Theoretic 3-D study of the high-frequency magnetic moment dynamics in thin ferromagnetic films with in-plane uniaxial anisotropy by considering eddy-current generation

摘要

In the present paper, theoretic investigations of polarisation vector precession trajectories represented by a macro spin in ferromagnetic films with in-plane uniaxial anisotropy were realised. For this purpose, the Landau-Lifschitz-Gilbert differential equation (LLG) in combination with the Maxwell equations were solved for three dimensions by considering a linear progression of the magnetisation or polarisation with an external field. The frequency and time dependent polarisation trajectories illustrate how a magnetic moment precesses if effective damping and eddy-currents impacts its motion. For computation, typical parameter values like the saturation polarisation J_S=μo.M_s= 1.4 T and in-plane uniaxial anisotropy μo.H_u=4.5mT were employed. The main focus of simulation was on the variation of the effective damping parameter α_(eff) between 0.01 and 0.05 and ferromagnetic film thickness t_m between 200 nm and 1200 nm. The frequency-dependent calculations were carried out between 50 MHz and 6 GHz. The time-dependent simulations were done for a duration between 5 and 30 ns.