Micromagnetic simulations of three dimensional core-shell nanostructures

Abstract

In the last 20 years, computer simulations, based on the micromagnetic model, have become an important tool for the characterisation of ferromagnetic structures. This work mainly uses the finite-element (FE) based micromagneticsolver Nmag to analyse the magnetic properties of ferromagnetic shell structures of different shapes and with dimensions below one micrometre. As the magnetic properties of structures in this size regime depend crucially on their shape, they have a potential towards engineering by shape manipulation. The finite-element method (FEM) discretises the micromagnetic equations on an unstructured mesh and, thus, is suited to model structures of arbitrary shape. The standard way to compute the magnetostatic potential within FE based micromagnetics is to use the hybrid finite element method / boundary element method (FEM/BEM), which, however, becomes computationally expensive for structures with a large surface. This work increases the efficiency of the hybrid FEM/BEM by using a data-sparse matrix type (hierarchical matrices) in order to extend the range of structures accessible by micromagnetic simulations.It is shown that this approximation leads only to negligible errors. The performed micromagnetic simulations include the finding of (meta-)stable micromagnetic states and the analysis of the magnetic reversal behaviour along certain spatial directions at different structure sizes and shell thicknesses. In the case of pyramidal shell structures a phase diagram is delineated which specifies the micromagnetic ground state as a function of structure size and shell thickness. An additional study demonstrates that a simple micromagnetic model can be used to qualitatively understand the magnetic reversal of a triangular platelet-shaped core-shell structure, which exhibits specific magnetic properties, as its core material becomes superconducting below a certain critical field Hcrit