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Modeling of macroscopic anisotropies
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Modeling of macroscopic anisotropies
Contents
1 Introduction
1 Magnetic nanoparticles and thin films
2 Size effects in nanomagnets
3 Surface effects in nanomagnets
4 The magnetic anisotropy
1 Magneto-crystalline anisotropy
2 Surface magnetic anisotropy
3 The shape magnetic anisotropy
5 Experimental approach
1 Effective and surface anisotropies
2 Surface anisotropy and thin films magnetism
6 The challenge of modeling of magnetic nanoparticles and thin films
7 About this thesis
2 Multi-spin nanoparticle as an effective one spin problem
1 Introduction
2 Model
1 Shape and surface of nanoparticles
2 Localized spin (atomistic or Heisenberg) model
3 Analytical background
1
Second-order surface-anisotropy energy
2
First-order surface-anisotropy energy
3
Mixed contribution to the energy
4 Effective one spin problem (EOSP) approximation
4 Numerical method
5 Effective energy landscapes of spherical nanoparticles
6 Effective energy landscapes of elongated nanoparticles
7 Effective energy landscape of an octahedral nanoparticle
8 Effective energy landscape in cobalt nanoparticle
9 Conclusions
3 Energy barriers of magnetic multispin nanoparticles with Néel surface anisotropy
1 Motivation
1 Phenomenological expression for the effective anisotropy constant in a system with surface anisotropy
2 Energy barriers from the effective one spin problem (EOSP)
3
Dependence of the energy barrier on the value of the surface anisotropy constant
4 Dependence of the energy barrier on the system size
5
On the applicability of the formula
6 Modeling of energy barriers in cobalt nanoparticle
7 Conclusions
4 The constrained Monte Carlo method and temperature dependence of the macroscopic anisotropy in magnetic thin films
1 Motivation and introduction
2 The constrained Monte Carlo method
1 Algorithm
2 Free energy and restoring torque
3 Numerical procedure
4 Tests of the method
3 Temperature dependence of macroscopic anisotropy in thin films with Néel surface anisotropy
1 The temperature dependence of the total effective anisotropy in thin films with surface anisotropy.
2 Temperature dependence of the effective surface anisotropy in thin films.
3 Modeling the effect of the anisotropy re-orientation due to the surface effects
4 The scaling of the macroscopic anisotropy with the magnetization
4 Conclusion
5 Temperature dependence of the surface anisotropy in nanoparticles
1 Introduction
2 Temperature dependence of macroscopic anisotropy in magnetic nanoparticles
1 Temperature dependence of the effective anisotropies in nanoparticle with sc lattice structure
2 Temperature dependence of the effective anisotropies in nanoparticles with fcc lattice structure
3 Scaling exponent
3 Conclusions
6
Multiscale modeling of magnetic properties of
thin films
1 Introduction
2 Density functional theory
1 Hohenberg-Kohn theorems
2 Kohn-Sham scheme
3
Approximation for the exchange-correlation energy
4 Screened Korringa-Kohn-Rostoker Green's function method
3 "Ab-initio" modeling of bulk Co and its interfaces
1 The studied system
2 Work function
3 Spin and orbital moments
4 Exchange interactions
5 Magneto-crystalline anisotropy energy
4 Temperature-dependent macroscopic properties
1 Magnetostatic interaction
2 Implementation of the exchange tensor interaction
3 Temperature-dependent magnetization
4 Temperature-dependent anisotropy
5 Conclusions
A. Appendix A
1 Hamiltonian of the spin system in the adiabatic approximation
2 Contribution to total uniaxial anisotropy due to "two-site" anisotropy
3 Determination of one-site anisotropy energy
Bibliography
Rocio Yanes