Modeling of magnetoelastic nanostructures with a fully coupled mechanical-micromagnetic model

Micromagnetic simulations of magnetoelastic nanostructures traditionally rely on either the Stoner-Wohlfarth model or the Landau-Lifshitz-Gilbert (LLG) model, assuming uniform strain (and/or assuming uniform magnetization). While the uniform strain assumption is reasonable when modeling magnetoelastic thin films, this constant strain approach becomes increasingly inaccurate for smaller in-plane nanoscale structures. This paper presents analytical work intended to significantly improve the simulation of finite structures by fully coupling the LLG model with elastodynamics, i.e., the partial differential equations are intrinsically coupled. The coupled equations developed in this manuscript, along with the Stoner-Wohlfarth model and the LLG (constant strain) model are compared to experimental data on nickel nanostructures. The nickel nanostructures are 100 × 300 × 35 nm single domain elements that are fabricated on a Si/SiO2 substrate; these nanostructures are mechanically strained when they experience an applied magnetic field, which is used to generate M vs H curves. Results reveal that this paper's fully-coupled approach corresponds the best with the experimental data on coercive field changes. This more sophisticated modeling technique is critical for guiding the design process of future nanoscale strain-mediated multiferroic elements, such as those needed in memory systems.