Magnetic Susceptibility and Curie Temperature

In summary: This seems to be a good answer - although the magnetisation wouldn't be close to zero, it is just less than the theoretical prediction. So, perhaps some of the domains get nudged out of place, and become non-aligned to the majority of domains which are pointing in the same direction. I think this is the typical explanation for how a permanent magnet can lose its magnetisation when you knock it on a hard surface a few times.
  • #1
unscientific
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Homework Statement



Part(a): Derive susceptibility
Part(b): Find field experienced by neighbour.
Part(c): State temperature range. What explains temperature dependence beyond curie temperature? Why is curie temperature so high?
Part(d): In practice, measured magnetic moment is far lower than theoretical. Why?

2014_B6_Q4.png


Homework Equations

The Attempt at a Solution



Part (a)[/B]
Hamiltonian for an electron is given by ##H = g \mu_B \vec B \cdot \vec \sigma##. Thus, partition function is given by
[tex]Z = e^{-\beta \mu_B B} + e^{\beta \mu_B B}[/tex]
[tex]m = -\frac{\partial F}{\partial B} = \mu_B tanh(\beta \mu_B B)[/tex]
[tex]\chi = \frac{\partial M}{\partial H} = \frac{n \mu_0 \mu_B^2}{k_B T}[/tex]

Part(b)
[tex]H = \approx \frac{m}{4\pi r^3} [/tex]
[tex]\frac{B}{\mu_0} \approx \frac{e\hbar}{m_e r^3}[/tex]
[tex]B \approx 0.2 T[/tex]
This gives temperature of about ##0.13 K##.

Part(c)
I suppose this material is a ferromagnet. Therefore, is the temperature range simply ##0 < T < T_C##? I know that curie temperature is defined as the point where material loses its permament magnetization and instead has induced magnetization.
Not sure what they mean by "outline a simple model". Do they simply mean the Ising Model? The paramagnetic susceptibility is calculated to be ##\chi \propto (T-T_C)## in accordance to "Curie-Weiss Law".
Not sure why for some materials curie temperature is so high at ##T_C \approx 1000K##.

Part(d)
I suppose due to non-zero temperature, thermal fluctuations interfere with its permament magnetic moments, as higher temperatures make permament magnets weaker.
 
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  • #2
bumpp
 
  • #3
bumpp
 
  • #4
Why is curie temp so high?
 
  • #5
Any physical explanation as to why curie temperature in some metals are higher than others?
 
  • #6
bump?
 
  • #7
curie temperature? anyone?
 
  • #8
Hi, sorry slow reply. Yes, if we just consider magnetic field, it would seem the Curie temperature should be much lower. So there must be some other kind of interaction which causes the measured Curie temperature to be much higher. What kind of interaction could this be? hint: you have been using a semi-classical treatment so far.

Also, yeah, I'm not sure what they mean by outline a simple model... Maybe you can just state the model in part a). I guess they are asking for any model which fits the curve above Tc.
Edit: actually, no the model in part a) is not good enough, unless you put in some shift in the temperature... ah I'm not sure about this one.

For part d) I don't think that's the right answer... Presumably, they are talking about a theoretical model which already takes temperature into account. (although they don't specifically mention it). What are some other possible reasons. For example, how might the theoretical Ising model be different from a real-life crystal?
 
  • #9
BruceW said:
Hi, sorry slow reply. Yes, if we just consider magnetic field, it would seem the Curie temperature should be much lower. So there must be some other kind of interaction which causes the measured Curie temperature to be much higher. What kind of interaction could this be? hint: you have been using a semi-classical treatment so far.

Also, yeah, I'm not sure what they mean by outline a simple model... Maybe you can just state the model in part a). I guess they are asking for any model which fits the curve above Tc.
Edit: actually, no the model in part a) is not good enough, unless you put in some shift in the temperature... ah I'm not sure about this one.

For part d) I don't think that's the right answer... Presumably, they are talking about a theoretical model which already takes temperature into account. (although they don't specifically mention it). What are some other possible reasons. For example, how might the theoretical Ising model be different from a real-life crystal?

Is it because of the presence of "islands" of magnetic domains where each island points in such a way that the overall magnetization is close to zero?

image.png
 
  • #10
that sounds like a good answer. Although, the magnetisation would not be close to zero, it is just less than the theoretical prediction. So, perhaps some of the domains get nudged out of place, and become non-aligned to the majority of domains which are pointing in the same direction. I think this is the typical explanation for how a permanent magnet can lose its magnetisation when you knock it on a hard surface a few times.
 
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Related to Magnetic Susceptibility and Curie Temperature

1. What is magnetic susceptibility?

Magnetic susceptibility is a measure of the extent to which a material can be magnetized in the presence of an external magnetic field. It describes the degree to which a material is attracted to or repelled by a magnetic field.

2. How is magnetic susceptibility measured?

Magnetic susceptibility is typically measured using a device called a magnetic susceptibility balance. This instrument measures the force experienced by a sample when placed in a magnetic field and can then calculate the magnetic susceptibility of the sample.

3. What factors affect magnetic susceptibility?

The main factors that affect magnetic susceptibility are the composition and structure of a material. Materials with more unpaired electrons and a looser atomic structure tend to have a higher magnetic susceptibility.

4. What is the Curie temperature?

The Curie temperature is the temperature at which a material undergoes a phase transition from a ferromagnetic or ferrimagnetic state to a paramagnetic state. Above this temperature, the material will no longer exhibit permanent magnetization.

5. How is the Curie temperature related to magnetic susceptibility?

The Curie temperature is directly related to magnetic susceptibility. As a material approaches its Curie temperature, its magnetic susceptibility will decrease, and at the Curie temperature, it will become paramagnetic and have a magnetic susceptibility of zero.

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