Lectures 1&2 (Basics, FM & Bohr-van Leeuwen)

Question 1

What is magnetisation?

Answer 1

Response of a material due to an applied magnetic field

Question 2

Flux density inside solenoid?

Answer 2

B = µ0 IN/L

(so H = IN/L)

Question 3

Magnetic moment equation?

Answer 3

µ = MV

Question 4

µ units?

Answer 4

Am^2

Question 5

Angular momentum equation for an electron?

Answer 5

l = m_e * r x v

Question 6

How is M defined?

Answer 6

Magnetic moment per unit volume

Question 7

Show that magnetic moment µ can be given in terms of the angular momentum l of the electron

Answer 7

l = m_e * r x v

and µ = -e/2 * r x v

µ = - e/2m * l

Question 8

Equation for µ in terms of orbital angular momentum?

Answer 8

µ = γl

Question 9

γ value?

Answer 9

γ = -e/2m or -ge/2m for > 1 electron

Question 10

Show that Bohr magneton comes from magnetic moment and orbital angular momentum

Answer 10

µ = -e/2m * l

µ_z = -e/2m * m_l * ℏ

µ_B = eℏ/2m

Question 11

Show that µ = µ0(1+X)

Answer 11

B = µ0(H+M) = µ0(H+XH) = µ0H(1+X) = µH

where µ = µ0(1+X)

Question 12

Which materials experience diamagnetism?

Answer 12

All

Question 13

Susceptibility of a diamagnet?

Answer 13

X < 0

Question 14

How do diamagnets react to magnetic fields?

Answer 14

Weakly repelled

(A small opposite moment is induced due to Lenz’s law)

Question 15

What gradient does a diamagnet have on the M vs H graph?

Answer 15

-ve

Question 16

Susceptibility of a paramagnet?

Answer 16

X > 0

Question 17

How do paramagnets react to magnetic fields?

Answer 17

Weakly attracted

Moments not aligned in absence of H_ext

Question 18

Which materials experience paramagnetism?

Answer 18

Those with net angular momentum on each atom

Question 19

Why does a FM remain magnetised at H=0?

Answer 19

Exchange interaction and anisotropy

Question 20

X of FM?

Answer 20

X_eff = ∂M/∂H

Question 21

What is Ms?

Answer 21

Magnetisation of the sample when all domains are aligned and characteristic of the material

Question 22

What is Mr?

Answer 22

Remanent magnetisation is that at zero field, and can depend on the sample

Question 23

What is Hc?

Answer 23

The coercive field (coercivity) is the reverse field that needs to be applied to zero magnetisation

Question 24

What is Mr/Ms?

Answer 24

Remanent fraction / loop squareness

Question 25

What is work density in a hysteresis loop?

Answer 25

µ0 ∫M.dH

= energy lost in the material by going around the loop

Question 26

Spin and orbital magnetic moment equations?

Answer 26

µ_z,l = -e/2m * m_l * ℏ

µ_z,s = -e/m * m_s * ℏ

Question 27

What does a skinny hysteresis loop mean?

Answer 27

Less energy lost

Question 28

Why is Permalloy good for magnetic recording?

Answer 28

Easily magnetisable (soft)

Question 29

What properties are good for permanent magnets?

Answer 29

High Ms and large Hc

Question 30

Are Ms, Hc and Mr sample independent?

Answer 30

Only Ms

Question 31

Does Ms depend on T?

Answer 31

Yes

Question 32

When does Ms vanish?

Answer 32

At Tc - above which material becomes paramagnetic

Question 33

What does the Bohr-van Leeuwen theorem show?

Answer 33

According to classical physics, there is no interaction between an applied field and the electrons in a material

Question 34

Brief steps to show the BvL theorem?

Answer 34

(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

Question 35

How can exchange energy be estimated?

Answer 35

kTc

Question 36

Why is there a discrepancy form g=2?

Answer 36

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