HD-07 Finite Element Method Modeling of Magnetoelastic Dynamics

This work explores the implementation of finite element method (FEM) modeling for fully coupled magnetoelastic formulation, incorporating the Landau-Lifshitz-Gilbert (LLG) and displacement wave elastic equations. Given the stiff nature of the elastic equations, partially integrated elements such as TET10, HEX8, and HEX20 are utilized. The Ritz method is employed for the variational formulation. The Newmark method is used for the time stepping of the elastic equations. Backward differentiation and midpoint rule are used for the time stepping of the LLG equation. The magnetization and displacements are updated via non-linear iterations to provide self-consistent magnetoelastic solutions. The magnetoelastic equations encompass both direct and reverse magnetostriction effects, enabling the simulation of the magnetization dynamics, such as skyrmions and spin-transfer torque (STT) oscillators, where strain fields drive their behavior. Furthermore, we demonstrate that strain-dependent Dzyaloshinskii-Moriya interaction can amplify the nonlinear breathing modes of skyrmions. Figure 1 shows spatial distribution of 1D magnetoelastic waves in thin ferromagnetic film.References: [1] R. Ludwig and W. Lord, "A finite-element formulation for the study of ultrasonic NDT systems," in IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 35, no. 6, pp. 809-820, 1988. [2] E. Savostin and V. Lomakin, "Giant phonon-skyrmion coupling in ferromagnet/heavy metal heterostructures", PRB, 2024.