Neel wall the direction of magnetization change in a domain wall goes from that of the Bloch

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Neel wall the direction of magnetization change in a domain wall goes from that of the Bloch wall to that of a Neel wall (Fig. 36) in thin films of material of negligible crystalline anisotropy energy, such as Permalloy. The intercept of the Bloch wall with the surface of the film creates a surface region of high demagnetization energy. The Neel wall avoids this intercept contribution, but at the expense of a demagnetization contribution throughout the volume of the wall. The Neel wall becomes energetically favorable when the film becomes sufficiently thin. Consider, however, the energetic of the Neel wall in bulk material or negligible crystalline anisotropy energy. There is now a demagnetization contribution to the wall energy density. By a qualitative argument similar to (56), show that ?0?=(?2JS2/Na2) + (2?M2sNa) find N for which ?w is a minimum. Estimate the order of magnitude of ?w for typical values of J, Ms. and a.

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