Heisenberg-type interaction

Since the interatomic distances between two R atoms are always about 0.4 nm in the basal plane and about 0.6 nm along the c-axis, the assumption of the Heisenberg type interaction is not justified. The models involving indirect coupling are usually adopted to explain the stability of particular magnetic structures. 

There are further models which do not introduce new ideas but use the above frame for more complicated types of interactions. Bari and SivardiSre215) discussed a two sublattice model in analogy to the molecular field theory of antiferromagnetism. In this case there are two different interaction constants, viz. the intrasublattice and the intersublattice interaction. They also expand the one-sublattice model by an Heisenberg type magnetic interaction term between the HS states. Such an interaction may only become important for degenerate spin states. 

The interactions are of the ferromagnetic-Heisenberg type with 1% XY-square anisotropy arising from both anisotropic exchange and dipole-dipole interactions99. The xOz plane is the easy one and the spins are weakly bound in the Ox direction80,". ... 

We assume that the true electrostatic interactions that couple iron spins together can be replaced by an interaction of the Heisenberg type ... 

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 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). 

WIGNER FORCE. Short-range nuclear force of noncxchangc type postulated phenomenologically as pait of the interaction between nucleons. Postulated exchange forces are Bartlett, Heisenberg, and Majorana forces. 

It was pointed out in Chapter II that the Heisenberg exchange Hamiltonian of equation 90, which can be directly related to the Weiss field parameters at T = 0°K by equation 94, is an excellent formal expression for the interactions between atomic spins (or moments) of neighboring atoms. There remains the problem of establishing the various spin-dependent mechanisms that contribute to the Jij. In general, there are two types of interaction cation- -cation and cation-anion-cation (or even cation-anion-anion-cation) interactions. 

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