Ferromagnetic Resonance by micromagnetic simulation in hollow pillars

Abstract

In this work, using computational simulation, unitary structures of nanopillars and nanopil- lar arrangements were analyzed. The study was carried out using The Object Oriented Micro- Magnetic Framework The Object Oriented MicroMagnetic Framework (OOMMF) simulator using Finite Difference Method (FDM) to simulate Ferromagnetic Resonance (FMR) in the studied systems. The square nickel nanopillars have lateral length D = 30 nm and height L = 120 nm. The size of the internal cavity in this system was also varied, with values of d = 0 nm (solid pillar), d = 10 nm and d = 20 nm. To study the column arrangements, they were arranged in a 3x3 matrix. In addition to inheriting the cavity variation characteristics, each column had an initial distance of a − D = 5 nm between its neighbors. This distance was changed to a− D = 10 nm, a− D = 20 nm and a− D = 50 nm to analyze the influence on the dipole interactions of this system. The Zeeman interaction was considered when an external magnetic field was placed on the surface. Due to the geometry of this system, the anisotropy field HA was studied for each nanopillar system. The theoretical model for ad- justing our parameters and analyzing the anisotropy field was the Kittel equations. Main and secondary peak frequencies were studied for unitary columns to obtain information about the anisotropy field of the sample. For the primary peaks, compared with works in the literature, it was noticed that the ferromagnetic resonance response came from the sides of the structure on the z-axis, in the secondary peaks, the values of HA for the perpendicular field have large divergences according to the model. It was also possible to observe that the adjustment for the anisotropy field improves the greater the value of d. Due to the analyzes made for unitary columns, the secondary peaks for column arrangements were not analyzed. For primary peaks with the applied perpendicular field, it was observed that the Kittel equation for FMR does not correctly adjust the values for HA. In the analysis of parallel fields, we tried to analyze the influence of neighboring columns on the value of HA. A model was used considering the system’s packaging factor. In this model, it was compared when considering the cavity in the center of the columns and assuming them to be solid columns. From the comparison with results in the literature, the packing factor that best described the system was the first, as more dipole effects are added to the system.