Exponential Temperature Effects on Skyrmion-Skyrmion Interaction

Abstract

Understanding the dynamic behaviors of magnetic skyrmions has great potential in the application of spintronics. This is especially the case for the interaction between two skyrmions. In the literature, the attractive and repulsive skyrmion-skyrmion interactions are demonstrated as strongly related to the distance of two skyrmions and external magnetic fields. However, as a natural property, the temperature effect on skyrmion-skyrmion interactions is unclear, which lacks understanding from thermodynamics, and accordingly its driving force equation is absent. Here, we employ a temperature-related phase-field simulation and demonstrate that the skyrmion-skyrmion interaction is dramatically changed by temperature (e.g., a temperature change of only a few kelvins results in an eightfold higher interaction), which can lead to critical temperature behavior of skyrmion phase. Detailed analysis shows the interaction potential decreases exponentially with an increase of temperature, and this pronounced temperature dependence originates from the temperature-related skyrmion structure. Then, an equation is proposed to describe the skyrmion interaction at finite temperatures. Therefore, this study provides a deeper understanding of the skyrmion kinetic behavior and explores the temperature control of skyrmion interactions coupled with other sources of interaction, which is a guidance for future study of skyrmions and their applications.