Magnetism: Heisenberg spins

The pure RKKY interaction is isotropic, and the canonical spin glass systems are therefore often referred to as Heisenberg spin glasses. However, some anisotropy is also present in those systems originating from dipolar interaction and interaction of the Dzyaloshinsky-Moriya (DM) type [73]. The latter is due to spin-orbit scattering of the conduction electrons by non-magnetic impurities and reads... 

In present-day quantum chemistry the Heisenberg Spin Hamiltonian is widely applied for the description of magnetic coupling in transition-metal clusters and may read in the case of a many-electron system,... 

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). 

As illustrated above, the microscopic explanation of observed magnetic properties hinges on the construction of an appropriate model. In most instances, simplifications have to be weighed and phenomenological models can be employed, such as the Heisenberg spin Hamiltonian. 

Here 0, is the isospin describing the C, orbital, Iy is the orbital exchange constant, and Jq is the Heisenberg spin-exchange constant. This Hamiltonian can describe many of the magnetic properties of TDAE-C60. 

An even more quantitative application of VB theory can be developed from the realization that the nearest-neighbor VB model as developed, for example, by Pauling [10], can be mapped exactly onto a Heisenberg spin Hamiltonian [17]. The Heisenberg spin Hamiltonian has long been used to study the interaction between magnetic atoms in transition metal compounds and other paramagnetic substances [18], and can be written most simply as... 

The magnetic properties of M2VF5 phases (M = K, Rb, Cs) have been studied by Padalko et al.197). The intrachain exchange constants have been calculated by means of the Bonner and Fisher method applied to 1-D Heisenberg spin lattices (Table 10) using the formula ... 

Although the spin state of atom (or a group of atoms) A within a molecule is not observable, local spins are employed for the description of spin-spin interactions between magnetic centers, similar to the metal centers of transition-metal clusters, in terms of a Heisenberg spin-coupling model and led to considerable interest in the development of partitioning schemes of the total spin expectation value during the past decade [20, 112-128]. 

Magnetic exchange phenomena have been reported for two amide complexes of UCI4, i.e. UCU-SDMBA and UCU-SMAA (DMBA = N, N -dimethylbenz-amide MAA = JV-methylacetanilide) [62]. Unfortunately, the crystal structures of these compounds are not known. However, the authors assume dimeric structures for the compounds and interpret the measured susceptibilities in terms of the Heisenberg spin-spin interaction between two U ions ... 

In general, the magnetic energy levels of a magnetic system are described by employing a Heisenberg spin Hamiltonian Hspi defined in terms of several different spin exchange parameters. 

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