Module Tasks:

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Module Tasks:

As a single ion module, so1ion provides to mcphas the magnetic properties of a single rare earth ion subject to the crystal field. Its main duty is to calculate the magnetic moment given an effective magnetic field. To be more explicit - given the effective magnetic field $H^s_{eff}$ by mcphas the module so1ion diagonalises the crystal field and Zeeman Hamiltonian (9) of the ion :

$\begin{displaymath} {\mathcal H_n}= B_l^m O_{lm}({\mathbf J}^n) - g_{Jn} \mu_B {\mathbf J}^n {\mathbf H^n_{eff}} \end{displaymath}$

(9)

and calculates the expectation value of the angular momentum $\langle \mathbf J^n \rangle$ according to

$\begin{displaymath} \langle \mathbf J^n \rangle = \sum_{\Gamma} p_{\Gamma} \langle \Gamma \vert \mathbf J^n \vert \Gamma \rangle \end{displaymath}$

(10)

with

$\displaystyle p_{\Gamma}$	$\textstyle =$	$\displaystyle \frac{\exp(-E_{\Gamma}/kT)}{z}$	(11)
$\displaystyle z$	$\textstyle =$	$\displaystyle \sum_{\Gamma} \exp(-E_{\Gamma}/kT)$	(12)

Here is the partition sum, $\vert\Gamma\rangle$ the eigenstate corresponding to the eigenvalue $E_{\Gamma}$ of the Hamiltonian (9). ¹¹

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martin rotter 2013-09-19