Observation of relativistic domain wall motion in amorphous ferrimagnets

TL;DR

The study shows that relativistic domain-wall motion, previously observed in crystalline ferrimagnets, can occur in easy-to-integrate amorphous RE-TM ferrimagnets. A relativistic sine-Gordon framework is developed with a maximum spin-wave group velocity $v_{g,max}$, and the domain-wall velocity $v_{DW}$ saturates toward this limit under damping-like SOT and in-plane fields, rather than diverging as in classical models. Experiments on amorphous GdFeCo near angular-momentum compensation yield $v_{g,max}$ values around $1.4$–$2.1$ km/s depending on composition, confirming relativistic dynamics in a technologically relevant material system. This work broadens the materials base for ultrafast spintronic devices and THz spin-wave sources by showing that amorphous ferrimagnets can reach the ultimate speed limit set by spin-wave propagation.

Abstract

Domain walls in ferrimagnets and antiferromagnets behave as relativistic sine-Gordon solitons with the spin-wave group velocity setting the ultimate velocity of domain walls and speed of magnetic devices. While this relativistic regime has been achieved in crystalline ferrimagnets, they cannot be routinely integrated in devices. To enable technological breakthroughs, relativistic dynamics must be demonstrated in easy-to-integrate ferrimagnets such as rare-earth -- transition-metal alloys. However, this scenario remains elusive due to the inherent magnetic disorder of these materials, complex spin-wave spectra, and challenges in modeling their ultrafast dynamics. Here, we demonstrate relativistic domain wall motion in amorphous ferrimagnetic GdFeCo devices operated in the proximity of the angular momentum compensation point. The current-induced domain wall velocity saturates within 10% of the spin-wave speed of 2 km/s, a behavior consistent with relativistic model of domain wall motion. Our observation of relativistic dynamics in technologically relevant ferrimagnets opens the way to magnetic devices operating at the ultimate speed limit.

Figures (3)

• Figure 1: (a) Classical (Equation \ref{['vsteadycomplete']}) and (b) relativistic (Equation \ref{['rel2']}) domain wall velocity as a function of the current density for different in-plane magnetic fields: $B_\mathrm{x}$ = 200 mT (continuous line), 150 mT (dashed line), 100 mT (dotted line). The relativistic model predicts a strong saturation close to the spin-wave group velocity (black dashed line). The parameters used for the calculation are taken from Table \ref{['paramextracted']}.
• Figure 2: (a) A sketch of a domain wall inside the dot driven by the electric current density $j$ and in-plane magnetic field $B_\mathrm{x}$. The upper and lower arrows indicate the spins $S_\mathrm{A, B}$ of the two sublattices A and B. (b) Electron microscopy image of the device and sketch of the experimental setup used to measure the domain wall motion across a GdFeCo dot. $j$ is the current density and $V = V_+ - V_-$ is the Hall voltage. (c) Exemplary switching trace of a 4 µ m-wide Gd$_{30}$Fe$_{63}$Co$_7$ dot, measured while injecting current pulses of amplitude $1.15\cdot 10^{12}~\mathrm{A/m^2}$ and duration 20 ns, in the presence of a magnetic field of $40~\mathrm{mT}$. $\mathrm{t}_0$ indicates the nucleation time of a seed domain, $\Delta \mathrm{t}$ is the transition time determined by the motion of the domain wall across the device, and $t'$ is the rest time until the end of the electric pulse. The switching trace is fitted to a Heaviside function that yields $t_0$ and $\Delta t$. (d) Transition time $\Delta t$, averaged over 250 independent acquisitions, at different external magnetic fields value, as a function of the current density.
• Figure 3: Domain wall speed as a function of the applied current density through the heavy metal layer for different in-plane magnetic fields in (a) 4 µ m-wide $\mathrm{Gd_{30}Fe_{63}Co_7}$ and (b) 3 µ m-wide $\mathrm{Gd_{31}Fe_{62}Co_{7}}$ dots. The lines are fits to Equation \ref{['rel2']}. The horizontal dashed lines define the spin-wave group velocity estimated from the fits. (c) Domain wall speed as a function of the in-plane magnetic field at several current densities in the same device as in (a). The error bars in (a) and (b) are evaluated as the standard error of the mean of 250 measurements.