Micromagnetic study of inertial spin waves in ferromagnetic nanodots

Here, we report the possibility to excite ultrashort spin waves in ferromagnetic thin films by using time -harmonic electromagnetic fields with terahertz frequency. Such ultrafast excitation requires to include inertial effects in the description of magnetization dynamics. In this respect, we consider the inertial Landau-Lifshitz-Gilbert equation and develop analytical theory for exchange-dominated inertial spin waves. The theory predicts a finite limit for inertial spin-wave propagation velocity, as well as spin-wave spatial decay and lifetime as functions of material parameters. Then, guided by the theory, we perform numerical micromagnetic simulations that demonstrate the excitation of ultrashort inertial spin waves (20-nm long) propagating at finite speed in a confined magnetic nanodot. The results are in agreement with the theory and provide the order of magnitude of quantities observable in realistic ultrafast dynamics experiments