Non-reciprocity and exchange-spring delay of domain-wall Walker breakdown in magnetic nanowires with azimuthal magnetization

Abstract

Domain wall (DW) motion is a crucial process involved in magnetization reversal, be it under magnetic field or spin-polarized current stimulus. In most cases DW speed does not exceed $\approx$100m/s and collapses above a given threshold of the stimulus, an effect known as Walker breakdown. A few specific material properties have been identified to delay the breakdown of speed by increasing the energy barrier preventing internal precession. We show that in a 3D nanomagnetic system, here with vortex-state domains, the topology of the magnetization distribution may intrinsically and robustly delay the Walker breakdown due to an exchange-spring effect. In addition, curvature induces a major non-reciprocal effect, delaying or not the Walker breakdown depending on the chirality of the azimuthal domain versus the direction of motion of the DW.

Figures (7)

• Figure 1: (a) Sketch of a wire with azimuthal magnetization (b,c) SEM images of a 200-diameter nanowire with Permalloy segments of average length 3.6, separated with 40-wide Fe_70Ni_30 chemical modulations: close-up and full view of an electrically-contacted nanowire. (d) Transmission and XMCD-TXM views of such NWs, with two consecutive chemical modulations highlighted with black triangular marks. [Source of data : ALBA Nov2023 R10 $144_\mathrm{pos}$$-143_\mathrm{neg}$]
• Figure 2: (a) Transmission and XMCD image of the initial state. (b) Starting from the same initial state, each row is a static XMCD image taken after the application of a current pulse of $J = \qty{1.1E11}{\ampere\per\meter\squared}$, with duration indicated on the left-hand side. After each step the initial state is recovered by applying a pulse with opposite polarity. The position of the chemical modulations is highlighted with vertical dashed red lines (c) Length of the nucleated domain versus the length of the current pulse. The horizontal lines are error bars (see End matter).
• Figure 3: Schematics for DWs. (a) Néel DW parallel to the axis, (b) Bloch DW (c) Néel DW antiparallel to the axis (d) Unrolled surface map, and cross section with sketches for the direction of magnetization, of a simulated DW (feeLLGood). The color codes the radial and longitudinal components of magnetization, respectively. (e) Schematics for (d). (f) Example of an experimental (ptychography) and (g) simulated transmission XMCD contrast of a DW of type (d-e).
• Figure 4: Simulated DW motion. (a) Longitudinal position of DW versus time for $j=\qty{1E11}{\joule\per\meter\squared}$ and $\alpha=0.01$ (feeLLGood), with three regimes identified as I, II and III, and domains positive with respect to the DW propagation direction (inset). The graph displays the position of Min, average and Max of the radial component at the periphery for regime I, surface vortex (V)/antivortex (AV) along with their polarity in regime II, with addition Bloch points in regime III (b) DW displacement versus time for three values of damping and the two cases of circulation of domains on either side of the DW (MuMax) (c,d) Unrolled surface maps and cross sections for $j=\qty{1E11}{\joule\per\meter\squared}$ and $\alpha=0.01$, typical of regimes II and III from (a), at $\qty{1.841}{\nano\second}$ and $\qty{2.842}{\nano\second}$, respectively, while regime I is qualitatively described by the static distribution shown in \ref{['fig-azimuthal-domains-walls']}d with the same color scale (feeLLGood).
• Figure 5: (a,b) The top TXM images show initial states. The following images in each sequence are after applying current pulses to the initial state of (a) $\qty{1.04E11}{}$ and $\qty{1.1E11}{\ampere\per\meter\squared}$ and (b) $\qty{2.2E10}{}$ and $\qty{6.9E9}{\ampere\per\meter\squared}$, respectively. (c) Injected (blue) and transmitted (orange) pulse shape for a pulse with nominal voltage $\qty{1.2}{\volt}$. The green and purple dashed lines correspond to the minimum injected voltage of the incoming pulse required for DW nucleation and motion, respectively. (d) Upper (blue) and lower (red) bounds, and the effective experimental (black) length of the pulse measured after the sample, versus the nominal length, and their corresponding linear fits. [Source of data : Sample R10 measured in ALBA, Nov2023]