MODELING OF MACROSCOPIC ANISOTROPIES DUE TO SURFACE EFFECTS IN MAGNETIC THIN FILMS AND NANOPARTICLES.

by

Rocío Yanes Díaz

Advisor:

Oksana Fesenko Morozova

Tutor:

Farkhad Aliev

A THESIS SUBMITTED TO UNIVERSIDAD AUTÓNOMA DE MADRID

DEPARTMENTO FÍSICA DE LA MATERIA CONDENSADA
MARCH 2011

Es necesario esperar, aunque la esperanza haya de verse siempre frustrada, pues la esperanza misma constituye una dicha, y sus fracasos, por frecuentes que sean, son menos horribles que su extinción.
Samuel Johnson

Table of Child-Links

• Contents
• Resumen
• 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
      • 1 The Néel model of the surface magnetic anisotropy
      • 2 Magneto-crystalline anisotropy: Bruno model
    • 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 $\mathcal {E}_{2}$
    • 2 First-order surface-anisotropy energy $\mathcal {E}_{1}$
    • 3 Mixed contribution to the energy $\mathcal {E}_{21}$
    • 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
  • Conclusiones
  
  
• 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 $k_s$
  • 4 Dependence of the energy barrier on the system size
  • 5 On the applicability of the formula ${\cal K}_\mathrm {eff} = {\cal K}_\infty + 6 {\cal K}_s/D$
  • 6 Modeling of energy barriers in cobalt nanoparticle
  • 7 Conclusions
  • Conclusiones
  
  
• 4 The constrained Monte Carlo method and temperature dependence of the macroscopic anisotropy in magnetic thin films
  • 1 Motivation and introduction
    • 1 Atomistic model
  • 2 The constrained Monte Carlo method
    • 1 Algorithm
    • 2 Free energy and restoring torque
    • 3 Numerical procedure
    • 4 Tests of the method
      • 1 Curie temperature
      • 2 Comparison of the constrained Monte Carlo method at low temperature with the Lagrange multiplier method
      • 3 Temperature dependence of the bulk anisotropy
  • 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.
      • 1 Scaling with the system size
      • 2 Separation of the surface torque
    • 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
  • Conclusiones
  
  
• 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
  • Conclusiones
  
  
• 6 Multiscale modeling of magnetic properties of $Co\setminus Ag$ thin films
  • 1 Introduction
  • 2 Density functional theory
    • 1 Hohenberg-Kohn theorems
    • 2 Kohn-Sham scheme
    • 3 Approximation for the exchange-correlation energy $E_{xc}[n]$
    • 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
      • 1 WF dependence on the surface
      • 2 Dependence of the WF with the structural relaxation
    • 3 Spin and orbital moments
      • 1 Spin and orbital moments on Co bulk system
      • 2 Spin and orbital moments on pure Co surface
      • 3 Spin and orbital moments on $Co\setminus Ag_{1}$ interface
    • 4 Exchange interactions
      • 1 Evaluation of the Exchange tensor
      • 2 Isotropic exchange interactions
      • 3 Symmetric anisotropic exchange tensor
      • 4 Antisymmetric anisotropic exchange tensor
    • 5 Magneto-crystalline anisotropy energy
      • 1 Evaluation of the total magneto-crystalline anisotropy
      • 2 Magneto-crystalline anisotropy energy dependence on the interface and cappings.
      • 3 Layer-resolved magneto-crystalline anisotropy energy
      • 4 Magneto-crystalline anisotropy energy as a function of the lattice relaxation.
      • 5 Magneto-crystalline anisotropy energy of a $Co(111)\setminus Ag_{1}$ thin films
  • 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
  • Conclusiones
  
  
• 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
• List of Publications of R. Yanes
• Agradecimientos
• About this document ...

End of Table of Child-Links