List of Figures

• . Larmor precession with damping
• . Triangulation of a 2D domain
• . Nodal basis functions
• . Common support of two basis functions
• . In the fixpoint iteration method the magnetization vectors are rotated towards the effective field.
• . Magnetization configurations in the $\mu$mag standard problem #3
• . Energy of flower ($\times$) and vortex ($\circ$) state
• . Trajectory of the magnetization vector
• . Dependence of switching time on damping constant
• . Definition of angles in the Stoner-Wohlfarth model
• . Hysteresis curves of a spherical single domain particle for different angles between anisotropy axis and external field [53]
• . Energy landscape
• . Thermally perturbed precession
• . Distributions in thermal equilibrium
• . Average magnetization for Boltzmann distribution
• . Number of switching events as a function of $1/\chi$. The solid line is a fit of the classical Arrhenius formula.
• . Time step dependence of numerical integration schemes
• . Time step dependence at higher temperatures
• . Magnetization reversal of a cubic particle
• . Snapshots of a switching event
• . Dependence of the number of switching events on the simulation parameters
• . Dependence of the number of switching events on damping constant and temperature
• . Results of switching time measurements
• . Probability of not switching for different time step sizes
• . Magnetization reversal mechanisms in small spherical particles
• . Nucleation of a droplet of reversed magnetization
• . Dependence of the metastable lifetime on the external field
• . Coherent rotation of the magnetization at an external field of $-0.75$ T
• . Nucleation and expansion of a single droplet at an external field of $-0.83$ T
• . Multi-droplet nucleation at an external field of $-1.5$ T
• . Horizontal arrangement of two particles with a centre to centre distance of $1.2$ times the diameter
• . Probability of not switching for a single (1) and two interacting particles at a centre to centre distance of 4 (2f) and 1.2 (2c) times the diameter
• . Vertical arrangement of two particles with a centre to centre distance of $1.2$ times the diameter
• . Probability of not switching for a single (1) and two horizontally (2h) and vertically (2v) aligned particles with a centre to centre distance of 1.2 times the diameter
• . Probability of not switching for a single (1) and two vertically aligned interacting particles at a centre to centre distance of 1.2 (2vc) and 4 (2vf) times the diameter
• . Probability of not-switching of magnetization as a function of the time for a 20 nm single crystalline Co particle at $0.5$ K. The full lines are fits to the data with an exponential [61]
• . Function header with precompiler directive
• . Header file with precompiler directives
• . Flow chart of the finite difference program
• . Initialization file mag.par
• . Flow chart of the finite element package
• . Subroutine header of the stochastic time integration
• . Sequence of subroutine calls for time integration