The Deformed Image Vortex Ansatz: A Perturbation-Aware Description of Magnetic Vortices in In-Plane Fields

Abstract: Thiele-based descriptions of magnetic vortex dynamics in thin ferromagnetic nanodots rely on magnetization ansätze that describe the equilibrium texture but cannot represent perturbation-induced deformations. We introduce the Deformed Image Vortex Ansatz (DIVA): a perturbation-aware ansatz in which the response to an external perturbation is built into the magnetization profile itself, rather than appended to the dynamics as a correction. Here, we demonstrate the concept for a uniform, stationary in-plane field applied to a Permalloy nanodot, for which the deformation is analytically tractable. A symmetry-based perturbative expansion identifies the leading deformation as a single $m = 1$ harmonic around the disk, while energy minimization and a dominant-balance analysis yield a closed-form interpolant for the radial profile. Benchmarked against micromagnetic simulations on Permalloy disks of aspect ratio $t/R = 0.1$ and $0.0125$, this realization reduces the disk-averaged angular deviation by a factor of 3 to 6 relative to the two-vortex ansatz, depending on geometry and field, and reduces the total-energy deviation by about a factor of six in the thicker disk.