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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.