Phase Field Simulation Of The Magnetic Domain Evolution In Ferromagnetic Nanostructures

Based on the time-dependent Ginzburg-Landau (TDGL) equation, a phase-field model was proposed to simulate the magnetic domain structure in ferromagnetic nanostructures and the magneto-mechanical behavior of ferromagnetic materials. The finite element formulation was derived from the weak form of governing equation and then solved through a program code. Differing from the application of periodic boundary condition adopted in general phase field simulation, the model in this paper doesn’t need this condition. So the model can be used to simulate3-D ferromagnetic nanostructures with limited size. Furthermore, due to the applicability of the finite element method for complex boundary, the model can be used for domain simulation in ferromagnetic nanostructures with different shapes. The vortex magnetization configuration is obtained in ferromagnetic nanostructures through the simulations, which is consistent with the experimental observations. The non-uniform stress and deformation of the structures caused by the non-uniform magnetization can be obtained simultaneously. The evolution process of the magnetization structure can be clearly showed in the simulation when the model is subjected to external magnetic field, stress or strain. The simulation results show that the magnetization configuration can be controlled effectively by changing the sample’s shape. The magnetic domain structure as well as its magnetic value can be changed by proper external stress and strain. The magnetization relaxation process can be controlled through adjusting the size of the structure, the number and size of the magnetic domain, and the external loading conditions.