Magnetic hopfions—three-dimensional topological solitons with knotted spin textures—have recently garnered attention in topological magnetism due to their unique knot topology characterized by the Hopf number $H$. In contrast with two-dimensional skyrmions, which are typically limited to small topological invariants, hopfions can, in principle, be stabilized with arbitrary $H$. However, the nonequilibrium dynamics, especially interconversion between different $H$ values, remain poorly understood. Here, we theoretically investigate the nonequilibrium dynamics of hopfions with various $H$ values by numerically solving the Landau-Lifshitz-Gilbert equation with spin-orbit torque (SOT). For $H=1$, we show that SOT induces both translational and precessional motion, with dynamics sensitive to the initial orientation. For $H=2$, we find that intermediate SOT strengths can forcibly split the hopfion into two $H=1$ hopfions. This behavior is explained by an effective tension picture, derived from the dynamics observed in the $H=1$ case. By comparing the splitting dynamics across different $H$ values, we identify a hierarchical structure governing SOT-driven behavior and use it to predict the dynamics of hopfions with general $H$. Furthermore, we show that, by appropriately scheduling the time dependence of the SOT, it is possible to repeatedly induce both splitting and recombination of hopfions. These results demonstrate the controllability of hopfion topology via SOT and suggest a pathway toward multilevel spintronic devices based on topology switching.

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• Magnetic texture
• Magnetism
• Magnetization dynamics
• Spin dynamics
• Spin state transition
• Spin texture
• Spin-orbit torque
• 3-dimensional systems
• Landau-Lifschitz-Gilbert equation