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CMP > 5.4 Magnetic Order > Flashcards

5.4 Magnetic Order Flashcards

1
Q

What two conditons must be allowed in order for spontaneous magnetisation to occur?

A
  • Spins on neighbouring atoms must be allowed to interact
  • Must be below a critical temperature
  • Allows for magnetisation in some materials even with no applied B field
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2
Q

Why can interacting spins between neighbours cause spontaneous magnetisation?

A

Due to the exchange interaction between the spins

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3
Q

Describe the pattern of the spins for a ferromagnet when T < T_c

A

All aligned with each other

  • Thermal fluctuations are small compared to the alignment energy
  • M is not 0
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4
Q

Describe the pattern of the spins for an antiferromagnet when T < T_N

A

Each neighbour has the opposite spin to another neighbour

  • Get same orientation along diagonals
  • Magnetic ordering
  • M = 0
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5
Q

Describe the pattern of the spins for an ferrimanget when T < T_c

A

Like an antiferromagnet, except the down spins are smaller in size than the up spins

  • 2 atoms in the basis anti align
  • M is NOT 0
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6
Q

What condition determines if we get ferromagnetism

A

If the exchange constant in the Hamiltonian, J_ij > 0

- Energy is lower if the spins align

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7
Q

What condition determines if we get antiferromagnetism

A

If the exchange constant in the Hamiltonian, J_ij < 0

- Energy is lower if the spins anti-align

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8
Q

How does considering the “nearest neighbour” model allow for simplification?

A

Sum over i,j and then extend this for the whole material

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9
Q

What is an easy axis?

A

A direction in a crystal which the spins like to align

- Creates an asymmetic environment in the crystal

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10
Q

What is a hard axis?

A

A direction in a crystal which the spins don’t like to align

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11
Q

When do we get an easy/hard axis?

A

Easy - Kappa (anisotropy) is > 0 as the spins want to be parallel to Z
Hard- Kappa (anisotropy) is < 0 as the spins want to be perpendicular to Z

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12
Q

Describe the Ising model

A

A special case where Kappa is large enough that spins only align along the Z axis
- Very simple model

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13
Q

Why is the Ising model very simple, and what is it useful for?

A

There is only one degree of freedom

- Useful for looking at phase transitions from one magnetic state to another

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14
Q

What is Weiss’ core assumption for his ferromagnetism model?

A

That spins align due to a molecular field that is proportional to the magnetism M

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15
Q

What wil happen to the magnetic moments in a ferromagnet at absolute 0?

A

They will all align

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16
Q

What happens to the magnetic moments as the temperature increases from absolute 0?

A

Thermal fluctuations start to have an increasing effect and will eventaully start to destroy the order

17
Q

In the spin 1/2 model, what are the solutions for M for low temperature?

A

3 solutions at 0 and ± the crossing point

- If M = 0, then any small fluctuations will move it to a non zero value. Not stable

18
Q

In the spin 1/2 model, what are the solutions for M for high temperature?

A

Only M = 0. No ordering at high temperatures

19
Q

In the spin 1/2 model, what are the solutions for M for Curie temperature?

A

Pass between two regimes. Have a similar sin(x) = x for small angles looking graph
- Valid in the paramagnetic (high temperature) state

20
Q

When is the Curie Weiss Law valid?

A

It is true just above T_c and in the paramagnetic state

21
Q

When do we use the spin J model?

A

When the spin is no longer 1/2

22
Q

Is the Curie Weiss law obeyed in the spin J model?

A

Yes, with a T_c that include the effects of J

23
Q

What is T_N?

A

The Neél temperature for antiferromagnetism

Above this, thermal effects dominate

24
Q

Describe how the Neél model for antiferromagnetism works

A

Split the crystal into two sub lattices

- One with diagonal spins up added to one with the diagonal spins down at B = 0

25
Q

How do the two sublattices interact for the Neél model?

A

Each sublattice experiences a molecular field proportional to the magnetism on the other sub lattice

26
Q

What happens to the magnetism at the Neél temperature for each sublattice?

A

It goes to 0

27
Q

How can we identify is a material is a magnet or not?

A
  • Measure the magnetic susceptability in the paramagnetic state
  • Fit it to χ ∝ 1 / (T - T_Weiss)
28
Q

Is the Weiss temperature is equal to 0, what type of magnet do we have?

A

A paramagnet

29
Q

Is the Weiss temperature is > 0, what type of magnet do we have?

A

Ferromagnet

30
Q

What is the critical temperature for a ferromagnet if the Weiss temp > 0?

A

T_c = T_Weiss

31
Q

Is the Weiss temperature is < 0, what type of magnet do we have?

A

Antiferromagnet

32
Q

What is the critical temperature for an antiferromagnet if the Weiss temp < 0?

A

T_c = - T_N

33
Q

What behaviour is observed at T = 0 and B is parallel to M?

A

Both sub lattices are saturated. The parallel components of both the magnetism and the magnetic susceptability are equal to 0

34
Q

What behaviour is observed at T = 0 and B is perpendicular to M?

A

The transverse/perp components of both B and M are not equal to 0
- The spins are tilted on both sub lattices

35
Q

What behaviour is observed at 0 < T < T_N and B is parallel to M_a?

A

M_a - sublattice with spins pointing upwards

  • B enhances M_a, reduces M_b
  • Strong effect on the susceptability
36
Q

What behaviour is observed at 0 < T < T_N and B is perpendicular to M?

A

The transverse/perp components of both B and M are not equal to 0
- The spins are tilted on both sub lattices

37
Q

What are M_a and M_b?

A

M_a is the sub lattice with spins up

M-B is the sub lattice with spins down

38
Q

How are the crysal atoms arranged in the rare earths?

A

In layers

CMP (23 decks)

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