Mechanical effect on skyrmion-skyrmion interaction

Understanding the dynamics of magnetic skyrmions is a prerequisite for their applications in advanced functional devices such as memory, logic, and computing devices. Especially, the skyrmion-skyrmion interaction is a key to comprehending diverse intrinsic skyrmion behaviors such as their ordering, melting, pinning, and moving. In literature, the skyrmions interactions are demonstrated to be affected by external fields like magnetic and temperature fields. However, as an important aspect, the mechanical effects on skyrmions interaction are still unclear due to the difficulty of studying complex magneto-elastic couplings. Here, we break the limitation by employing a phase-field simulation and demonstrate that strain-induced large skyrmion distortions drastically change the skyrmions interaction under applied mechanical loads. Then, an exponential equation is proposed to describe the skyrmions interaction under both positive and negative uniaxial strain loads with good accuracy. Therefore, we developed a phase-field simulation with high-order magneto-elastic coupling, provided an in-depth thermodynamic understanding of the mechanical effect of skyrmion dynamics, and proposed the according equation, which provided a new concept of mechanical-controlled magnetism and should be beneficial for further studies of skyrmion behaviors and advanced magnetic materials.