On the generality of the LLG equation to the optical limit: An optically-induced helicity dependent torque emerging from the LLG equation

It is well known that the Gilbert relaxation time of a magnetic moment scales inversely with the magnitude of the externally applied field, H, and the Gilbert damping, α. Therefore, in ultrashort optical pulses, where H can temporarily be large, the Gilbert relaxation time can momentarily be extremely short, reaching even picosecond timescales. Here we show that for typical ultrashort pulses, the magnetization can respond within the optical cycle such that the optical control of the magnetization emerges by merely considering the optical magnetic field in the Landau-Lifshitz-Gilbert (LLG) equation. Interestingly, when circularly polarized optical pulses are introduced to the LLG equation, an optically induced helicity-dependent torque results. We find that the strength of the interaction is determined by N = ayH/F_"#, where fc_!"# and yare the optical frequency and gyromagnetic ratio. Our results illustrate the generality of the LLG equation to the optical limit and the pivotal role of the Gilbert damping in the general interaction between optical magnetic fields and spins in solids.