A generalized Heisenberg approach to magnetism

One can also assume a disordered, DLM, medium as the reference state [134], and make the same expansions to get the exchange parameters, that now reads [105]  

A case where the FM-MFT should work very well, is for small 9 spin spirals, where in our calculations we have set 9 = 7r/10. This is also the fact, as shown in Fig.(7.4). 

The FM-MFT seems to give almost exact results for both fee Co and Ni, while it is a bit off for Fe near the H point, where effects of the RKKY interactions can be seen. These effects are of course absent from the DLM-MFT because of its short ranged interactions. The DLM-MFT overestimates the energy of the small 9 spin spirals rather much, except for fee Co, which again seems to be quite well described by both methods. 

One of the big problems of the classical Heisenberg Hamiltonian is the lack of possibility to account for longitudinal fluctuations of the moments. One way to take this into consideration is to introduce a moment size dependence of the exchange interactions and to introduce an on-site term, which couples the intrasite 

This should be an improvement to having only transverse effects. To find these on-site terms j(° it can be noticed that if one uses the DLM-MFT, the spin product vanishes, leading to  

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