Dynamics of magnetic skyrmions under steady and time-varying deformation

Since 2009, magnetic skyrmions have been identified in diverse materials, attracting interest for their small size, intriguing emergent physics and new device concepts. Over the years, the interplay between deformation and dynamics has been an important topic of magnetic textures, with well-known phenomena like Döring mass, domain wall Walker breakdown and vortex oscillations. This topic is being extended to magnetic skyrmions and is critical for their practical applications. While topological invariance is preserved under continuous deformation, magnetic skyrmions display rich and complex deformation modes, including variations in size, shape, and helicity, which significantly impact their dynamics. These deformations challenge both theoretical and experimental efforts but offer opportunities for 'deformation engineering' strategies aimed at optimizing device performance and discovering new functionalities. In this review, we summarize the recent research progresses on magnetic skyrmion dynamics under steady and time-varying deformation. It begins with an introduction on the basic concepts of magnetic skyrmions and analytical descriptions of skyrmion deformation. Subsequently, theoretical and experimental methods for the study of magnetic skyrmion dynamics under deformation are introduced. The characteristics and influencing factors of various deformation modes (including steady and time-varying modes) of magnetic skyrmions are discussed. Finally, we discuss the device applications and open questions related to magnetic skyrmions beyond rigid particles.