MulPCalc: k-space spin density matrix resolved to each atom

MulPCalc can extract data to analyze the Mulliken population from AtomMulP files, MulP_xx files, AMulPBand files or AMulPBand_xx files obtained by kSpin. The executable file can be obtained by compilation in the directory 'source' as follows:

    % make MulPCalc

After the successful compilation, you will find the executable file 'MulPCalc' in the directory 'work'. Also, you find an example of an input file 'SiC_Primitive_BD.dat' in the directory 'work'. After the SCF calculation, please perform a BandDispersion calculation by 'kSpin' with the following settings:

    Filename.scfout    sic_primitive.scfout # default: default
    Filename.outdata   sic_primitive_BD     # default: default
    Calc.Type          BandDispersion       # default: MulPOnly
    Energy.Range       -10.0  6.0           # eV; default: 0.0  0.0

Next, please execute MulPCalc as

    % ./MulPCalc SiC_Primitive_BD.dat

with the following settings to extract data of $p_z$ orbitals on a carbon atom:

    Filename.atomMulP sic_primitive_BD.AMulPBand_p3 # default: default
    Filename.xyzdata   sic_primitive_BD_MC_C_p3     # default: default
    Num.of.Extract.Atom        1                 # default: 1
    Extract.Atom               1                 # default: 1 2 ... (Num.of.Extract.Atom)

In addtion, you can adjust data for making better figures by the following keywords and values:

    MulP.Vec.Scale       0.1  0.1  0.1           # default: 1.0  1.0  1.0
    Data.Reduction             2                 # default: 1

Figure 69 can be obtained by executing MulPCalc several times similarly and plotting extracted data of the eleventh, four, and fifth columns stored in MulPop files by using the circles style of gnuplot.

Figure 69: k-space spin density matrix resolved to each atom for the SiC primitive cell in a two-dimensional haneycomb structure without imperfection as explained in the subsection of 52.1 Analysis of band structures under the section of 52 Unfolding method for band structures. The green and purple circles represent the number of elecrons occupying $s$, $p_x$, and $p_y$ orbitals on a carbon atom, and that occupying $p_z$ orbitals on it, respectively. The radius reflects the magnitude of the number of electrons. Using MulPCalc, the data can be extracted from AMulPBand_xx files 'sic_primitive_BD.AMulPBand_s', 'sic_primitive_BD.AMulPBand_p1', 'sic_primitive_BD.AMulPBand_p2', or 'sic_primitive_BD.AMulPBand_p3' or 'sic_primitive_BD.AMulPBand_p'.

In addition, in the directory 'work', there is another example of an input file 'Au111Surface23_FL.dat' for a slab model with two clean Au(111) surfaces, which may take much more time than the other examples. You can try it similarly. After the SCF calculation and subsequent FermiLoop calculation, you may find the band dispersion and spin textures as shown in Figs. 70(a) and 70(b), respectively, where there are two pairs of Rashba bands, which are degenerated because one surface is equivalent to the other. In this case, you may need to obtain the contribution of atoms in one surface by MulPCalc. By using MulPCalc, you can get it and find spin texture in one surface as shown in Fig. 70(c).

Figure 70: (a) Band dispersion for the Rashba spin splitting at both the Au(111) surfaces stored in a Band file 'Au111Surface23.Band' (See the section of 53.4 BandDispersion). The red curves show the Rashba bands, which correspond to band indices 413, 414, 415 and 416. This highlight of the Rashba bands can be reproduced by modifing a GNUBAND file 'Au111Surface23.GNUBAND' or using OMXTool [146]. Spin textures for the Rashba spin splitting around $\Gamma$-point at (b) both the Au(111) surfaces and (c) one of the Au(111) surfaces. The vectors represent the expectation values of the Pauli matrices vectors at each k-point stored in Pxyz_YY files 'Au111Surface23_FL.Pxyz_413', 'Au111Surface23_FL.Pxyz_414', 'Au111Surface23_FL.Pxyz_415' and 'Au111Surface23_FL.Pxyz_416', and 'Au111Surface23_FL_MC.Pxyz_413', 'Au111Surface23_FL_MC.Pxyz_414', 'Au111Surface23_FL_MC.Pxyz_415' and 'Au111Surface23_FL_MC.Pxyz_416', respectively. The closed curves represent the constant-energy level stored in FermiSurf_YY files 'Au111Surface23_FL.FermiSurf_413', 'Au111Surface23_FL.FermiSurf_414', 'Au111Surface23_FL.FermiSurf_415' and 'Au111Surface23_FL.FermiSurf_416', and 'Au111Surface23_FL_MC.FermiSurf_413', 'Au111Surface23_FL_MC.FermiSurf_414', 'Au111Surface23_FL_MC.FermiSurf_415' and 'Au111Surface23_FL_MC.FermiSurf_416', respectively. The central cross point corresponds to $\Gamma$-point. You can get these figures by plotexample files 'Au111Surface23_FL.plotexample' and 'Au111Surface23_FL_MC.plotexample', respectively.

The specification of each keyword is explained below:

List of keywords (common) relevant to MulPCalc

Filename.atomMulP
Specify the name of an AtomMulP file, a MulP_xx file, an AMulPBand file or an AMulPBand_xx file.

Filename.xyzdata
Specify a name for output files. This keyword corresponds to the keyword 'System.Name'.

Num.of.Extract.Atom
Specify the number of atoms for which MulPCalc should extract data of the Mulliken population. The default is '1'.

Extract.Atom
Specify atoms for which MulPCalc should extract data of the Mulliken population. The default is '1 2 ... (the value for the keyword 'Num.of.Extract.Atom')'.

Data.Reduction
Specify the number of k-points every which MulPCalc should extract data of the Mulliken population. This keyword is useful in thinning out k-points or reducing data size.

MulP.Vec.Scale
Specify a scale to draw vectors expressing spin textures. For example, values '0.1 0.2 0.3' specifies the scale as follows: 0.1 for x-axis, 0.2 for y-axis, 0.3 for z-axis. The default is '1.0 1.0 1.0'.

Filename.outdata
Keep the specification in kSpin.

Calc.Type
Keep the specification in kSpin.

List of keywords (Calc.Type = FermiLoop or GridCalc) relevant to MulPCalc

Search.kCentral
Keep the specification in kSpin.

Calc.Type.3mesh
Keep the value in kSpin.

Energy.Range
Keep the value in kSpin.

List of keywords (Calc.Type = BandDispersion) relevant to MulPCalc

Energy.Range
Keep the value in kSpin.

Band.Nkpath
Keep the value in kSpin.

Band.kpath
Keep the value in kSpin.

List of keywords (Calc.Type = MulPOnly) relevant to MulPCalc

Calc.Type.3mesh
Specify a plane to calculate as follows: Set a value '1', '2', and , '3', for the case of $k_ak_b$-, $k_bk_c$-, and $k_ck_a$- planes, respectively. The default is '1'.

Output files

After the calculation by 'MulPCal' is completed normally, you obtain the following output files in the working directory'.

MulPop file
This file stores data for each k-point. The first, second, and third columns correspond to the $k_x$, $k_y$, and $k_z$ components of the k-points in units of Å$^{-1}$, respectively. The fourth column corresponds to the energy in units of eV; The fifth, sixth, and seventh columns correspond to the number of electrons: Total, $\alpha$-spin, and $\beta$-spin, respectively. The eighth, nineth, and tenth columns correspond to the expectation value of the $\sigma_x$, $\sigma_y$, and $\sigma_z$ in units of the Bohr magneton, respectively. If the value for the keyword 'Calc.Type' is 'BandDispersion', the eleventh column corresponds to the distance for the k-points along each k-path in units of Bohr$^{-1}$.

MulPop_YY file
This file stores data for each k-point with the band index YY. The notation of contents of this file is the same as the MulPop file.

plotexample file
If the value for the keyword 'Calc.Type' is not 'GridCalc', this file supplies an example of gnuplot scripts.

plotexample_YY file
If the value for the keyword 'Calc.Type' is 'GridCalc', this file supplies an example of gnuplot scripts for the band with the band index YY.