Magnetic- Micromagnetic Modelling Flashcards
What are degrees of freedom?
The number of variables needed to describe a system. Tells you how many equations need to be solved
What is micromagnetics?
A mathematical modelling technique that allows us to predict the behaviour of magnetic materials at sun-micrometer length scales
What can micromagnetics tell us?
The energy of a magnet in a given magnetisation state. The magnetisation dynamics of a magnet in response to external stimuli
How does exchange energy help micromagnetics to work?
It resists the formation of abrupt domain walls. Means spins of adjacent atoms will always be similar. Don’t need to consider the magnetisation of discrete atoms but can model magnetisation as a continuously varying vector m. This is the continuum approximation
What is the total energy of a magnetic state?
The sum of all the MAZE energy terms
What is the exchange length?
Length scale over which magnetisation is effectively uniform.
lex=rt(A/K)
lex=rt(2A/μ0Ms^2)
A is strength of exchange
K is strength of anisotropy
μ0Ms^2 represents strength of magnetostatic effects
Which formula for exchange length to use
Anisotropy one applies in bulk systems with strong magnetocrystalline anisotropy. Magnetostatic one applies to thin films with weak anisotropy. In practice calculate both and use whichever is smaller. Normally about 5nm
How is a magnet split up in micromagnetics?
Split into cells of exchange length size. Cubic (finite difference simulation) or tetrahedra (finite element simulation). Each cell contains a macro-spin that represents the magnetic moment of several atoms. They have a constant size but variable direction. Computers then use numerical techniques to calculate energies in magnets of any geometry
What happens if the cell size is too big?
Shale of magnet will not be approximated well (particularly curves). Calculated energies of states won’t be accurate. The energy converted to a value as the cell size decreases
What are the dynamics of a magnetic moment in an applied field modelled by?
The Landau-Lifshitz-Gilbert equation. Page 14 lecture 3
Sections of LLG equation
Equation for dM/dt. Precessional term mxH causes M to rotate in a cone around H. The damping term mx(mxH) represents energy dissipation and causes M to gradually align to H. γ is gyromagnetic ratio. α is damping constant. Numerically integrate equation to determine magnetisation dynamics
What does low or high damping mean?
Low damping means magnetisation vector aligns slowly to the field and dynamics are complex. High damping means magnetisation aligns quickly and dynamics are simple
What is effective field?
Takes into account all of MAZE effects. Used in LLG.
Heff=-(1/μ0Ms)(dEtotal/dm) or
Heff=Hd-(2K/μ0Ms)(m•u)u+Hexternal+(2A/μ0Ms)nabla^2m
What is micromagnetics good for?
Assisting interpretation and explanation of experimental data. Make broad/generalised predictions about behaviour of systems. Exploring feasibility of new devices/experiments
What is micromagnetics bad at?
Precisely predicting how a specific device/experiment will behave. Assumes 0K and no defects in material
