Numerical Modeling of Spin Waves in Magnetic Thin Films

Magnonics is a newly emerging area of magnetism, wherein new classes of devices can be foreseen. Here magnetic spin waves can be utilized to store, carry and process information. Due to particular properties of spin wave spectra, magnonic devices offer new functionalities that are currently unavailable in electronic devices. For example, magnonic devices are easily manipulated by the applied magnetic field. As an emerging area, it opens up a number of challenges and problems that need to be addressed, such as governing the propagation of spin waves using nano-patterned media. From a computation point of view, the governing dynamics can be modeled by extending the mathematical formalism of Landau- Lifshitz (LL) equation. This lead to the development of micromagnetic solvers for the modeling of magnetization dynamics and for the interpretation of the experimental results in complex magnetic structures. For this purpose we developed a micromagnetic solver in MATLAB for the solution of LL equation. For a micromagnetic solver the computation of the effective field and an efficient time-stepping scheme are of significant importance. For this purpose we have utilized the Fast Fourier Transforms (FFT) in our solver for the computation of the magnetostatic field that reduced the computational complexity of the system. A novel time stepping scheme is also proposed which exploited the properties of the mid-point rule and Runge-Kutta scheme. The proposed scheme preserves the magnetization dynamics and provides a larger time step with fewer computations of the effective field per time step. The solver was validated by simulating μ-mag standard problem 4 and the results were compared to the standard micromagnetic solver OOMMF, which were in close agreement.