Magnetic- Domains and Domain Walls

Question 1

How can magnetostatic energy be reduced using domains?

Answer 1

The magnitude of the demagnetising field is reduced by splitting the magnet into multiple domains. The magnetostatic energy is inversely proportional to the number of domains.

Question 2

Formula for magnetostatic energy for a certain number of domains

Answer 2

En=E1/N
Where E1 is magnetostatic energy of uniformly magnetised configuration (1 domain)
N is number of domains and is even otherwise there is still a net N and S

Question 3

Formula for magnetostatic energy density with domains (more complicated)

Answer 3

Em/V=1.7(td/L^2)μ0Ms^2
t is thickness of magnet
d is domain width
L is length of domain (account for shale anisotropy)
Ms is saturation magnetisation

Question 4

What limits the number of domains formed?

Answer 4

The exchange energy. This increases with the number of domains. This has to be balanced with the magnetostatic energy

Question 5

What are domain walls?

Answer 5

They separate domains but have a finite width. They are non-uniform transition regions where the spin of adjacent atoms is slightly different

Question 6

What does the domain wall width depend on?

Answer 6

Exchange energy wants to minimise angle between the spins (widen wall). Anisotropy energy wants to maximise alignment of spins to easy axis (narrow wall)

Question 7

Exchange energy and anisotropy energy per unit area formulae

Answer 7

σex=Aπ^2/δ
σK=Kuδ
A is exchange stiffness
Ku is anisotropy constant
δ is domain wall width

Question 8

How to find optimum domain wall width

Answer 8

Add exchange energy and anisotropy energy per unit area and differentiate
δ0=πrt(A/Ku)

Question 9

Formula for domain wall energy density

Answer 9

EDW/V=σDW/d

d is domain width

Question 10

How to find optimum domain width

Answer 10

Add domain wall and magnetostatic energy densities and differentiate.
d=Lrt(σDW/1.7μ0Ms^2)
Balances saturation magnetisation, exchange energy, anisotropy

Question 11

Flux-closed states

Answer 11

Where magnetisation loops around in a closed circuit so no magnetic poles are present at the nanostructure’s surface and there is no demagnetising field. Minimises magnetostatic energy and forms in systems where magnetostatic effects dominate (high magnetisation and low magnetocrystalline and induced anisotropy)

Question 12

Domains in bulk magnets

Answer 12

Contain huge numbers of domain and form complex defect dominated domain structures

Question 13

What happens at micrometer magnet sizes?

Answer 13

Magnetisation configurations become simpler and magnets contain just a few domains

Question 14

When will a particle be single domain?

Answer 14

When half (N=2) the magnetostatic energy of bi-domain state and energy of domain wall is greater than magnetostatic energy if single domain state. Normally between 10 and 100nm

Question 15

Radius of spherical nanoparticle at which single and bi-domain state have same energy

Answer 15

rc=9σDW/μ0Ms^2

Question 16

How does a single domain particle behave in a magnetic field?

Answer 16

It must switch by coherent rotation to align itself with the applied field

Question 17

Domains on hysteresis loop

Answer 17

At saturation they all align with field. As field decreases, domain nucleation (normally at defect sites). As reduced and reversed, domain wall motion so those aligned to new direction of field expand and antiparallel contract. All the way to saturation in other direction

Question 18

How can the Barkhausen effect be heard?

Answer 18

Connect coil of wire to amplifier so any induced voltage in wire causes sound. Voltage proportional to rate of change of flux density. Put magnetic material inside coil. Move a magnet close to it.

Question 19

What is heard in experiment for Barkhausen effect?

Answer 19

The bulk magnetic material is reversing its magnetisation. There is hissing noise due to there being a large number of small steps for it to reverse. These are the unpinning of domain walls at non-magnetic defects in the material.

Question 20

How do defects pin domain walls?

Answer 20

As the domain wall moves to touch the defect, formation of flux closure domains on the sides where the domain wall touches it occurs allowing a reduction of magnetostatic energy. Creates an energy barrier against the domain wall’s propagation.