Magnetic- Useful Revision

Question 1

What is a magnet?

Answer 1

A material that produces a magnetic field, H

Question 2

What is magnetisation?

Answer 2

Magnetic moment of the magnet divided by the volume of the magnet

Question 3

What happens when a paramagnet has a magnetic field applied to it?

Answer 3

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.

Question 4

What energies are used in equations for MAZE?

Answer 4

Energy densities, E/V

Question 5

Zeeman energy

Answer 5

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

Question 6

Zeeman energy and torque for different angles between H and M

Answer 6

0°: low energy and torque
180°: high energy and low torque
90°: zero energy and high torque

Question 7

Exchange energy

Answer 7

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)

Question 8

What does a positive or negative J mean?

Answer 8

Positive J favours spins to align parallel

Negative J favours spins to align anti-parallel

Question 9

What does exchange energy do in a ferromagnet?

Answer 9

Acts to try and keep the magnetisation configuration uniform. It effectively creates an exchange stiffness quantified by Aex.

Question 10

Magnetostatic energy

Answer 10

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.

Question 11

Magnetisation and field inside a magnet

Answer 11

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

Question 12

Describe shape anisotropy with magnetostatic energy

Answer 12

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

Question 13

Demagnetising factor equations

Answer 13

Hd=-NdM
EMs/V=-1/2 μ0Hd•M
Sub in
EMs/V=1/2 μ0NdMs^2
E subscript Ms magnetostatic energy

Question 14

What do the demagnetising factors in all dimensions add to?

Answer 14

1

Question 15

Magnetocrystalline anisotropy energy

Answer 15

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.

Question 16

Easy and hard axes for bcc, fcc, hcp

Answer 16

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

Question 17

Magnetocrystalline anisotropy energy density for uniaxial systems

Answer 17

EA/V=K1sin^2(θ)
K1 also Ku anisotropy constant
θ angle M makes with easy axis

Question 18

How can polycrystalline materials have an effective anisotropy

Answer 18

Induced during processing. Magnetic fields during film growth/solidification. Rolling. Magnetic annealing.
Typically uniaxial anisotropies

Question 19

What is magnetostriction?

Answer 19

Phenomenon where a ferromagnet changes in physical dimensions when it undergoes a change in magnetisation. Could be change of direction or in domains

Question 20

Saturation magnetostriction constant

Answer 20

Symbol λs. If positive it expands along field direction. If negative it contracts along field direction. Can vary for different crystallographic axes

Question 21

Inverse of magnetostriction

Answer 21

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.