Spin-torque induced wall motion in perpendicularly magnetized discs: ballistic versus oscillatory behavior

TL;DR

This study investigates the complex spin-torque induced domain wall motion in perpendicular magnetic discs, revealing stochastic switching paths, oscillatory behaviors in the Walker regime, and a transition to ballistic motion below 40 nm diameter.

Contribution

It provides a detailed analysis of domain wall dynamics in nanodiscs, combining experimental measurements with a collective coordinate model to explain stochastic and ballistic behaviors.

Findings

Domain walls exhibit oscillatory and ballistic motion depending on disc size.

A collective coordinate model explains the energy exchange causing oscillations.

The transition from stochastic to ballistic motion occurs around 40 nm diameter.

Abstract

We use time-resolved measurement and modeling to study the spin-torque induced motion of a domain wall in perpendicular anisotropy magnets. In disc of diameters between 70 and 100 nm, the wall drifts across the disc with pronounced back-and-forth oscillations that arise because the wall moves in the Walker regime. Several switching paths occur stochastically and lead to distinct switching durations. The wall can cross the disc center either in a ballistic manner or with variably marked oscillations before and after the crossing. The crossing of the center can even occur multiple times if a vertical Bloch line nucleates within the wall. The wall motion is analyzed using a collective coordinate model parametrized by the wall position $q$ and the tilt $\phi$ of its in-plane magnetization projection. The dynamics results from the stretch field, which describes the affinity of the wall to reduce its length and the wall stiffness field describing the wall tendency to reduce dipolar energy by rotating its tilt. The wall oscillations result from the continuous exchange of energy between to the two degrees of freedom $q$ and $\phi$. The stochasticity of the wall dynamics can be understood from the concept of the retention pond: a region in the $q-\phi$ space in which walls are transiently bound to the disc center. Walls having trajectories close to the pond must circumvent it and therefore have longer propagation times. The retention pond disappears for a disc diameter of typically 40 nm: the wall then moves in a ballistic manner irrespective of the dynamics of its tilt. The propagation time is then robust against fluctuations hence reproducible.