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These simplifications are made, since we are interested in the magnon modes which cause the instabilities, and anisotropy or a larger number of layers, will only cause the appearance of an out-of-plane magnetization at the vortex core.
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0023669950
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In this paper, it was shown that the effect of multipolar terms is present only for nearest neighbor blocks, and is 17 % of the dipolar interaction. For further neighbors, its effect can safely be neglected.
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Schabes M.E., and Aharoni A. IEEE Trans. Magn. 23 (1987) 3882 In this paper, it was shown that the effect of multipolar terms is present only for nearest neighbor blocks, and is 17 % of the dipolar interaction. For further neighbors, its effect can safely be neglected.
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We would like to thank the referee for pointing out the sqrt(N) Log N dependence of the magnetostatic energy in the case of uniformly magnetized dots.
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The first-order phase transition is defined strictly for an infinite system. Here, because of the presence of a potential barrier and thus a hysteresis, we have referred to the vortex-HSDF transition as a "first-order" one.
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The frequency is not strictly zero as there is a very small in-plane anisotropy due to dipole interaction which couples spin to space and breaks spin rotational invariance.
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