Spin-orbit coupling vibronic problem

In the following sections we will consider the interplay of the vibronic interaction, spin-orbital coupling and static trigonal held with regard to the problem of the magnetic properties of the low-symmetry d5-complexes. 

Inspecting Table 2 there is no doubt that electron-electron interactions and high-symmetry contribution of the ligand field have to be taken into account first. The problem arises when one wants to introduce vibronic interactions, which are often greater than or comparable with spin-orbit coupling or low-symmetry static fields. In such cases JT effect cannot be neglected, but has to be treated simultaneously with the other interactions. 

The OOA, also known as Kugel-Khomskii approach, is based on the partitioning of a coupled electron-phonon system into an electron spin-orbital system and crystal lattice vibrations. Correspondingly, Hilbert space of vibronic wave functions is partitioned into two subspaces, spin-orbital electron states and crystal-lattice phonon states. A similar partitioning procedure has been applied in many areas of atomic, molecular, and nuclear physics with widespread success. It s most important advantage is the limited (finite) manifold of orbital and spin electron states in which the effective Hamiltonian operates. For the complex problem of cooperative JT effect, this partitioning simplifies its solution a lot. 

The aim of this work is to elucidate these problems. To this end, we calculate the effective spin Hamiltonian of the 5f2—5f2 superexchange interaction between the neighboring U4+ ions in the cubic crystal lattice of UO2 and we calculate T5 <%> eg, rs f2g(l) ancl r5 f2g(2) linear vibronic coupling constants. These data are then used to draw a more definite conclusion about the driving force of the phase transition and especially about the actual mechanism of the spin and orbital ordering in U02. 

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