Quantitative determination of domain wall coupling energetics

The magnetic dipolar coupling of head-to-head domain walls is studied in 350 nm wide NiFe and Co nanostructures by high resolution magnetic imaging. We map the stray field of a domain wall directly with sub-10-nm resolution using off-axis electron holography and find that the field intensity decreases as 1/r with distance. By using x-ray magnetic circular dichroism photoemission electron microscopy, we observe that the spin structures of interacting domain walls change from vortex to transverse walls, when the distance between the walls is reduced to below (77 +/- 5) nm for 27 nm thick NiFe and (224 +/- 65) nm for 30 nm thick Co elements. Using measured stray field values, the energy barrier height distribution for the nucleation of a vortex core is obtained.