Physics-informed analytical modeling of dzyaloshinskii-moriya interaction gradient-driven magnetic skyrmion

The future of spintronic devices hinges on energy-efficient and reliable manipulation of magnetic skyrmions. Conventional current-driven schemes based on spin-transfer torque or spin-orbit torque are limited by Joule heating, electrical noise, and reduced device longevity. In contrast, microscopic electric field induced, strain-controlled gradient mechanisms offer a fundamentally low-power alternative by harnessing spatial variations in intrinsic material parameters. In this work, we propose a detailed physics-informed analytical modeling framework to describe and predict the dynamics of magnetic skyrmions under a Dzyaloshinskii-Moriya interaction (DMI) gradient. First, we derived closed-form expression of force, which is derived from gradient of the total energy of the magnetic skyrmion, that depends on skyrmion size, DMI gradient strength, and spatial variation. Using a simplified Thiele formalism which enables a quantitative relation between driving force and velocity, we derived the skyrmion velocities ( v _x and v _y) under DMI gradient. Our model demonstrates that a moderate DMI gradient (∼0.5 mJ/m²/μm) can propel skyrmions with longitudinal velocities exceeding ∼60 m/s with an induced force in the order of pico-Newton. Furthermore, we derive an analytical expression for magnetization variation arising from position dependent skyrmion size modulation under the DMI gradient, followed by the corresponding conductance variation along the nanotrack (∼0.75μS/nm). Beyond deepening the theoretical understanding of gradient-driven dynamics, this work establishes a predictive modeling tool for designing next-generation, current-free skyrmion-based devices. Such an approach paves the way toward ultra-low-power neuromorphic and in-material computing architectures, where engineered spatial gradients, rather than charge currents, act as the primary driving mechanism for skyrmion motion.