Hamiltonian exchange interaction

The dipole and exchange interactions of an ion, i, with the neighboring magnetic ions, j, can be described by the Hamiltonians Hdd and Hex... 

Schematically, the double exchange interaction can be written in the form of a spin Hamiltonian operator (working on the system spin AB —for short, S) as...

The interaction Hamiltonian that appears in Equation (5.37) can involve different types of interactions namely, multipolar (electric and/or magnetic) interactions and/or a quantum mechanical exchange interaction. The dominant interaction is strongly dependent on the separation between the donor and acceptor ions and on the nature of their wavefunctions. 

In order to study the decoherence effect, we examined the time evolution of a single spin coupled by exchange interaction to an environment of interacting spin bath modeled by the XY-Hamiltonian. The Hamiltonian for such a system is given by [104]... 

In order to take into account these intra-atomic terms, and in a way similar to the Stoner s model, Hubbard ), see also adds to the Hamiltonian (11) an exchange interaction term ... 

Several exchange interactions are possible in a trinuclear cluster of paramagnetic centres. The general configuration of a trinuclear cluster is shown in structure (413). The spin Hamiltonian for this configuration is... 

When both 10ns of a Cr dimer are in the electronic ground state, the exchange interaction can be represented by the well-known Heisenberg Hamiltonian... 

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