\(\alpha\)-Ce with spin-orbit interaction

In this example, you will learn how to perform a DFT+G calculation using Wien2k plus CyGutz packages, including some typical post-analyses.

1. Finish a self-consistent lapw + spin-orbit calculation

   for \(\alpha\)-Ce using WIEN2k. Please follow the following steps:

   1. create a directory with name ‘Ce’, change to that directory, and download the structure file Ce.struct.

   2. type the following command to initialize the wien2k job:

      $ ${WIENROOT}/init_lapw
      

      use the answers below for the questions:

      • Enter reduction in %: enter (choose default)
      • Use old or new scheme (o/N): enter
      • Do you want to accept these radii… (a/d/r): enter
      • nn (14:13:54) specify nn-bondlength factor: enter
      • continue with sgroup or edit the Ce.struct file (c/e): enter
      • continue with symmetry (old case.struct) …: enter
      • continue with lstart or edit the Ce.struct_st file (c/e/x): enter
      • Eventually specify switches for instgen_lapw: enter
      • lstart … SELECT XCPOT: 5
      • SELECT ENERGY to separate core and valence states: -6.0
      • continue with kgen or edit the Ce.inst file … (c/e): enter
      • in 2nd line of Ce.in1_st file, change 7.00 (R-MT*K-MAX) to 9.00
      • kgen NUMBER OF K-POINTS IN WHOLE CELL: 5000
      • continue with dstart or execute kgen again or exit (c/e/x): enter
      • do you want to perform a spinpolarized calculation ? (n/y): n

   3. type the following command to run lapw job:

      $ ${WIENROOT}/run_lapw
      

      check the last line of Ce.scf file, which should give a LDA total energy close to -17717.65311 Ryd.

   4. type the following command to add spin-orbit interaction:

      $ ${WIENROOT}/initso_lapw
      

      use the answers below for the questions:

      • Please select the direction of the moment ( h k l ): enter
      • for which you would NOT like to add SO interaction: enter
      • Please enter EMAX(default 5.0 Ryd): 7.5
      • Add RLO for NONE, ALL, CHOOSE elements? (N/a/c) : enter
      • in Ce.inso file, change the 3rd line by replacing 1.5 with 4.5 (Emax)
      • Do you have a spinpolarized case …: enter

   5. type the following command to run lda calculation with spin-orbit:

      $ ${WIENROOT}/run_lapw -so
      

      check the last line of Ce.scf file, which should give a LDA+so total energy close to -17717.67370 Ryd. Use the following command to save the result:

      $ ${WIENROOT}/save_lapw -d lapwso
      

2. We are ready to initialize the DFT+G calculation.

   Type:

   $ ${WIEN_GUTZ_ROOT2}/init_ga.py
   

   Use the following answers or the questions:

   • Do you want to BREAK SPIN-SYMMETRY: n
   • Do you want to COMPLETELY break orbital-symmetry: n
   • Do you want to take into account the SPIN-ORBIT interaction: y
   • Do you want to take into account the CRYSTAL FIELD effect: n
   • Please select the method to parametrize Coulomb U-matrix: 1
   • Please select method for U-interaction double counting: 12
   • Symmetrically-equivalent atom indices …: y
   • atom 0 Ce:
     • Is this atom correlated: y
     • Enter correlated shells: f
     • Please provide interaction parameters U,J … (eV): 6.0 0.7
     • Please provide initial guess … of localized f-electrons: 1.0
   • Please select the method to solve G-RISB equations: 0
   • Please select the method to solve embedding Hamiltonian: -1

   Thus it finishes the setup of all the necessary files for CyGutz. The main output file of the initialization is stored in init_ga.slog file. The user-provided entries is stored in HDF5 file ginit.h5 for the convenience of re-initialization.

3. To run the DFT+G calculation,

   type:

   $ ${WIEN_GUTZ_ROOT2}/run_ga.py
   

   Check the last line of Ce.scf file, which should give a LDA+so+G total energy close to -17717.60065 Ryd. The main output message of CyGutz calculation is printed in GUTZ.LOG file in text format. The DFT+G calculation can be saved using the following commands:

   $ ${WIEN_GUTZ_ROOT2}/save_ldag -d lapwg
   

4. Let us learn how to plot the density of states of Ce

   after the self-consistent DFT+G calculation. To plot density of states with Ce-4f character, type:

   $ ${WIEN_GUTZ_ROOT2}/plot_dos_tf.py -h # help info
   $ ${WIEN_GUTZ_ROOT2}/plot_dos_tf.py -el -3.0 -eh 5.0
   

   you will get dos like

   

   The above scirpt calls a predefined functions, which serves a s a template to be adapted by users for specific purposes.

5. Another important analysis is the eigen-values of

   the local reduced many-body density matrix using the exponential form \(\rho=e^{-F}\), as shown in the figure below:

   

   Follow the steps below to get the analysis done for the first impurity.

   1. type:

      $ ${WIEN_GUTZ_ROOT2}/exe_spci_j2_mott_analysis 1
      

   2. Use plot_hist_ce.py to plot by typing:

      $ python ./plot_hist_ce.py
      

   The above scirpt calls two predefined functions, which serves a s a template to be adapted by users for specific purposes.

6. To calculate the bands structure along selected k-path,

   follow the steps below:

   1. Prepare the Ce.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 fcc.klist file. Type the command to get the file:

      $ cp ${WIENROOT}/SRC_templates/fcc.klist Ce.klist_band
      

   2. Type the following command to calculate the band structure:

      $ ${WIEN_GUTZ_ROOT2}/run_ga.py -band
      

   3. To plot the band structure with Ce-3f character, type:

      $ ${WIEN_GUTZ_ROOT2}/plot_band_tf.py -h # help info
      $ ${WIEN_GUTZ_ROOT2}/plot_band_tf.py
      

      You will see the band structure like the following

      

      The above scirpt calls a predefined function, which serves a s a template to be adapted by users for specific purposes.