Synchronization and Spatiotemporal Phases in Driven Precessing Domain Walls

The dynamics of extended magnetic domain walls driven by constant and alternating magnetic fields are studied using a collective coordinate $u$-$ϕ$ model. While purely constant-field driven systems exhibit deterministic spatiotemporal chaos and roughening, the alternating component can lock the precessional frequency via Shapiro-like steps. Using linear stability analysis and Floquet theory, the phase boundaries of stable, synchronized flat wall states are mapped. By studying the nonlinear dynamics of the extended system, a rich phase diagram is identified, composed of five dynamical regimes characterized by the combination of domain wall spatial order (flat, rough, or periodic) and domain wall precession temporal order (pinned, synchronized, or unsynchronized). Notably, the macroscopic temporal order of the synchronized phases can lead to a flat domain wall or to a periodic structure dominated by a narrow band of linearly unstable modes, both with coherent precession of the domain wall magnetization, while unsynchronized phases can be flat, with coherent precession, or rough with spatiotemporal chaos and incoherent precession.