Spin spirals in fee Fe

Another spin spiral with q = [0,0, rx] with rx = 0.5 — 0.6 depending on volume, was found theoretically very early [138, 139, 140, 141, 142], but it was only recently that a spin spiral with a wave vector near the experimental value was found theoretically [143, 144], and then at much lower volumes. In all these calculations one has assumed bulk geometry, which seems reasonable since the number of Fe atoms is quite big 105 — 107. The other common approximation is the use of local or semi-local exchange-correlation functionals, and this might be one of the reasons for the failure of reproducing experimental results. 

In Fig. (7.8) are shown direct calculations of the planar spin spirals as a function of moment and of volume, the moment is seen to increase monotonically with the volume. One can see that the spin spiral qxw is stable for low volumes and moments, while the spin spiral qrx is stable at higher volumes and moments. Now, we calculate the spin spirals for fixed moments, both with the BGFM and with with the Heisenberg model with both FM and DLM interactions, just as described above for bcc Fe, fee Ni, and fee Co. We also calculate the spin spirals directly with the force theorem without the Heisenberg expansion by doing one calculation with the potentials from either the ferromagnetic or anti-ferromagnetic solution and the new spin spiral structure. The results can be seen in Fig.(7.9). 

If we assume that the force theorem is correct for this system, the other pos- 

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