Enhanced Longitudinal Relaxation of Magnetic Solitons in Ultrathin Films

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.