:math:`\alpha`-Fe with ferromagnetic calculation
------------------------------------------------
In this example, you will learn how to perform a ferromagnetic
DFT+G calculation using Wien2k plus CyGutz packages,
including some typical post-analyses.

1) Finish a self-consistent LDA paramagnetic calculation (run_lapw) 
    for :math:`\alpha`-Fe (bcc) using Wien2k.
    Here is the structure file
    :download:`Fe.struct <./_files/Fe.struct>`. 
    To compare with the provided results, 
    one should keep the R\ :sub:`MT` = 2.33 as specified in the Fe.struct,
    R\ :sub:`MT` * K\ :sub:`MAX` = 8.0 and total 
    number of k-points = 5000 (17x17x17). 
    We do not shift k-points here.
    In the end, check the total LDA energy in the `Fe.scf` file, 
    which should be close to -2541.12378 Ryd. 

2) Use the following command to initialize the Gutzwiller calculation,
    Type::

        $ ${WIEN_GUTZ_ROOT2}/init_ga.py 

    Answer the questions as follows:

    * Do you want to BREAK SPIN-SYMMETRY: y
    * Do you want to COMPLETELY break orbital-symmetry: n
    * Do you want to take into account the SPIN-ORBIT interaction: n
    * Do you want to take into account the CRYSTAL FIELD effect: y
    * Please select the method to parametrize Coulomb U-matrix: 1
    * Please select method for U-interaction double counting: 12
    * Symmetrically-equivalent atom indices ...: y
    * Enter up(1) dn(-1) or 0 for spin-moment of the atoms: 1
    * Is this atom correlated: y
    * Enter correlated shells: d
    * Please provide interaction parameters U,J: 7.0 0.8
    * Please provide initial guess ... localized d-electrons: 6.5
    * Please select the method to solve G-RISB equations: 0
    * Please select the method to solve embedding Hamiltonian: -1

    Check the file `init_ga.slog` and you will see that 
    the local self-energy structure has the following form 
    in the single-particle basis with spin (up,down) 
    as the faster index::

        [[1 0 0 0 0 0 0 0 0 0]
         [0 3 0 0 0 0 0 0 0 0]
         [0 0 1 0 0 0 0 0 0 0]
         [0 0 0 3 0 0 0 0 0 0]
         [0 0 0 0 1 0 0 0 0 0]
         [0 0 0 0 0 3 0 0 0 0]
         [0 0 0 0 0 0 2 0 0 0]
         [0 0 0 0 0 0 0 4 0 0]
         [0 0 0 0 0 0 0 0 2 0]
         [0 0 0 0 0 0 0 0 0 4]]

    Different integers are used for the spin-up and down conponents, 
    inidcating spin-polarization. 
    The self-energy is diagonal due to cubic symmetry.
    
    To set up the magnetic configuration, type::

        $ ${WIEN_GUTZ_ROOT2}/init_magnetism.py

    Answer the questions as follows:

    * enter spin up or down: up
    * please enter the magnitude of the field: 0.3
    * Is the external field applied only at initial step (0) ...: 0

    Here we add a 0.3 eV/Bohr magneton local magnetic field to 
    break spin symmetry **INITIALLY**.

3) Type the command below to 
    run the DFT+G calculation::

        $ ${WIEN_GUTZ_ROOT2}/run_ga.py

    After convergence, check the total energy in `Fe.scf` file, 
    which should be close to -2540.94918 Ryd. 
    You can also find ``total magnetic moment`` = 2.14
    in the main output text file `GUTZ.LOG`.

4) To plot the spin-resolved density of states 
    with overall Fe-3d character, type::

        $ ${WIEN_GUTZ_ROOT2}/plot_dos_tf.py

    you will get figure as below

    .. image:: _images/fe_dos.png
       :alt: alternate text
       :scale: 100 %
       :align: center

6) To calculate the bands structure along selected k-path, 
    follow the steps below:

    (a) Prepare the fe.klist_band file for the high-symmetry k-path 
        of the primitive Brillouin Zone. 
        The SRC_templates directory of Wien2k has some examples.
        For instance, we can use `bcc.klist` file.
        Type the command to get the file::

            $ cp ${WIENROOT}/SRC_templates/bcc.klist Fe.klist_band

    (b) Type the following command 
        to calculate the band structure::

            $ ${WIEN_GUTZ_ROOT2}/run_ga.py -band

    (c) To plot spin-resolved band structure with Fe-3d character,
        type::

            $ ${WIEN_GUTZ_ROOT2}/plot_band_tf.py -h # help info
            $ ${WIEN_GUTZ_ROOT2}/plot_band_tf.py -el -8 -eh 10

        You will see the band structure like the following

        .. image:: _images/fe_bands.png
          :alt: alternate text
          :scale: 100 %
          :align: center