Lectures 5&6 (Stoner Criterion, Slater-Pauling Curve & Rare Earth FMs)

Question 1

Why does anisotropic exchange occur?

Answer 1

Spin orbit interaction

Question 2

Show how spin-orbit interaction arises, from a nucleus orbiting an electron.

Answer 2

+vely charged particle forms current loop In=zv/2πr

This creates magnetic field B=µIn/2r => B_SOI=µ0Zv/4πr^3

Which acts on electron spin

And acts M direction

Question 3

What does SOI lead to?

Answer 3

Competition between exchange interaction (driving spins parallel)

Or H = -D(s1xs2)

Question 4

Hamiltonian for anisotropic exchange mean for angle between spins?

Answer 4

Prefers 90º between for lowest energy

Question 5

Where do we see the Hamiltonian for anisotropic exchange coming in?

Answer 5

Thin layer systems

Question 6

What is Pauli PM?

Answer 6

Splitting down from up by ∆E, transfer down electrons to now vacant up levels

So end up with PM

Question 7

What field to add in to derive stoner criterion?

Answer 7

M = Xp(H+Hm) = Xp(H+λM)

(exchange field)

Question 8

Stoner factor?

Answer 8

1 / (1-Ig(Ef))

Question 9

When does exchange enhance PM?

Answer 9

Ig(Ef) > 1

Question 10

What happens to X when the Stoner criterion equals 1?

Answer 10

It diverges and we have spontaneous FM

Question 11

According to Stoner criterion, what do we need to get FM?

Answer 11

Large λ and large g(Ef)

Question 12

Which materials satisfy the Stoner criterion?

Answer 12

Fe, Co, Ni only

Question 13

What is a strong FM?

Answer 13

If the splitting is sufficient to push one spin d-band below Ef completely

Question 14

Is Fe a strong FM?

Answer 14

No. But it has the largest magnetisation

Question 15

Why do Fe, Co, Ni not have µ of 4, 3, 2?

Answer 15

Band (itinerant FM)

Question 16

Do Hund’s rules apply to 3d FM?

Answer 16

No