Magnetic- Domains and Domain Walls Flashcards
How can magnetostatic energy be reduced using domains?
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.
Formula for magnetostatic energy for a certain number of domains
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
Formula for magnetostatic energy density with domains (more complicated)
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
What limits the number of domains formed?
The exchange energy. This increases with the number of domains. This has to be balanced with the magnetostatic energy
What are domain walls?
They separate domains but have a finite width. They are non-uniform transition regions where the spin of adjacent atoms is slightly different
What does the domain wall width depend on?
Exchange energy wants to minimise angle between the spins (widen wall). Anisotropy energy wants to maximise alignment of spins to easy axis (narrow wall)
Exchange energy and anisotropy energy per unit area formulae
σex=Aπ^2/δ σK=Kuδ A is exchange stiffness Ku is anisotropy constant δ is domain wall width
How to find optimum domain wall width
Add exchange energy and anisotropy energy per unit area and differentiate
δ0=πrt(A/Ku)
Formula for domain wall energy density
EDW/V=σDW/d
d is domain width
How to find optimum domain width
Add domain wall and magnetostatic energy densities and differentiate.
d=Lrt(σDW/1.7μ0Ms^2)
Balances saturation magnetisation, exchange energy, anisotropy
Flux-closed states
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)
Domains in bulk magnets
Contain huge numbers of domain and form complex defect dominated domain structures
What happens at micrometer magnet sizes?
Magnetisation configurations become simpler and magnets contain just a few domains
When will a particle be single domain?
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
Radius of spherical nanoparticle at which single and bi-domain state have same energy
rc=9σDW/μ0Ms^2
How does a single domain particle behave in a magnetic field?
It must switch by coherent rotation to align itself with the applied field
Domains on hysteresis loop
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
How can the Barkhausen effect be heard?
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.
What is heard in experiment for Barkhausen effect?
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.
How do defects pin domain walls?
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.
