Spin Inertia as a Driver of Chaotic and High-Speed Ferromagnetic Domain Walls

Abstract

Ferromagnetic domain walls -transitional regions between magnetic domains- are an essential ingredient for racetrack memory, a device concept that promises to deliver faster and more compact memory storage compared to other non-volatile memory devices. Motivated by recent experiments that have found inertial effects in spin dynamics, we explore its consequences on domain wall motion. We find that the inertial dynamics of the individual magnetic moments induce massive dynamics of the domain wall. We investigate these massive dynamics driven by a magnetic field, spin-transfer torque, and spin-orbit torque. We show that, in the absence of Gilbert damping, the domain wall dynamics become chaotic, resembling that of an electron in a two-dimensional crystal. For finite damping, field-like driving of the inertial domain wall significantly increases its velocity compared to conventional massless dynamics, potentially enabling faster racetrack operations. Additionally, in the limit of low driving, we observe that the domain wall width contracts due to the spin inertia of the ferromagnet.

Figures (7)

• Figure 1: The setup is given by a conducting ferromagnetic (FM) and heavy metal (HM) layer. The ferromagnet has a domain wall texture, which is driven by the spin transfer torque, spin orbit torque, and an external magnetic field $\vec{B}$.
• Figure 2: The Poincaré section shows 33 trajectories, each represented by a different colour. Every trajectory is generated by Eqs. (\ref{['eq:Ch1']}-\ref{['eq:Ch1']}) using different initial conditions with $H\approx 1$ (Eq. \ref{['eq:chaoticH']}). Each time the four-dimensional trajectory passes through a hyperplane defined by $\dot{\tilde{r}}=0$ and satisfies $\dot p_r<0$, the coordinates $(r,\phi_0)$ are recorded. We used the values $m=0.5$ and $\mu_r=2$ for the numerical evaluation. The dimensionless $m$ parameter corresponds to the following values: $\eta\approx1\space ps$ and $K_\perp\approx 6.6\cdot10^{-22}J=4.1\space\text{meV}$. The field-like driving $\mu_r$ is achieved by using an external magnetic field that is similar to the in-plane anisotropy. If we assume that $\gamma\approx2.8\cdot 10^{11}\space\text{Hz}\space T^{-1}$, then this would imply $B\approx0.3\space T$.
• Figure 3: The correspondence between the largest Lyapunov exponent (LLE) and the Poincaré section. Parameters are identical to those used in Fig. \ref{['fig:PoincareSection']}.
• Figure 4: The DW velocity in function of field-like driving, $\mu_r$, for different values of $m=\{0,0.5,1.0,1.5\}$. The gray dashed lines are the analytically derived limits.
• Figure 5: The trajectories on the potential landscape are given by the time evolution of the DW variables, $(\tilde{r},\phi_0)$, at $\mu_r=1.35$. The colors match the normalised inertial parameter $m$ of Fig. \ref{['fig:DWmass']}.