General

In this subsection, the calculation of spin textures is illustrated with a simple model of an Au(111) surface. The spin texture/k-space spin density matrix are analyzed by the following two or three steps:

1. SCF calculation

First, please perform a conventional SCF calculation using an input file 'Au111Surface_FL.dat' stored in the directory 'work'. Then, the following keywords 'scf.SpinPolarization' and 'HS.fileout' should be switched to 'NC' and 'ON', respectively, as follows:

    scf.SpinPolarization         NC    # On|Off|NC
    HS.fileout                   ON    # on|off, default=Off

Also, when you consider to investigate spin texture, the keyword 'scf.SpinOrbit.Coupling' should be switched on:

    scf.SpinOrbit.Coupling       ON    # On|Off

Once the calculation is completed normally, you can obtain an output file 'Au111Surface.scfout' in the directory 'work'. Figure 64 shows the band structure of the Au(111) surface.

Figure 64: Band structure for the Rashba spin splitting at the Au(111) surface. This figure is obtained by a Band file 'Au111Surface.Band' (See the section of 19 Band dispersion). The red curves show the Rashba bands, which correspond to band indices 55 and 56. This highlight of the Rashba bands can be reproduced by modifing a GNUBAND file 'Au111Surface.GNUBAND' or using OMXTool [146].

2. Calculation of the spin texture and k-space spin density matrix

Let us analyze Rashba bands with a spin splitting shown in Fig. 64. The spin texture and k-space spin density matrix are calculated by a post-processing code 'kSpin'. The executable file can be obtained by compilation in the directory 'source' as follows:

    % make kSpin

After the successful compilation, you can find the executable file 'kSpin' in the directory 'work'. Then, please move to the directory 'work', and perform as follows:

    % ./kSpin Au111Surface_FL.dat

Note that the input file must include appropriate keywords about 'kSpin', which will be explained later on. 'kSpin' has four ways to calculate the k-space spin density matrix: FermiLoop, GridCalc, BandDispersion, and MulPOnly. The details of the four ways are provided in each subsection. The example 'Au111Surface_FL.dat' is for FermiLoop so that you can proceed with this exercise by moving to the subsection of 53.2 FermiLoop.

3. (Optional) Analysis of the k-space spin density matrix

You may need to analyze the k-space spin density matrix, or atomic decomposition of it. Moreover, it can be decomposed into the $s$-, $p$-, $d$-, or $f$-character components. You can use a post-processing code 'MulPCalc' to analyze the k-space spin density matrix resolved atom and pseudo-atomic orbital. How to do that will be explained in the subsection of 53.6 MulPCalc.