A Numerical Method to Determine Demagnetization Factors of Stadium-Shaped Nanoislands for Artificial Spin Ices

The shape of nanoislands gives rise to a demagnetizing field that is primarily responsible for the orientation of the magnetization along an axis. In the context of magnetization dynamics, the demagnetization field also determines the resonant frequencies captured by Kittel's equations. Analytically, we require demagnetization (demag) factors that can be obtained exactly for a few geometries, including ellipsoids and prisms. However, analytical expressions are not available for other shapes, limiting the use of Kittel equation as a predictive model. Here, we present a method to obtain the demag factors from micromagnetic simulations with good accuracy. Similar to experiments, we obtain ferromagnetic resonance but we use orthogonal field conditions to fit Kittel equation unambiguously and obtain the demag factors with good accuracy. This method will be useful to determine demag factors under the ellipsoidal approximation for stadium-shaped nanoislands used in artificial spin ices (ASIs) and thus lead to better prediction in their ferromagnetic resonance and band structures.