Abstract

In materials with the gradient of magnetic anisotropy, spin-orbit-torque-induced magnetization behaviour has attracted attention because of its intriguing scientific principle and potential application. Most of the magnetization behaviours microscopically originate from magnetic domain wall motion, which can be precisely depicted using the standard cooperative coordinate method (CCM). However, the domain wall motion in materials with the gradient of magnetic anisotropy using the CCM remains lack of investigation. In this paper, by adopting CCM, we established a set of equations to quantitatively depict the spin-orbit-torque-induced motion of domain walls in a Ta/CoFe nanotrack with weak Dzyaloshinskii–Moriya interaction and magnetic anisotropy gradient. The equations were solved numerically, and the solutions are similar to those of a micromagnetic simulation. The results indicate that the enhanced anisotropy along the track acts as a barrier to inhibit the motion of the domain wall. In contrast, the domain wall can be pushed to move in a direction with reduced anisotropy, with the velocity being accelerated by more than twice compared with that for the constant anisotropy case. This substantial velocity manipulation by anisotropy engineering is important in designing novel magnetic information devices with high reading speeds.

Highlights

  • MethodsNumerical Calculation based on collective coordinate model

  • This result is consistent with the reported ones[3, 11, 13] and is justified, since spin-orbit torque (SOT) which drives the domain wall to move is proportional to J, and it contributes to the motion of domain wall given that the gradient of magnetic anisotropy does not exist

  • As to the track with magnetic anisotropy gradient, we found that when J is as small as ±5 × 1010 A/m2, the gradient of the anisotropy constant has little effect on the motion of the domain wall

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Summary

Methods

Numerical Calculation based on collective coordinate model. The polar angle θ and the azimuthal angle φ marked in Fig. 1 are included in the ansatz for the DW magnetization:. Represents the width of the domain wall and A, μ0, MS, and K are the exchange stiffness constant, vacuum permeability, saturation magnetization, and magnetic anisotropy constant for the PMA film, respectively. This linear function K(x) is the simplest form for numerical calculation. To determine the parameters a and b in the function K(x), one can pattern the sample into an array of Hall bar and fit the K-x relationship composed by the K data collected at different sites (x) using extraordinary Hall effect measurement[6]

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