Reversible and irreversible dynamical topological transitions of magnetic Hopfions

Abstract

Magnetic Hopfions are three-dimensional (3D) topological solitons characterized by a nonzero Hopf invariant and offer a promising platform for 3D spintronics. While their static stabilization has been widely studied, their nonlinear dynamics under alternating magnetic (AM) fields remain largely unexplored. We show, using 3D micromagnetic simulations and analytical mode analysis, that an AM field drives two qualitatively distinct dynamical regimes of a confined magnetic Hopfion. In the weak-field regime, resonant excitation of intrinsic Hopfion modes induces a nonlinear instability and an irreversible topological reconfiguration from a Hopfion to a toron. In contrast, in the strong-field regime, the system undergoes reversible field-locked topological switching at GHz frequencies, with the magnetization periodically alternating between a topologically trivial ferromagnetic configuration and a Hopfion state. The switching pathway is selected by the driving frequency: a 2 GHz field drives a breathing pathway associated with the low-frequency collective response, whereas a 40 GHz field produces a nonresonant rotational pathway governed by strong Zeeman-torque-driven precession and field locking. These results identify field amplitude and frequency as independent control knobs and reveal that reversible Hopfion switching can arise either from nonlinear continuation of low-frequency collective motion or from nonresonant high-frequency field locking.