Rocket-like dynamics of ferrimagnetic domain walls in graded materials

Abstract

Domain wall motion underpins emerging spintronic technologies, such as high-speed racetrack devices and THz logic. Spatially non-uniform magnetic exchange and anisotropy in ferromagnets can pin or accelerate domain walls. In ferrimagnets, where Walker breakdown is suppressed, walls can approach the magnon speed. Here, we show that in non-uniform ferrimagnets such gradients not only exert a net force on the wall, but also modify its effective mass, enabling an entirely new acceleration mechanism. As a wall traverses regions of varying exchange or anisotropy, it can shed or gain mass leading to a "rocket effect" as in variable-mass systems. This phenomenon becomes increasingly pronounced as the wall approaches the magnon velocity, providing a natural route to ultrafast domain wall propulsion. The findings establish variable-mass domain walls as a new paradigm for efficient, high-velocity spintronics and THz-frequency magnetic technologies.

Figures (4)

• Figure 1: (a) The antiferromagnetic mass $m_{\mathrm{af}}$ originates from the net magnetic moment associated with spin canting between the sublattices, which generates a torque on the spins and is conjugate to the translational coordinate $q$ of the domain wall. (b) The ferromagnetic mass $m_{\mathrm{f}}$ arises from the net magnetic moment due to uncompensated sublattices. This degree of freedom vanishes in the fully compensated limit.
• Figure 2: Schematic representation of a magnetic racetrack featuring a segment with spatially varying parameters. The color gradient from blue to red denotes a gradual decrease of the magnetic anisotropy $K$ (or increase of the exchange stiffness $A$) along the racetrack. A Néel-type domain wall separates a down-magnetized domain from an up-magnetized one.
• Figure 3: Rocket-like acceleration of a domain wall in a ferrimagnetic racetrack, where: (a) the anisotropy changes from $14\cdot 10^3\,\mathrm{J/m^3}$ to $5\cdot 10^3\,\mathrm{J/m^3}$ in $200 \, \mathrm{nm}$; (b) the antiferromagnetic exchange interaction varies from $1\,\mathrm{pJ/m}$ to $4\,\mathrm{pJ/m}$ in $200$ nm. The domain wall velocity is plotted as a function of its position along the racetrack. The numerical simulation (dotted black line) is compared with the full analytical model of Eq. \ref{['finalEq1']} (red line), the same model neglecting the rocket effect (blue line), and considering only Zeeman field (black line). The dashed black lines indicate the magnon velocity. The initial velocity is acquired over the first (a) $1.15~\mu\mathrm{m}$ with a Zeeman field of 100 mT, and (b) $0.5~\mu\mathrm{m}$ with a Zeeman field of 150 mT. The reduction of the antiferromagnetic mass provides an additional “boost”, allowing the domain wall to approach the magnon velocity. The rocket effect is more pronounced in (b) than in (a), because $m_{\mathrm{af}} \propto K^{1/2}A^{-3/2}$. The parameters of the simulation are reported in Table \ref{['param1']}.
• Figure S1: (a) Reference system; (b) Schematic representation of a magnetic domain wall. $\Delta$ is the domain wall width, $\Gamma$ is the tilting angle of the domain wall neglected by our analytical model, $q$ is the center of the domain wall diona2022.