Lecture 13 Flashcards
Describe the shape of the M-H curve for magnetically hard materials
There is large hysteresis because it is magnetically hard.
Describe the magnetic moments of a ferromagnet when the temperature is 0K?
They’re in an ordered state: all the moments are parallel.
What is magnetic anisotropy?
The dependency of magnetic properties on a preferred crystallographic direction if magnetisation. The preferred directions are called ‘easy axes’.
What are the 3 physical origins of magnetic anisotropy?
- Crystal
- Shape
- Strain
When does crystalline ferromagnetic anisotropy occur?
Anisotropy arises from the arrangement of nearest neighbours. It is highest when there is high symmetry of the crystal and an additional contribution to the energy due to spin-orbit coupling.
When does strain anisotropy occur?
When there is strain that results in the atoms being (slightly) closer together along specific directions, resulting in an anisotropic exchange interaction.
When does shape anisotropy occur?
In non-spherical samples.
What is a uniformly magnetised ferromagnet?
A ferromagnet with a magnetic ‘north’ and ‘south’ pole.
What is a demagnetising field?
The field produced by the poles inside the ferromagnet.
Give the equation for the energy cost associated with a demagnetising field
E_d = energy cost
H_d = demagnetising field§
Are ferromagnets usually uniformly magnetised?
No
Ferromagnets for _______ _______ to minimize the external magnetic flux, B.
Magnetic domains
Describe the magnetic flux produced by a single domain magnet
Describe an anti-parallel magnetic domain
Anti-parallel magnetic domains reduce the external magnetic flux.
Describe a flux closure domain
What are domain walls?
The intermediate region between the two domains of a ferromagnet.
Why does a domain wall increase anisotropy energy?
Because the magnetisation is not along a low energy direction. A larger length, L, results in a larger increase in energy.
Why does a domain wall increase exchange energy?
Because the neighbouring moments are not parallel. A larger length, L, results in a smaller increase in energy.
Describe the dimensions of a domain wall
a = lattice constant
L = wall width
s = moment
N = L/a = number of atoms
Give the equation for the width of a domain wall
L = wall width
N = number of atoms
a = atomic spacing
s = spin
J = total angular momentum
k = wavenumber
Give the equation for the energy per unit area of the domain wall
∆U = energy
s = spin
J = total angular momentum
k = wavenumber
a = atomic spacing
L = wall width
Describe the position of different domains on the M-H curve of a ferromagnetic material
How are magnetic domains used in data storage?
Hard drives contain magnetic materials that are magnetised in different directions of magnetisation, allowing data to be stored based on these directions.
What value of H-susceptibility is considered ‘low’?
~100
