Kinematic Model of Magnetic Domain Wall Motion for Fast, High-Accuracy Simulations

Abstract

Domain wall (DW) devices have garnered recent interest for diverse applications including memory, logic, and neuromorphic primitives; fast, accurate device models are therefore imperative for large-scale system design and verification. Extant DW motion models are sub-optimal for large-scale system design either over-consuming compute resources with physics-heavy equations or oversimplifying the physics, drastically reducing model accuracy. We propose a DW model inspired by the phenomenological similarities between motions of a DW and a classical object being acted on by forces like air resistance or static friction. Our proposed phenomenological model predicts DW motion within 1.2% on average compared with micromagnetic simulations that are 400 times slower. Additionally our model is seven times faster than extant collective coordinate models and 14 times more accurate than extant hyper-reduced models making it an essential tool for large-scale DW circuit design and simulation. The model is publicly posted along with scripts that automatically extract model parameters from user-provided simulation or experimental data to extend the model to alternative micromagnetic parameters.

Figures (4)

• Figure 1: (a) and (b) Free body diagram of DW motion for the proposed model alongside analogous classical system in which a box is pushed along a surface by a constant applied force through a viscous fluid. In this analogy, the current-induced force $F_J$ is represented by the applied classical force, the micromagnetic damping force is represented by the fluid drag, and the DW pinning force is represented by the static friction when the box is resting. (c) The component accelerations of Equation \ref{['eq:acc']} applied to the DW when a current pulse is applied and later removed. As the current density is sufficiently large, there is no pinning.
• Figure 2: (a) DW position in response to a current pulse, for both micromagnetic simulation and the kinematic model, with Aex = 11x$10^{-12}$ J/m, Ku = 4.05x$10^5$ J/m$^3$, $\alpha$ = 0.01, $M_{\text{sat}}$ = 7.95x$10^5$ A/m, and track width = 100 nm. (b) Median, lower quartile, and upper quartile of four different error metrics averaged across tested values of all parameters.
• Figure 3: (a) - (e) Median, lower quartile, and upper quartile of four different error metrics averaged across tested values of all parameters but one: $\alpha$ in (a), W in (b), Aex in (c), and Ku in (d) and (e). (f) Averaged percent error over the ten runs of various current density $J$ for each parameter corner simulated. In total this figure summarizes our model performance over 320 micromagnetic simulations.
• Figure 4: (a) Predictive nature of model for complex input sequences, with Aex = 11x$10^{-12}$, Ku = 4.05x$10^5$, $\alpha$ = 0.01, $M_{sat}$ = 7.95x$10^5$, and track width = 100x$10^{-9}$. (b) Model accuracy and speedup compared relative to previously published work. Python implementations of the linear model doi:10.1063/1.3536793, inertial model 9180675, kinematic model (this work), 1D CC model with and without variable wall width 9662302, and 1D CC model with fitting parameters 9072283 are compared. Speedup is normalized relative to the mumax3 simulations. Time to simulate a very-large-scale circuit is normalized to one hour.