5) Zeeman energy

What is the Zeeman energy

energy associated with aligning the magnetic moment with the field

Zeeman energy equation

E_z = -μ_0 m.H; E/V = -μ_0Μ.Η

Τοrque from the Zeeman energy

τ = μ_0 H x m = μ_0 H m sin(θ)

How can a magnet respond to a magnetic field

align its body or align its magnetism (focus on this one)

Magnetism rotation

large volume of magnetisation coherently changes direction (happens when switching along a hard axis); as H decreases anisotropy dominates and magnetisation rotates towards easy axis; reversibly follows energy minimum

Anisotropy field

magnetic field of equilavent strength to the influence of anisotropy (where the hysterisis curve flattens in hard axis); Hk = -2K/(μ_0 Ms)

Domain nucleation

magnetism doesn’t rotate gradually in most cases but changes abruptly; reverse domain suddenly nucleates at a critical field strength and begins to grow; irreversible, sudden change; occurs at weak points in the magnetisation structure eg edges (strongest demag field) or defects

Domain wall motion

Nucleated domain walls can move, flipping adjacent domains to align with it

What is Barkhaussen noise

changing magnetic flux induces a voltage/current which can be amplified through a speaker producing a hissing noise; shows the material is changing via a large number of small steps rather than perfectly smoothly

What causes these small steps

domain walls become pinned against non magnetic defects and form stable closed flux domains; this is an energy barrier against domain wall motion; field increases until enough energy to ping off defect and form full domain

Describe how magnetisation is changing in this hysterisis loop

1) moments mostly saturated, small relaxation by rotation;

2) Nucleation of reverse domains due to demag and applied field;

3) Irreversible domain wall motion, bulk of reversal process;

4) small magnetisation rotation to be fully saturated

Magnetisation reversal along the hard axis

reversal via gradual rotation of magnetisation, no metastable states to go through as always fighting the anisotropy energy; produces linear reversible hysterisis plot