Magnetism and Numerical Methods

Micromagnetics and Discrete Spin Model

• Core equations
  • Interactions
  • Landau-Lifshitz-Gilbert (LLG) equation
• Extended equations
  • Stochastic LLG equation
  • Spin transfer torque (Zhang-Li model)
  • Nonlocal spin transfer torque (full version of Zhang-li model)
  • Spin transfer torque (current-perpendicular-to-plane, CPP)
• Monte Carlo Simulation
• Time integration
  • The stabilisation term
  • How much does the value matter?
  • Choosing an integrator
  • The analytical Jacobian
• Energy minimisation
  • Gradient descent on the sphere
  • The Hubert minimiser
  • Barzilai-Borwein step lengths
  • The steepest descent minimiser
  • How this compares with OOMMF
• Nudged Elastic Band Method (NEBM)
  • NEBM relaxation
  • Vectors
  • Projections
  • Distances
  • Algorithm
• Fidimag Code
  • Arrays
  • Cython Codes
  • Geodesic distances code
  • Convergence criteria and force units
  • CVODE linear solver and memory usage
  • Spherical coordinates code
• FMM/Barnes-Hut Demagnetising Field
  • FFT-based Demag
  • The Barnes-Hut and Fast Multipole Methods
  • Usage
  • 2D systems
  • Performance
  • Where FMM/Barnes-Hut is worth it
  • References