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

Abstract

We use time-resolved measurement and modeling to study the spin-torque induced motion of a domain wall in perpendicular anisotropy magnets. We show that the most important factor governing domain wall dynamics is the energy difference between a wall at the center of the disk with either a Bloch-type configuration or the N\'eel-type configuration; this energy difference strongly depends on the disk diameter. When between 70 and 100 nm, the wall drifts across the disk 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 disk 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 $\ensuremath{\phi}$ 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 $\ensuremath{\phi}$. The stochasticity of the wall dynamics can be understood from the concept of the retention pond: a region in the $q\text{\ensuremath{-}}\ensuremath{\phi}$ space in which walls are transiently bound to the disk center. Walls having trajectories close to the pond must circumvent it and therefore have longer propagation times. The retention pond disappears for a disk 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.