Commit JT 102819

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\begin{document}

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  \begin{equation}

  \begin{equation}

    \bm{H}_{zeeman} = -\mu_{B}\mu_0\sum_{i=0}^{N}g_{i} \vec{s}_{i} \cdot \vec{H}_{ext} \nonumber 

    \bm{H}_{Zeeman} = -g \sum_{i=0}^{N}\mu_{i}\, 

    \vec{s}_{i} \cdot\vec{B}_{ext} \nonumber

  \end{equation}

  \end{equation}

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between the magnetic spins in the defined group and an external

between the magnetic spins in the defined group and an external

magnetic field:

magnetic field:

:c,image(Eqs/force_spin_zeeman.jpg)

:c,image(Eqs/fix_spin_zeeman.jpg)

with mu0 the vacuum permeability, muB the Bohr magneton (muB = 5.788 eV/T

with:

in metal units).

Bext the external magnetic field (in T) :ulb,l

g the Lande factor (hard-coded as g=2.0) :l

si the unitary vector describing the orientation of spin i :l

mui the atomic moment of spin i given as a multiple of the

Bohr magneton muB (for example, mui ~ 2.2 in bulk iron).  :l

:ule

The field value in Tesla is multiplied by the gyromagnetic

ratio, g*muB/hbar, converting it into a precession frequency in

rad.THz (in metal units and with muB = 5.788 eV/T).

As a comparison, the figure below displays the simulation of a

single spin (of norm mui = 1.0) submitted to an external

magnetic field of |Bext| = 10.0 Tesla (and oriented along the z

axis). 

The upper plot shows the average magnetization along the

external magnetic field axis and the lower plot the Zeeman

energy, both as a function of temperature.

The reference result is provided by the plot of the Langevin 

function for the same parameters.

:c,image(JPG/zeeman_langevin.jpg)

The temperature effects are accounted for by connecting the spin

i to a thermal bath using a Langevin thermostat (see 

"fix_langevin_spin"_fix_langevin_spin.html for the definition of 

this thermostat).

Style {anisotropy} is used to simulate an easy axis or an easy plane

Style {anisotropy} is used to simulate an easy axis or an easy plane

for the magnetic spins in the defined group:

for the magnetic spins in the defined group: