Type of domain wall as a function of in-plane field (scaled field h) and DMI (expressed by the scaled parameter δ), for increasing values of the domain wall magnetostatic energy (scaled parameter κ). For these drawings, a fixed direction in the plane is considered, so that negative fields are figured, and ϕ spreads over the [0, π] interval. The color code represents the cut angle ϕ, plotted over the extended range from 0 to π so as to differentiate the two chiralities of Néel walls. The constrained model predicts a switching at h = −δ, the φ isovalues being parallels to that line.

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... located at h = −δ (i.e. H = −H DMI ), because the domain wall magnetostatic energy is not negligible. Repeating this calculations for various values of κ, δ and h, phase diagrams can be constructed, as shown in Fig. 4. They illustrate that the switching of the domain wall from one polarity of Néel wall to the other takes place around h = −δ/ √ 1 + κ, with a mixed Bloch-Néel region that gets larger as κ increases. The above switching field relation can be obtained by equating σ + (Eq. 5a) to σ − (Eq. 5b) under the assumption that ϕ = 0 (i.e. Néel ...

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... these energy maps, maps of energy differences can be constructed, by comparing for the same angle the results for positive and negative fields. These are shown in Fig. 14, for the surface energy and for the surface tension. For Au/Co/Pt which has a positive DMI, and as up-down walls are considered, one expects that σ(H) < σ(−H) for positive fields. This is indeed obtained [ Fig. 14(a)]. However, and as remarked for the Figure 13. Computed domain wall surface energy σ (a) and tension γ (b) for the ...

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... differences can be constructed, by comparing for the same angle the results for positive and negative fields. These are shown in Fig. 14, for the surface energy and for the surface tension. For Au/Co/Pt which has a positive DMI, and as up-down walls are considered, one expects that σ(H) < σ(−H) for positive fields. This is indeed obtained [ Fig. 14(a)]. However, and as remarked for the Figure 13. Computed domain wall surface energy σ (a) and tension γ (b) for the Au/Co/Pt sample, by the small circle model incorporating the additional demagnetizing energy. Note that such noiseless maps, containing 360x200 pixels, would have required very long numerical micromagnetics calculation ...

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... domain wall anisotropy sample, the domain wall tension difference changes sign twice as field is increased [ Fig. 14(b)]. Therefore, if domain wall tension γ alone were determining the domain wall velocity, one would expect that the asymmetry of a circular-shape domain expanding in the presence of an in-plane field would reverse twice, giving a sign in accord with that of the energy difference only at intermediate fields. This directly relates to ...