Lectures 13&14 (Shape Anisotropy, Domains and DWs) Flashcards
Equation for stray field energy (integral version)?
εm = -µ0/2 ∫H.MdV
Equation for stray field energy (component version)?
εm = -µ0V/2 (DxMx^2 + DyMy^2+DzMz^2)
What can stray field energy also be referred to as?
Magnetostatic energy, shape anisotropy energy
What happens if you have an out of plane H applied to a thin film?
Opposite charges build up on top and bottom of film and large Hd
Where does the 1/2 factor come from in the stray field energy?
Avoid double counting - each dipole contributes as field source and as moment
What is the only shape that can be uniformly magnetised by a uniform field?
Ellipsoids
Is shape anisotropy a real anisotropy?
No, but a demagnetising effect
Value of K for thin film out of plane?
K = 1/2 µ0 M^2 D
Which direction will M lie in a thin film? Why?
In plane as this is the lower energy state
How to derive saturation field?
Energy of SW particle - subs ø=90 (H direction)
∂E/∂theta = 0
Subs theta = 90
Equation for saturation field?
H = 2K / µ0M
Difference between Bloch and Neel walls?
Block walls rotate sideways, Neel forwards/backwards
Where do Bloch walls occur?
Bulk samples and thick films
Where to Neel walls occur?
Thin films
Features of Block vs Neel walls?
Bloch - poles associated with them and a corresponding stray field
Neel - shape anisotropy stronger where they occur, so in-plane rotation is favoured and there is no stray field outside the film
How to measure K?
Thin film strained on piezoelectric stressor
Induced anisotropy in material
Difference in divergence of Bloch and Neel walls?
Bloch ∇.M = 0 no component of M in x-direction, spins in each y-z plane are parallel
Neel ∇.M ≠ 0 i.e., it has some changes
What do we minimise E with respect to when calculating DW energy, and why do we need to minimise it?
N
Minimise because anisotropy and exchange energy are competing
