3D versus 2D domain wall interaction in ideal and rough nanowires

• Free transverse domain walls behave differently in cylindrical and planar nanowires.
• The shape anisotropy influences largely the 2D domain walls (DWs).
• Pinned at artificial constrictions, the 2D and 3D DWs behave similarly.
• The DW interaction is well described by the point charge model.
• Surface deformation leads to lower depinning fields and local resonances.

The interaction between transverse magnetic domain walls (TDWs) in planar (2D) and cylindrical (3D) nanowires is examined using micromagnetic simulations. We show that in perfect and surface deformed wires the free TDWs behave differently, as the 3D TDWs combine into metastable states with average lifetimes of 300 ns depending on roughness, while the 2D TDWs do not due to 2D shape anisotropy. When the 2D and 3D TDWs are pinned at artificial constrictions, they behave similarly as they interact mainly through the dipolar field. This magnetostatic interaction is well described by the point charge model with multipole expansion. In surface deformed wires with artificial constrictions, the interaction becomes more complex as the depinning field decreases and dynamical pinning can lead to local resonances. This can strongly influence the control of TDWs in DW-based devices.