Lectures 1&2 (Basics, FM & Bohr-van Leeuwen) Flashcards
What is magnetisation?
Response of a material due to an applied magnetic field
Flux density inside solenoid?
B = µ0 IN/L
(so H = IN/L)
Magnetic moment equation?
µ = MV
µ units?
Am^2
Angular momentum equation for an electron?
l = m_e * r x v
How is M defined?
Magnetic moment per unit volume
Show that magnetic moment µ can be given in terms of the angular momentum l of the electron
l = m_e * r x v
and µ = -e/2 * r x v
µ = - e/2m * l
Equation for µ in terms of orbital angular momentum?
µ = γl
γ value?
γ = -e/2m or -ge/2m for > 1 electron
Show that Bohr magneton comes from magnetic moment and orbital angular momentum
µ = -e/2m * l
µ_z = -e/2m * m_l * ℏ
µ_B = eℏ/2m
Show that µ = µ0(1+X)
B = µ0(H+M) = µ0(H+XH) = µ0H(1+X) = µH
where µ = µ0(1+X)
Which materials experience diamagnetism?
All
Susceptibility of a diamagnet?
X < 0
How do diamagnets react to magnetic fields?
Weakly repelled
(A small opposite moment is induced due to Lenz’s law)
What gradient does a diamagnet have on the M vs H graph?
-ve
Susceptibility of a paramagnet?
X > 0
How do paramagnets react to magnetic fields?
Weakly attracted
Moments not aligned in absence of H_ext
Which materials experience paramagnetism?
Those with net angular momentum on each atom
Why does a FM remain magnetised at H=0?
Exchange interaction and anisotropy
X of FM?
X_eff = ∂M/∂H
What is Ms?
Magnetisation of the sample when all domains are aligned and characteristic of the material
What is Mr?
Remanent magnetisation is that at zero field, and can depend on the sample
What is Hc?
The coercive field (coercivity) is the reverse field that needs to be applied to zero magnetisation
What is Mr/Ms?
Remanent fraction / loop squareness
What is work density in a hysteresis loop?
µ0 ∫M.dH
= energy lost in the material by going around the loop
Spin and orbital magnetic moment equations?
µ_z,l = -e/2m * m_l * ℏ
µ_z,s = -e/m * m_s * ℏ
What does a skinny hysteresis loop mean?
Less energy lost
Why is Permalloy good for magnetic recording?
Easily magnetisable (soft)
What properties are good for permanent magnets?
High Ms and large Hc
Are Ms, Hc and Mr sample independent?
Only Ms
Does Ms depend on T?
Yes
When does Ms vanish?
At Tc - above which material becomes paramagnetic
What does the Bohr-van Leeuwen theorem show?
According to classical physics, there is no interaction between an applied field and the electrons in a material
Brief steps to show the BvL theorem?
(Model material as system of charges. Check affect of H as to whether M induced)
Electron energy: E = -µ.B = -µ.µ0H = -µBcosø
But m. field means Lorentz force F = q(E + vxB) - so the B always produces forces perp. to the velocity
No work is done by the magnetic field, so there is no change in energy
So µ ~ E/B doesn’t depend on m. field
How can exchange energy be estimated?
kTc
Why is there a discrepancy form g=2?
Because interactions are due to virtual photons. Electrons emit and reabsorb virtual photons if µ is measured during the lifetime of a virtual photon there is an extra orbital component
