Engineering droplet soliton dynamics in a gradient magnetic structure

Abstract Magnetic droplet solitons—self-localised, strongly nonlinear spin-wave states—offer compact microwave sources in nanocontact (NC) spin–torque oscillators, yet their frequency agility and coherence remain sensitive to device geometry. Here we introduce a wedge-shaped (thickness-graded) free layer to engineer the internal demagnetising field and thereby control droplet nucleation, frequency and linewidth within a single device. Using micromagnetic simulations (MuMax3) of spin–valve with strong perpendicular anisotropy Co/Ni free layer, we place NC at systematically varied positions along the gradient and extract the formation of droplet as well as nucleation time and current and steady-state spectra. We find that thicker regions require higher current and exhibit wider hysteresis-like loops, while the nucleation frequency increases monotonically towards the thin side, accompanied by improved phase coherence. In dual-contact geometries, we map a thickness-gradient-dependent critical merging distance and its current scaling. These results establish thickness gradients as a practical, fabrication-compatible knob for tuning droplet dynamics and suggest gradient-engineered free layers for fast, coherent droplet-based microwave oscillators.