Vanishing Gilbert damping limit problem of Landau–Lifshitz–Gilbert equation

Abstract

The vanishing Gilbert damping limit problem of the Landau–Lifshitz–Gilbert (LLG) equation has been an open problem for a long time, and even the explicit dynamic solution of LLG equation has not been seen so far. In this paper, a necessary and sufficient condition for a solution of Landau–Lifshitz (LL) equation to be generalized to a solution of LLG equation is given. Moreover, some explicit dynamic solutions of LLG equation are constructed. These solutions show that a solution of LLG equation with Gilbert damping does not necessarily tend to a solution of LL equation without Gilbert damping in the sense of maximum modulus.