Heisenberg spin behavior

For organic spin systems, one frequently assumes applicability of Heisenberg spin behavior, in which all interactions can be reasonably modeled by pairwise exchange interactions. A typical Heisenberg spin Hamiltonian for exchange Jy between various spin sites i and j, with spin quantum numbers S, and Sj, is given in the following equation ... 

However, magnetic coupling behavior may be more complex to model than possible with a simple isotropic Heisenberg Spin Hamiltonian as defined in Eq. (79) and several recent studies set out to improve this description by modification of this Hamiltonian (86-89). 

In molecules, the interaction of surrogate spins localized at the atomic centers is calculated describing a picture of spin-spin interaction of atoms. This picture became prominent for the description of the magnetic behavior of transition-metal clusters, where the coupling type (parallel or antiparallel) of surrogate spins localized at the metal centers is of interest. Once such a description is available it is possible to analyze any wave function with respect to the coupling type between the metal centers. Then, local spin operators can be employed in the Heisenberg Spin Hamiltonian. An overview over wave-function analyses for open-shell molecules with respect to local spins can be found in Ref. (118). 

A few papers have dealt with the effects of Heisenberg electron spin exchange on low-field DNP behavior. Bates and Drozdoski s initial description of spin exchange effects on DNP was tested against data collected at 7 mT,31 and further work by Bates showed the changes in the DNP-detected ESR spectra at 5-9.5 mT as radical concentration was increased 92 Tregubenkov et al. presented the calculated effects of spin... 

In 2-D and 1-D systems even in non-uniaxial materials, the Neel model can still be used since the anisotropic field in the plane where the moments can rotate is small compared with the exchange field in the perpendicular direction. After first considering the particular case of CsNiF3, we will described several 2-D and 1-D Heisenberg fluorides showing spin-flop behavior. 

The origin of these interactions, called exchange, was first realized by Heisenberg and Dirac in 1926. The interpretation of the exchange effect as formally equivalent to the coupling between spins permits the use of a vector-coupling scheme to model the quantitative behavior of coupled spins with the... 

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