Orbitally ordered state

In summary, our Raman study of the lightly doped manganites LaMn03+<5 reveals that the orbital ordered state in the AFI phase evolves into an orbital fluctuating state in the FM and even FI phase. 

Up to now, we have concentrated on the physics at zero kelvin. In this section, we extend the studies to finite temperatures and discuss finite temperature phase diagrams. The physics at finite temperatures is dominated by thermal fluctuations between low lying excited states of the system. These fluctuations can include spin fluctuations, fluctuations between different valence states, or fluctuations between different orbitally ordered states, if present. Such fluctuations can be addressed througih a so-called alloy analogy. If there is a timescale that is slow compared to the motion of the valence electrons, and on which the configurations persist between the system fluctuations, one can replace the temporal average over all fluctuations by an ensemble average over all possible (spatially... 

Fig URE 7.5 (a) Schematic orbital ordered state in ab plane in LaMn03. (b) Energy depend-... 

Figure 1- Representatiori of degenerate states from nonrelativistic components, (a) Degenerate zeroth-order states at (b) Spin-orbit interaction splits 11 state, (c) With full spin-orbit...

One-dimensional model Onsanger cavity field Onsanger equation Orbital polarization Ordered phase Ordered state... 

We first examine the relationships between electron structure and the emission and absorption spectroscopy of metal complexes. Transition metal complexes are characterized by partially filled d orbitals. To a large measure the ordering and occupancy of these orbitals determines emissive properties. Figure 4.2 shows an orbital and state diagram for a representative octahedral MX6 d6 metal complex where M is the metal and X is a ligand that coordinates or binds at one site. The octahedral crystal field of the ligands splits the initially degenerate five atomic d-orbitals by an amount... 

The value of P is important only with respect to technical considerations. The presence of finite orbital overlap between the initial and final states shghtly alters the p dependence of the relationship between Ft and A, The overlap corrections for the instanton analysis arise from the slightly different normalization of the symmetric and antisymmetric eigenstates, which can be obtained from the simple model in Fig. 2. The coefficients of the symmetric and antisymmetric eigenstates in terms of the zeroth order states, nominally + become instead... 

Iwasa Y, Takenobu T (2003) Superconductivity, Mott-Hubbard states, and molecular orbital order in intercalated fullerides. J Phys Condens Matter 15 R495-R519... 

Kadomtseva et al. (2000) measured thermal expansion and longitudinal and transverse magnetostriction in pulsed magnetic fields up to 25 T in Lai - Sr MnOj single crystals (x = 0.1,0.125 and 0.15). The results were ascribed to a suppression of the O phase and field-induced transitions to a new orbital-ordered ferromagnetic state. 

Figure 7 Energy orderings of the orbitals and states of some [CrX(NH3)5]2+ complexes (X is Cl, Br, NCS) (from ref. 35)...

The ground state of an atom is obtained by placing all available electrons in the orbitals in the order of increasing energy, following Hund s rule, when there are isoenergetic orbitals. An excited state is formed when one or several of these electrons are displaced to other orbitals. These states then correspond to one-electron or two-electron , etc., excitations, as illustrated in Figure 3.2. 

It is possible to assume that the absorption intensity originates mainly from the locally excited zero-order state since the AB+ zero-order state should barely contribute at all owing to the small overlap density of donor and acceptor orbitals. Therefore, the S, or T( should be reached at planar geometries by vertical excitation into the dominantly locally excited states. Only for the best donor-acceptor subunit combinations and high-lying locally excited states, a motion from planar minimum toward twisted minimum in S, or T, will be barrierless. Otherwise, a thermal activation is needed to overcome the barrier caused by crossings of zero-order states. 

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