Faculty of Engineering, Science and Mathematics

School of Engineering Sciences

A thesis submitted in partial satisfaction

of the requirements for the degree of

Doctor of Philosophy

Richard P. Boardman

Computational Engineering and Design Group

School of Engineering Sciences

University of Southampton

United Kingdom

Supervisors: Dr. Hans Fangohr, Prof. Simon J. Cox

17 May 2005

Computational Engineering and Design Group

School of Engineering Sciences

University of Southampton

United Kingdom

Supervisors: Dr. Hans Fangohr, Prof. Simon J. Cox

17 May 2005

UNIVERSITY OF SOUTHAMPTON

__ABSTRACT__

FACULTY OF ENGINEERING, SCIENCE AND MATHEMATICS

SCHOOL OF ENGINEERING SCIENCES

__Doctor of Philosophy__

COMPUTER SIMULATION STUDIES OF MAGNETIC NANOSTRUCTURES

Richard Paul Boardman

FACULTY OF ENGINEERING, SCIENCE AND MATHEMATICS

SCHOOL OF ENGINEERING SCIENCES

COMPUTER SIMULATION STUDIES OF MAGNETIC NANOSTRUCTURES

Richard Paul Boardman

Scientific and economic interest has recently turned to smaller and smaller magnetic structures which can be used in hard disk drives, magnetoresistive random access memory (MRAM), and other novel devices. For nanomagnets the geometric shape of the object becomes more important than other factors such as magnetocrystalline anisotropy -- the smaller the object, the more strongly the shape anisotropy affects the hysteresis loop.

We investigate the micromagnetic behaviour of ferromagnetic samples of various geometries using numerical methods. Finite differences and finite elements are used to solve the Landau-Lifshitz-Gilbert and Brown's equations in three dimensions. Simulations of basic geometric primitives such as cylinders and spheres of sub-micron size orders provide hysteresis loops of the average magnetisation, and additionally our computations allow the study of the microscopic configuration of the magnetisation. We show different mechanisms of vortex penetration for these geometries, and investigate part-spherical geometries whose magnetisation pattern demonstrates qualities of other primitives.

Developing this further, we calculate the hysteresis loops for a
*droplet* shape -- a part-sphere capped with an half-ellipsoid.
This resembles the shapes formed by some chemical self-assembly
methods, a low-cost and efficient way of creating a commercially
viable product. When examining the magnetic microstructure of this
geometry we find different types of vortex behaviour, and reveal the
dependence of this on the physical characteristics of the droplet.

We also examine the hysteresis loops and magnetic structures of other geometries formed through the self-assembly method such as antidots -- honeycomb-like arrays of spherical holes in a thin film. We show magnetisation patterns and comparison between experimental and computed magnetic force microscopy (MFM) measurements.

- Contents
- List of Tables
- List of Figures

- Introduction
- Historical context
- Modern magnetism
- Hard disk drives
- Overview of relevant interactions
- Computer simulations
- Summary

- Micromagnetics
- Introduction
- From quantum mechanics to micromagnetics
- Interactions between atomic magnetic moments
- Micromagnetic description
- From static to dynamic
- Computational models
- Simulation
- Micromagnetic systems
- Computational Issues
- Applications

- Basic geometries: flat cylinders and spheres

- Cones

- Nanodots
- Introduction
- Half-sphere
- Part-spherical nanodots
- Multiple vortex states
- ``Droplet'' nanodots
- Applying an out-of-plane external field
- Summary

- Antidots
- Introduction
- Parameters of the antidot system
- Three-dimensional model
- Two-dimensional model
- Stray field measurement
- Monte Carlo simulation
- Results
- Summary

- Summary and outlook

- Analytical calculation of the stray field
- Supporting equations for the 3D/1D Monte Carlo method
- Material parameters
- CGS and SI (MKS) unit systems
- Complete simulation process

- Constructive solid geometries
- Bibliography
- About this document ...