Commit JT 102819

- corrected issue in Zeeman precession
- improved documentation of Zeeman interaction

doc/src/Eqs/fix_spin_zeeman.tex

@@ -5,7 +5,8 @@
 \begin{document}
 \begin{varwidth}{50in}
   \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{varwidth}
 \end{document}

doc/src/fix_precession_spin.txt

@@ -41,10 +41,37 @@ Style {zeeman} is used for the simulation of the interaction
 between the magnetic spins in the defined group and an external
 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
-in metal units).
+with:
+
+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
 for the magnetic spins in the defined group: