Magnetism of Solids: Homework Solutions for Fe2+

[decerto]

Homework Statement

2. Homework Equations

$\mathcal{X}=\frac{\mu^2_BNg^2_j}{3k_BT}J(J+1)=\frac{C}{T}$

$M=\mathcal{X}H$

The Attempt at a Solution

[/B]
$Fe^{2+}$ has a value 4 of J from hunds rules.

So I know what the curie factor for iron is

$M=\frac{m}{V}=\frac{HC}{T}$

$m=\frac{HVC}{T}$

I don't know how I am supposed to treat the sample, assuming that MgO has a temp independent, diamagnetic susceptibility means that the changing magnetic moment is just from the iron but I am not sure how to use this?

 

[Simon Bridge]

You will need to think around the subject for a bit to seek inspiration.
i.e. if you were to plot a graph of magnetic moment vs temp - what sort of curve would the MgO alone get you? What sort of curve for Fe aone? What sort of shape is the combined curve likely to be?
What happens to the magnetic moment of the sample as the temperature increases? Describe in terms of the relative moments of the MgO and the Fe.

 

[decerto]

You will need to think around the subject for a bit to seek inspiration.
i.e. if you were to plot a graph of magnetic moment vs temp - what sort of curve would the MgO alone get you? What sort of curve for Fe aone? What sort of shape is the combined curve likely to be?
What happens to the magnetic moment of the sample as the temperature increases? Describe in terms of the relative moments of the MgO and the Fe.

Drawing the graph helped, thanks, the combined graph goes as 1/T and tends towards the magnetic moment of MgO as T increases.

What do you mean by "Describe in terms of the relative moments of the MgO and the Fe."?

Also what should I try to be working out, the susceptibility of Mg0, the volumes?

The equation for the curve I have is

$m_{total}=HV_{FE}\frac{C}{T}+HV_{MgO}\mathcal{X}_{MgO}$

$m_{total}=H(V_{FE}\frac{C}{T}+V_{MgO}\mathcal{X}_{MgO})$

 

[Simon Bridge]

You are supposed to be working out the mass ratio...

 

[decerto]

You are supposed to be working out the mass ratio...

I'm aware of that but I can't see how to get to it, I have a formula with volume in it due to the magnetization/magnetic moment relation which I don't know how to deal with.