Dynamics of Domain Walls in Magnetic Nanostrips

We express the dynamics of domain walls in ferromagnetic nanowires in terms of collective coordinates, generalizing Thiele’s steady-state results. For weak external perturbations the dynamics is dominated by a few soft modes. The general approach is illustrated on the example of a vortex wall relevant to recent experiments with flat nanowires. A two-mode approximation gives a quantitatively accurate description of both the steady viscous motion of the wall in weak magnetic fields and its oscillatory behavior in moderately high fields above the Walker breakdown.

Figure 1

Top: A model of the vortex domain wall proposed in Ref. 12. Dashed lines denote Néel walls emanating from the topological edge defects. Bottom: Absorption and reemission of the vortex at the edge. Note the reversal of the polarization $p$ of the vortex core.

Figure 2

The drift velocity $V_d$ of the domain wall as a function of the applied field $H$ for a permalloy strip of width $w=200\mathrm{nm}$ and thickness $t=20\mathrm{nm}$. Dashed vertical lines mark the critical fields $H_{c-}$ and $H_{c+}$. Symbols are results of numerical simulations with in-plane mesh sizes as shown.

Figure 3

Top: The transverse vortex coordinate $Y(t)$ for several values of the applied field $H$. Deviations from the expected behavior (10) in weak fields are due to stray field from the strip ends. Bottom: The width of the wall $\Delta (t)$. Curves for different fields are shifted vertically by 150 nm for clarity. The initial width in all cases was $\Delta (0)=190\mathrm{nm}$.