Relaxation fundamentally determines the operation speed and energy efficiency of spintronic and spinorbitronic devices. We develop a theory of the longitudinal contribution to the relaxation of domain walls in ferromagnetic films of any thickness with the Dzyaloshinskii-Moriya interaction, which allows quantitative comparison with experiments. We show that the longitudinal contribution increases with a decrease of the transversal relaxation (e.g., the Gilbert constant). We predict a substantial enhancement of the contribution of the longitudinal relaxation to the damping of magnetic solitons with a decrease of the film thickness. We demonstrate that for ultrathin ferromagnetic films, the contribution of the longitudinal relaxation to the damping of domain walls is comparable to or stronger than any other traditional transversal mechanisms, including spin pumping. Although in this work we focus on the analysis of longitudinal relaxation for domain walls, in ultrathin samples it should be taken into account also for other magnetic solitons including skyrmions. This work adds to the fundamental understanding of the design and optimization of spintronic and spinorbitronic devices based on moving solitons in ultrathin films.

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• Domain walls
• Dzyaloshinskii-Moriya interaction
• Magnetization dynamics
• Magnons
• Spintronics
• Ferromagnets
• Solitons
• Ultrathin films