Magnetics- Effects of Temperature

Question 1

What does increasing temperature do for a ferromagnetic material?

Answer 1

Reduces the magnetisation (Ms) of it and becomes zero a a critical temperature (Curie temperature Tc)

Question 2

Graph of M/M0 vs T/Tc

Answer 2

M0 is saturation magnetisation at zero K. Curves down form 1 getting steeper until M/M0 is 0 at T/Tc=1 (almost vertical here)

Question 3

Curie’s law

Answer 3

χ=C/T

Where C is constant (see paramagnetism)

Question 4

Weiss theory for ferromagnetism

Answer 4

Ferromagnets have interactions that causes spontaneous alignment of atomic moments. This is the exchange interaction and can be thought of as an internal molecular field Hw that aligns the spins. Formula is Hw=γM

Question 5

Two expressions for M as function of T

Answer 5

M=kBTα/μ0mγ (B subscript)

M=NmL(α) (paramagnetism)

Question 6

How to solve two expressions for M in terms of T graphically

Answer 6

The M=NmL(α) graph starts steepest then curves until horizontal (M vs α). The M=kBTα/μ0mγ lines have increasing gradient with temperature. Line will intersect curve until Tc is reached and there is no solution other than at the origin where M=0

Question 7

What happens to ferromagnets above Tc?

Answer 7

They become paramagnetic. So χ=M/H becomes:
χ=M/(H+Hw)=M/(H+γM)=C/T
Rearrange to get Curie-Weiss law:
M/H=C/(T-Tc)

Question 8

What does temperature above 0K do to ferromagnets?

Answer 8

The temperature causes random fluctuations in atomic moment alignments. This results in gradual loss in magnetisation although each atomic moment retains its strength.

Question 9

How does increasing temperature affect MAZE?

Answer 9

Magnetostatic reduces through reduction in Ms.
Magnetocrystalline anisotropy May change as interatomic spacing changes due to thermal expansion.
Zeeman energy reduces as Ms decreases.
Exchange may change due to changes in interatomic spacing but is usually limited effect

Question 10

How does coercivity change with T?

Answer 10

Decreases linearly with increasing T

Question 11

How does temperature affect domain nucleation?

Answer 11

There is an energy barrier in the new magnetic domain in direction of applied field. Thermal fluctuations help to overcome energy barrier by increasing the probability of overcoming the energy barrier. Increasing the magnetic field reduced the energy barrier so increased temperature allows switching at lower magnetic fields.

Question 12

How does temperature affect domain wall pinning?

Answer 12

The domain walls are in energy (potential) wells at defects and need additional energy to overcome pinning. Temperature increases probability of overcoming this energy barrier

Question 13

Arrhenius-Néel law

Answer 13

τ=(1/f0)exp(ΔE/kBT)
Where τ is average switching time.
f0 (subscript) is attempts per second to overcome energy barrier by vibrations in magnetic ordering.
ΔE is energy barrier
kBT (B subscript) is thermal energy

Question 14

What can be deduced from Arrhenius-Néel law?

Answer 14

Higher energy barriers (low field) give longer switching times.
Low energy barriers (high field) give shorter switching times.
Higher temperatures give shorter switching times so switching at higher energy barriers (lower fields) becomes more likely.

Question 15

How does a hysteresis loop change for greater temperature?

Answer 15

Area enclosed smaller. Coercivity and remanence both lower