Topology is a powerful tool for categorizing magnetization textures by defining a topological index in both two-dimensional (2D) systems, such as thin films or curved surfaces, and in 3D bulk systems. In the emerging field of 3D nanomagnetism, both volume and surface topological numbers must be considered, requiring the identification of a proper global topological invariant to support categorization.

Snapshots of magnetic textures on the unrolled surface of the cylindrical wire and XMCD image of the Bloch point domain wall.

Here we consider domain walls (DWs) in cylindrical nanowires as an excellent playground for 3D nanomagnetic systems, excited by a charge current, that generates an OErsted field. We first provide experimental evidence of previously unreported domain-wall transformations of topology occurring at the nanosecond timescale.

DWs in cylindrical nanowires made of magnetically soft materials represent a textbook case for investigating 3D nanomagnetism in finite-size systems. When nanowire diameter exceeds approximately seven times the dipolar exchange length (i.e., up to a few tens of nanometers), complex 3D magnetization textures may develop, involving 3D nanostructure features. The moderate dimensions of these structures allow for accurate micromagnetic simulations, and experiments are feasible using electrodeposition as a versatile growth method for high quality nanomaterials.

Two types of DWs topologies exist in such wires, both energetically metastable and with very similar energy: the Bloch-point wall and the transverse vortex wall. Experimental observations have demonstrated that these DWs can dynamically change topology under the application of a sufficiently large stimulus of charge current inducing an OErsted field.

We investigate these transformations with micromagnetic simulations, tracking both bulk and surface topological signatures. We demonstrate a topological invariant combining both signatures, while the topological charge varies from bulk to surface during the dynamics. The experimental change of topology is reproduced when the pulse duration matches the timescale of the internal transformations of the wall, and the current is switched off before the transformation is complete. We expect that the topological categorization and dynamical exploitation apply to any 3D nanomagnetic system.

Team: Spin textures and Theory & simulation

Collaboration: IMDEA (Madrid), ALBA (Barcelona), Max Planck Institute (Dresden)

Funding: ANRs MATEMAC-3D, DIWINA

Further reading: Topological analysis and experimental control of transformations of domain walls in magnetic cylindrical nanowire, L. Álvaro-Gómez, J. Hurst, S. Hegde, S. Ruiz-Gómez, E. Pereiro, L. Aballe, J. C Toussaint ,L. Pérez, A. Masseboeuf, C. Thirion, O. Fruchart, and D. Gusakova, Physical Review Research 7(2), 023092 (2025), Open access: hal-04558642v1

Contact: Daria Gusakova and Olivier Fruchart