are Mn. If A is the composition of trivalent and divalent ions, both of Mn and Mn are present. Recently, it’s been shown that its electrical conductivity has a large dependence on the external magnetic fields. These are also know as colossal magneto-resistance(CMR). Double Exchange One of remarkable attempt to understand doped manganites is the Double exchange mechanism. Zener propose this exchange mechanism in 1951. This still remain the core understanding of manganese these days. We know that the electronic structures are mostly determined by the d-orbital of Mn. In the presence of the cubic crystal field, the degenerate d-orbitals split into t2 and e2g orbitals. And it is believed that the Hund’s exchange energy is large enough that all electrons in the e2g orbital are aligned and form a S = 3/2 states. e2g orbital is hybridized with oxygen 2p orbital. In doped manganites, Mn and Mn ions coexist and following two configurations are degenerate ψ1 : Mn3+O2−M4+ and ψ2 : Mn3+O2−M4+