Lecture 11 Flashcards
Describe the M-H graph for a diamagnet and a paramagnet
Paramagnet: magnetisation in the direction of the field
Diamagnet: magnetisation in the opposite direction to the field
Describe the graph of magnetic susceptibility against temperature for a diamagnet and a paramagnet
Paramagnet: susceptibility temperature dependent
For paramagnetic there is ____ magnetisation when there is no applied field as the magnetic moments are oriented _______.
Zero
Randomly
Give the quantum mechanical equation for the magnetic moment of an orbiting electron
µ = magnetic moment
L = angular momentum
Electrons have an intrinsic ____ angular momentum.
Spin
Give the equation for the magnetic moment of an electron in terms of spin
µ = magnetic moment
g = g-factor
s = spin angular momentum
What is the value of the electron g-factor?
g = 2.0023
Give the equation for the effective magnetic moment of atom with a total angular momentum
µ_eff = effective magnetic moment
g = g-factor
µ_B = Bohr magneton
J = total angular momentum
Give the equation for the energy of a magnetic moment in a B-field
E = energy
µ = magnetic moment
B = magnetic field
How many allowed J-states are there (for J_z)?
(2J +1): -J to +J
Give the equation for the energy of a magnetic moment in a B-field in terms of J_z
E = energy
g = g-factor
µ_B = Bohr magneton
J = total angular momentum
B = magnetic field
Describe the energy states of a two-level spin system in zero field and in a magnetic field greater than 0
Give the equation for the number density of atoms in the lower state of a two-level spin system
N1 = number density of atoms in the lower state
N = number density
x = E/kT
Give the equation for the number density of atoms in the upper state of a two-level spin system
N2 = number density of atoms in the upper state
N = number density
x = E/kT
Give the equation for net magnetisation in terms of the distribution of energy in a two-level spin system
M = magnetisation
N1 = number density of atoms in lower state
N2 = number density of atoms in upper state
N = number density
Describe the shape of a tank(x) function
Give the equation for the magnetisation of a paramagnet in terms of temperature
M = magnetisation
N = number density
T = temperature
Give the equation for the susceptibility of a paramagnet in terms of temperature
χ = susceptibility
C = Curie constant
T = temperature
Describe the energy levels of all the possible total angular momentum states in a magnetic field
Give the equation for the magnetisation over all the energy levels in a material
M = magnetisation
N = number density
g = g-factor
J = total angular momentum
Describe the shape of a graph of the Bohr magnetisation per ion against B/T for a paramagnet
Experimental results for different temperatures all fall on the same curve depending on the ion being measured.
The magnetisation saturates at the correct number of Bohr magnetons per ion compared the magnetisation equation.
Give the equation for the susceptibility of conduction electron in a metal
χ = susceptibility
M = magnetisation
B = magnetic field
N = number density
T = temperature
Describe the graph of the free electron density of states
At T = 0 all states fill up to the Fermi energy with two electrons of opposite spin per state.
What happens to the density of energy states when an electric field is applied?
The energy of electron states is lowered by µB when the magnetic moment is parallel to B (red).
The energy of electron states is raised by µB when the magnetic moment is antiparallel to B (blue).
Hatched area = number of moment up electrons - number of moment down electrons
