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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?
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.