The Unexpected Shape Effects on Magnetic Properties of Films of Nanometer Thickness and Micrometer Extension

Abstract

The analysis of ferromagnetic resonance (FMR) through micromagnetic simulations is a powerful tool used to gain insight into the effects of shape on magnetization dynamics. Mathematical models incorporated into simulation programs have greatly facilitated the understanding of resulting magnetic behaviors. The present study aimed to investigate the influence of shape on the magnetization dynamics of Permalloy discs and stadium-like geometries of finite dimensions. The finite element numerical method was used to perform simulations, employing the Nmag simulator. To simulate the FMR spectra, the ringdown method was utilized, a common technique in computational micromagnetism. Resonance modes were identified using Fourier transform analysis. The novelty of this work is to demonstrate that in a film with a thickness of 50 nm and lateral dimensions less than 1000 nm, it cannot be considered as an infinite film. The results of the calculations showed that, for an in-plane field in a Py disk with these dimensions, there are resonance fields affected when the geometry is slightly stretched. This phenomenon was observed applying a field parallel to the plane of a stadium-shaped geometry. The effects of shape anisotropy remain relevant even in a 50 nm film with lateral dimensions exceeding 1000 nm. The aim of the study is to review results that are normally used for work with thin films. Assuming infinite dimensions and disregarding shape effects always requires care, since depending on the study in question, artifacts due to the shape effect may arise and be interpreted incorrectly.