An effect of the Gilbert damping constant on the skyrmion Hall effect

We investigate the skyrmion Hall effect using the Landau-Lifshitz-Gilbert (LLG) equation and the Thiele equation, respectively. Then, we find that these methods give different values for the ratio of in-plane skyrmion velocity components when the Gilbert damping constant is relatively small. Since the Thiele equation is derived from the LLG equation by assuming that the skyrmion structure does not change and behaves like a rigid body, the above result suggests that this assumption does not hold when the Gilbert damping constant is relatively small. Therefore, we conclude that the Thiele equation can not describe the systems precisely under the relatively small Gilbert damping constant due to the distortion of the skyrmion structure and that it is mandatory to solve the LLG equation numerically in order to investigate the skyrmion Hall effect accurately. This result is very important since the Gilbert damping constants of metal materials are generally very small.