Diffusive and Fluidlike Motion of Homochiral Domain Walls in Easy-Plane Magnetic Strips

Propagation of easy-plane magnetic precession can enable more efficient spin transport than conventional spin waves. Such easy-plane spin transport is typically understood in terms of a hydrodynamic model, partially analogous to superfluids. Here, using micromagnetic simulations, we examine easy-plane spin transport in magnetic strips as the motion of a train of domain walls rather than as a hydrodynamic flow. We observe that the motion transitions from diffusive to fluidlike as the density of domain walls is increased. This transition is most evident in notched nanostrips, where the domain walls are pinned by the notch defect in the diffusive regime but propagate essentially unimpeded in the fluidlike regime. Our findings suggest that spin transport via easy-plane precession, robust against defects, is achievable in strips based on realistic metallic ferromagnets and hence amenable to practical device applications.

Figure 1

(a) Illustration of small angle precession constituting diffusive spin waves and associated exponential decay of spin flow. (b) Easy-plane precession constituting superfluidlike spin transport and associated linear decay of spin flow.

Figure 2

(a) Micromagnetic simulation setup of the synthetic antiferromagnet nanostrip. (b) The resulting torque generated by the out-of-plane spin-polarized electric current $J_c$, lifting the magnetization out of the plane in the injector region. (c) The out-of-plane component of the magnetization creates a demagnetizing field, generating a precessional torque that drives easy-plane precession.

Figure 3

Micromagnetic snapshots of an isolated DW, taken every 0.5 ns from the start of the simulation in the (a) perfect and (b) notched nanostrips. The associated DW velocity as a function of simulation time is shown for the (c) perfect and (d) notched nanostrips. The inset in (c) shows the DW velocity on a logarithmic scale.

Figure 4

Micromagnetic snapshots of a weakly interacting DW train in the (a) perfect nanostrip and (b) notched nanostrip. In the notched nanostrip, note the momentary pinning of the first DW and the subsequent pinning of the DW train. The average DW velocity as a function of simulation time for the (c) perfect nanostrip and (d) second DW in the train in the notched nanostrip. The inset in (c) shows the average DW velocity on a logarithmic scale.

Figure 5

Micromagnetic snapshots of a weakly interacting DW train in the (a) perfect nanostrip and (b) notched nanostrip with the DW interactions strong enough to overcome the pinning potential. The associated average DW velocity is shown for the (c) perfect and (d) notched nanostrips.

Figure 6

(a),(b) Micromagnetic snapshots of the densely packed DW train that resembles superfluidlike spin transport. (c),(d) The average DW velocity as a function of simulation time for the (c) perfect and (d) notched nanostrips. (e),(f) Time-averaged superfluid velocity and equivalent DW velocity, computed via Eq. (2), as a function of DW position for the (e) perfect and (f) notched nanostrips.

Figure 7

(a) Time-averaged superfluid velocity at $x=1500$ nm as a function of driving current density $J_c$ for the perfect (black squares) and notched (red circles) nanostrips. The error bars indicate the standard deviation. (b) Precessional frequency of the magnetization. (c) Equivalent DW velocity computed using Eq. (2) at $x=1500$ nm.

Figure 8

Micromagnetic snapshots of vortex formation in single layer (a) perfect and (b) notched nanostrips.

Figure 9

FMR resonance field as a function of microwave frequency. The solid line is a fit according to Eq. (B1).

Figure 10

FMR linewidth as a function of microwave frequency. The solid line is a fit according to Eq. (B2).