# Scaling of intrinsic domain wall magneto-resistance with confinement in electromigrated nanocontacts

## TL;DR

This study investigates how intrinsic domain wall magnetoresistance (DWMR) in permalloy nanocontacts varies with domain wall confinement, revealing a monotonic scaling law supported by experimental and quantum-mechanical simulations.

## Contribution

It demonstrates a quantitative scaling law for DWMR with domain wall width in nanocontacts, combining experimental measurements with ab-initio simulations.

## Key findings

- Intrinsic positive MR dominates over anisotropic MR.
- DWMR scales as 1/δ_DW^b with b≈2.31.
- Experimental results are supported by quantum-mechanical simulations.

## Abstract

In this work we study the evolution of intrinsic domain wall magnetoresistance (DWMR) with domain wall confinement. Clean permalloy notched half-ring nanocontacts are fabricated using a special ultra-high 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 domain wall width 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/$\delta_{DW}^b$, with $b=2.31\pm 0.39 $. The experimental result is supported by quantum-mechanical transport simulations based on ab-initio density functional theory calculations.