Sub-nanosecond Electromagnetic-microma- Gnetic Dynamic Simulations Using the Finite- Difference Time-domain Method

This paper presents an efficient and simple approach of implementing the Landau-Lifshitz-Gilbert (LLG) equation of magnetisation motion within the Finite-difference Time-domain (FDTD) method. This combined electromagnetic-micromagnetic simulation technique is particularly important for modeling electromagnetic interaction with lossy magnetic material in the presence of current and magnetic sources, particularly at very high frequencies. The efficient implementation involves simple two-point spatial interpolations that are applicable to two and three-dimensional FDTD grids, and uses a stable iterative algorithm for the time integration of the LLG equation. A ferromagnetic resonance numerical experiment on a rectangular Permalloy prism excited through its cross-section by a non-uniform pulse field from a transmission line was carried out for the purpose of verifying the combined FDTD-LLG computations. The numerical results were in good agreement with linearised analytical solutions of the LLG equation for uniform and non-uniform precession modes. This paper also presents a brief investigation on the use of non-staggered FDTD grid schemes to model magnetic material using the LLG equation, and indicates that the classical FDTD staggered scheme offers simplicity in implementation and more accuracy for modeling wave interaction with lossy magnetic material than the non-staggered schemes based on Maxwell’s equations formulation.