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To numerically calculate the domain wall equilibrium ground state energy per unit cross-sectional area following procedure was used. For a given wire width, a vortex domain wall was artificially introduced into a rectangular shaped element 10 nm thick and 6000 nm long and allowed to relax to its equilibrium configuration at zero applied field. A simulation was also performed with the wire at saturation, i.e., containing no domain wall. The energy of the domain wall was deduced by subtracting Etotal (wire containing domain wall) - Etotal (wire at saturation) to account for magnetostatic energy associated with the flat end shapes of the nanowire element. This value was then divided by the cross-sectional area to normalize all domain wall energies relative to one another.
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