Lecture 12 Flashcards
What is an ordered magnetic state?
One that arises from interactions between the individual magnetic moments in a material. Many types of magnetic order exist.
What is a simple ferromagnet?
A permanent magnet where all the magnetic moments align in the same direction.
Which elements are ferromagnetic?
Iron: Fe
Nickel: Ni
Cobalt: Co
Gadolinium: Gd
What is the Curie temperature?
The critical temperature for ferromagnets. Below this temperature ferromagnetic materials have spontaneous magnetisation in the absence of an applied magnetic field.
Compare the difference between the order of a ferromagnet below and above the Curie temperature
The magnetic moments become more fully aligned with _________ temperature.
Decreasing
Give the equation for pair exchange energy between two neighbouring atoms
U = pair exchange energy
J = total angular momentum = constant
s_i = spin
s_j = nearest neighbour spin
Give the equation for mean field approximation of the exchange energy
U = exchange energy
s_i = spin
<s> = average neighbour spin for all lattice sites
</s>
What is the Weiss molecular field?
An effective magnetic field that tends to orientate the individual spin moments towards the direction of the net magnetisation. It is equivalent to the exchange energy.
Give the equation for the exchange energy in terms of the Weiss molecular field
U = exchange energy
µ = molecular moment
B_eff = Weiss magnetic field = effective B-field
Give the equation for the spontaneous magnetisation of a ferromagnet with zero applied magnetic field
M = spontaneous magnetisation
How can spontaneous magnetisation be used to see if a material ia a paramagnet or a ferromagnet?
Use the spontaneous magnetisation to find a dimensionless quantity of magnetisation: m. Plot m against tanh(m/t) and m = m on a graph and compare where m = tanh(m/t)
For t > 0, the only solution is m = 0 so no spontaneous magnetisation occurs (paramagnet).
For t < 0, a solution exists where m > 0 (ferromagnet).
For t = 0, m = 1 so M = Nµ_B so all the magnetic moments are parallel
For t = 1, m = tanh(m). This is only in the limit where m tends to 0.
Give the equation for the Curie temperature
T_c = Curie temperature
What are magnons?
Spin waves. They are like photons and can be modelled as chains of moments coupled to nearest neighbours.
Give the equation for the mean field (Curie Weiss) prediction of the susceptibility above the Curie temperature
χ = susceptibility
M = magnetisation
B_app =applied magnetic field
C = Curie constant
T = temperature
T_C = Curie temperature
