Next: MulPCalc: k-space spin density Up: Analysis of spin texture Previous: BandDispersion: Calculation on the Contents Index
'kSpin' has four ways to calculate the k-space spin density matrix, which can be specified by a keyword 'Calc.Type'. Here we introduce MulPOnly among the four ways. MulPOnly can calculate the k-space spin density matrix on user-specified k-points for user-specified bands. The calculation of spin texture using MulPOnly and MulPCalc is illustrated here with a simple model of an Au(111) surface.
After a calculation of OpenMX with an input file 'Au111Surface_MO.dat' stored in the directory 'work', you may try to run 'kSpin'. The keywords relevant to the executation of kSpin can be found at the bottom of the input file 'Au111Surface_MO.dat' stored in the directory 'work' as shown below:
List of keywords relevant to kSpin
Filename.scfout Au111Surface.scfout
Filename.outdata Au111Surface_MO
Calc.Type MulPOnly # FermiLoop, GridCalc,
BandDispersion, or MulPOnly
default: MulPOnly
Filename.kpointdata kpoint.in
In addition, another input file, whose file name is specified by the keyword 'Filename.kpointdata', is required to
specify k-points on which the k-space spin density matrix is calculated by MulPOnly.
For the exercise, the file 'kpoint.in' is stored in the directory 'work'.
The notation follows the following rule: In the first row, you need to specify the number of k-points
where MulPOnly will calculate the k-space spin density matrix.
Then, specify a k-point (the first, second, and third columns correspond to 
, 
, and 
, respectively, in Bohr-1.)
and a band index (the fourth column) for it.
The file 'kpoint.in' stores information of the k-points on the circle around the 
-point in the reciprocal space.
For example, you can prepare this file as follows:
rm -f kpoint.in && awk '{for (i=0; i<$1; i++){printf "%17.14f %17.14f %17.14f %d\n", 0, $2*cos(2*atan2(0, -1)/$1*i),
$2*sin(2*atan2(0, -1)/$1*i), $3 >> "buffer"}; sum+=$1; if (!$1) {print sum; exit}}' - > N.in && cat N.in buffer >> kpoint.in && rm N.in buffer
After that, if you give values as follows:
40 0.18 55 <- # of k-points; radius; state (band index) (outer circle in k-space) 40 0.15 56 <- # of k-points; radius; state (band index) (inner circle in k-space) 0 <- exitThen, you will get 'kpoint.in' and you can see the content of 'kpoint.in' as follows:
% cat kpoint.in 80 0.00000000000000 0.18000000000000 0.00000000000000 55 0.00000000000000 0.17778390130712 0.02815820370724 55 0.00000000000000 0.17119017293313 0.05562305898749 55 0.00000000000000 0.16038117435391 0.08171828995312 55 0.00000000000000 0.14562305898749 0.10580134541265 55 0.00000000000000 0.12727922061358 0.12727922061358 55 0.00000000000000 0.10580134541265 0.14562305898749 55 0.00000000000000 0.08171828995312 0.16038117435391 55 0.00000000000000 0.05562305898749 0.17119017293313 55 0.00000000000000 0.02815820370724 0.17778390130712 55 0.00000000000000 0.00000000000000 0.18000000000000 55 0.00000000000000 -0.02815820370724 0.17778390130712 55 ... ..
Specification of keywords
The specification of each keyword is explained below:
Filename.scfout
Specify the name of the scfout file which will be read by 'kSpin'.
Filename.outdata
Specify a name for output files. This keyword corresponds to the keyword 'System.Name'
for OpenMX calculations.
Calc.Type
Choose either FermiLoop, GridCalc, BandDispersion, or MulPOnly.
The default setting is MulPOnly. Here we choose MulPOnly for the exercise.
Filename.kpointdata
Specify the name of an data file of k-points and band indices.
Calculation
The k-space spin density matrix resolved to each atom is calculated by a post-processing code 'kSpin' in the directory 'work'. Please move to the directory 'work', and perform a calculation as follows:
% ./kSpin Au111Surface_MO.dat
or for the MPI calculation, for example, the case with 4 MPI processes
% mpirun -np 4 ./kSpin Au111Surface_MO.dat
As the calculation proceeds, you may see the following standard output:
******************************************************************
******************************************************************
kSpin:
code for evaluating spin related properties
in momentum space of solid state materials.
Copyright (C), 2019,
Hiroki Kotaka, Naoya Yamaguchi and Fumiyuki Ishii.
This software includes the work that is distributed
in version 3 of the GPL (GPLv3).
Please cite the following article:
H. Kotaka, F. Ishii, and M. Saito,
Jpn. J. Appl. Phys. 52, 035204 (2013).
DOI: 10.7567/JJAP.52.035204.
******************************************************************
******************************************************************
Input filename is "Au111Surface.scfout"
Start "MulPOnly" Calculation (6).
########### ORBITAL DATA ##################
ClaOrb_MAX[0]: 2
ClaOrb_MAX[1]: 8
Total Band (2*n): 124
###########################################
############ CALC TIME ####################
Total Calculation Time: 0.642631 (s)
###########################################
############ CALC TIME ####################
Total Calculation Time: 0.660566 (s)
###########################################
When the calculation is completed normally as shown above, you can find the following output files in the directory 'work':
Au111Surface_MO.AtomMulP
Au111Surface_MO.MulP_s
Au111Surface_MO.MulP_p
Au111Surface_MO.MulP_p1
Au111Surface_MO.MulP_p2
Au111Surface_MO.MulP_p3
Au111Surface_MO.MulP_d
Au111Surface_MO.MulP_d1
Au111Surface_MO.MulP_d2
Au111Surface_MO.MulP_d3
Au111Surface_MO.MulP_d4
Au111Surface_MO.MulP_d5
Au111Surface_MO.atominfo
temporal_12345.input
Output files
The content of each output file is explained below:
AtomMulP file
This file stores data of the k-space spin density matrix resolved to each atom,
and can be analyzed by 53.6 MulPCalc.
MulP_xx file
This file stores data of the xx-component of the k-space spin density matrix resolved to each atom,
and can be analyzed by 53.6 MulPCalc.
atominfo file
This file supplies information of lattice vectors and PAOs.
temporal_12345.input
This file is a copy of the input file stored in the scfout file.
Analysis of the k-space spin density matrix resolved to each atom
MulPCalc can extract data to analyze the k-space spin density matrix resolved to each atom from AMulPBand files or AMulPBand_xx files. The executable file can be obtained by compilation in the directory 'source' as follows:
% make MulPCalc
After the successful compilation, you can find the executable file 'MulPCalc' in the directory 'work'.
Let us analyze spin textures for the Rashba spin splitting in the Au(111) surface. First, add the following
keywords and values into the input file 'Au111Surface_MO.dat', for example:
Filename.atomMulP Au111Surface_MO.AMulPBand # default: default
Filename.xyzdata Au111Surface_MO_MC # default: default
Num.of.Extract.Atom 3 # default: 1
Extract.Atom 1 2 3 # default: 1 2 ... (Num.of.Extract.Atom)
Calc.Type.3mesh 2 # default: 1
And, after the above calculation, you can analyze spin textures as follows:
% ./MulPCalc Au111Surface_MO.dat
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 1 # default: 1
After executing MulPCalc, you can find the following output files in the directory 'work'.
Au111Surface_MO_MC.MulPop
Au111Surface_MO_MC.MulPop55
Au111Surface_MO_MC.MulPop56
Au111Surface_MO_MC.plotexample
As an example, by executing the following command, you can obtain a figure of spin textures for the Rashba
spin splitting in the Au(111) surface as shown in Fig. 68.
% gnuplot Au111Surface_MO_MC.plotexample
For more information of MulPCalc, see also the subsection of 53.6 MulPCalc.
![\includegraphics[width=10.0cm]{Rashba-Fig-MulPOnly.eps}](img434.png)
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