Magnetic- Useful Revision Flashcards
What is a magnet?
A material that produces a magnetic field, H
What is magnetisation?
Magnetic moment of the magnet divided by the volume of the magnet
What happens when a paramagnet has a magnetic field applied to it?
The H applied fights against the disorder thermal energy causes and the material develops a weak M along the H direction as the individual magnetic moments rotate from being randomly orientated.
What energies are used in equations for MAZE?
Energy densities, E/V
Zeeman energy
The interaction of a magnet’s magnetisation with an external magnetic field. Alignment of M parallel to H is energetically favourable. Them being antiparallel is energetically unfavourable.
Ez=-μ0HMcosθ
τ=μ0HMsinθ
Zeeman energy and torque for different angles between H and M
0°: low energy and torque
180°: high energy and low torque
90°: zero energy and high torque
Exchange energy
A quantum mechanical interaction that causes local ordering of magnetic moments. Uniform magnetisation states are energetically favourable. Non-uniform ones (more twisted) are energetically unfavourable.
Eex=-2JexSxS (exchange interaction between two electrons)
What does a positive or negative J mean?
Positive J favours spins to align parallel
Negative J favours spins to align anti-parallel
What does exchange energy do in a ferromagnet?
Acts to try and keep the magnetisation configuration uniform. It effectively creates an exchange stiffness quantified by Aex.
Magnetostatic energy
The interaction of a magnet’s magnetisation with its own demagnetising field. Flux closed states, multi-domain states, magnetisation alignment along the magnet’s long axis are energetically favourable. Single domain configurations and magnetisation alignment along the short axis is energetically unfavorable.
Magnetisation and field inside a magnet
The magnetisation of the magnet points south to north. The magnetic field points north to south. These are in opposite directions which is energetically unfavourable for exchange energy. This field wants to reduce the net magnetisation of the magnet so is called the demagnetising field Hd
Describe shape anisotropy with magnetostatic energy
When magnetised along the short axis there are more poles created and they N and S are closer together creating a stronger Hd. This means the magnetostatic energy is higher than when magnetised along the long axis
Demagnetising factor equations
Hd=-NdM EMs/V=-1/2 μ0Hd•M Sub in EMs/V=1/2 μ0NdMs^2 E subscript Ms magnetostatic energy
What do the demagnetising factors in all dimensions add to?
1
Magnetocrystalline anisotropy energy
The interaction of a magnet’s magnetisation with its crystal lattice via the spin-orbit interaction. Alignment of magnetisation along easy crystal axes is energetically favourable. Alignement of magnetisation along hard crystal axes is energetically unfavourable.
Easy and hard axes for bcc, fcc, hcp
BCC: easy along edge of cube, hard diagonally through body
FCC: easy diagonally through body of cube, hard along edge
HCP: easy vertically through centre, hard along top or bottom face from centre to equidistant edge atoms
Magnetocrystalline anisotropy energy density for uniaxial systems
EA/V=K1sin^2(θ)
K1 also Ku anisotropy constant
θ angle M makes with easy axis
How can polycrystalline materials have an effective anisotropy
Induced during processing. Magnetic fields during film growth/solidification. Rolling. Magnetic annealing.
Typically uniaxial anisotropies
What is magnetostriction?
Phenomenon where a ferromagnet changes in physical dimensions when it undergoes a change in magnetisation. Could be change of direction or in domains
Saturation magnetostriction constant
Symbol λs. If positive it expands along field direction. If negative it contracts along field direction. Can vary for different crystallographic axes
Inverse of magnetostriction
Villari effect. Change in the anisotropy of a material when strained along a given direction. Induced anisotropy proportional to the stress acting on the material.
