Scaling of intrinsic domain wall magnetoresistance with confinement in electromigrated nanocontacts

In this work we study the evolution of intrinsic domain wall magnetoresistance (dwmr) with domain wall confinement. notched half-ring nanocontacts are fabricated from permalloy using a special ultrahigh vacuum electromigration procedure to tailor the size of the wire in situ and through the resulting domain wall confinement, we tailor the domain wall width from a few tens of nm down to a few nm. through measurements of the dependence of the resistance with respect to the applied field direction, we extract the contribution of a single domain wall to the mr of the device, as a function of the width of the domain wall in the confining potential at the notch. in this size range, an intrinsic positive mr is found which dominates over anisotropic mr, as confirmed by comparison to micromagnetic simulations. moreover, the mr is found to scale monotonically with the size of the domain wall, delta(dw), as 1/delta(b)(dw), with b = 2.31 /- 0.39. the experimental result is supported by quantum-mechanical transport simulations based on ab initio density functional theory calculations