1. KKR GREEN’S FUNCTION
METHOD
MACHIKANEYAMA2000
(AKAIKKR)
KKR Hands-On

2. c----------------------Fe------------------------------------
go data/fe
c------------------------------------------------------------
c brvtyp a c/a b/a alpha beta gamma
bcc 5.27 , , , , , ,
c------------------------------------------------------------
c edelt ewidth reltyp sdftyp magtyp record
0.001 1.0 nrl mjw mag 2nd
c------------------------------------------------------------
c outtyp bzqlty maxitr pmix
update 4 50 0.023
c------------------------------------------------------------
c ntyp
1
c------------------------------------------------------------
c type ncmp rmt field mxl anclr conc
Fe 1 1 0.0 2
26 100
c------------------------------------------------------------
c natm
1
c------------------------------------------------------------
c atmicx atmtyp
0 0 0 Fe
c------------------------------------------------------------
Inputfile

3. #----------------------Fe------------------------------------
go data/fe
#------------------------------------------------------------
# brvtyp a c/a b/a alpha beta gamma
bcc 5.27 , , , , , ,
#------------------------------------------------------------
# edelt ewidth reltyp sdftyp magtyp record
0.001 1.0 nrl mjw mag 2nd
#------------------------------------------------------------
# outtyp bzqlty maxitr pmix
update 4 50 0.023
#------------------------------------------------------------
# ntyp
1
#------------------------------------------------------------
# type ncmp rmt field mxl anclr conc
Fe 1 1 0.0 2
26 100
#------------------------------------------------------------
# natm
1
#------------------------------------------------------------
# atmicx atmtyp
0 0 0 Fe
#------------------------------------------------------------
Inputfile

4. go data/fe
bcc 5.27 , , , , , ,
0.001 1.0 nrl mjw mag 2nd
update 4 50 0.023
1
Fe 1 1 0.0 2
26 100
1
0 0 0 Fe
Inputfile

5. go data/fe bcc 5.27,,,,,,0.001 1.0 nrl mjw mag 2nd
update 4 50 0.023 1 Fe 1 1 0.0 2 26 100
1 0 0 0 Fe
Inputfile

6. It actually is system standard input. Therefore,
input directly to the prompt (actually a null character)
would be enough.
> specx (or ./specx, run specx, etc.)
go
data/fe
bcc
5.27,,,,,,
0.001 1.0 nrl mjw mag 2nd
update 4 50 0.023 1 Fe 1 1 0.0 2 26 100
1 0 0 0
Fe
(calculation start)
...
Ctl-d
>
Inputfile

7. c----------------------Fe------------------------------------
go data/fe
c------------------------------------------------------------
c brvtyp a c/a b/a alpha beta gamma
bcc 5.27 , , , , , ,
c------------------------------------------------------------
c edelt ewidth reltyp sdftyp magtyp record
0.001 1.0 nrl mjw mag 2nd
c------------------------------------------------------------
c outtyp bzqlty maxitr pmix
update 4 50 0.023
c------------------------------------------------------------
c ntyp
1
c------------------------------------------------------------
c type ncmp rmt field mxl anclr conc
Fe 1 1 0.0 2
26 100
c------------------------------------------------------------
c natm
1
c------------------------------------------------------------
c atmicx atmtyp
0 0 0 Fe
c------------------------------------------------------------
Inputfile
go : Perform a band structure calculation
dos : Calculate a density of states

8. c----------------------Fe------------------------------------
go data/fe
c------------------------------------------------------------
c brvtyp a c/a b/a alpha beta gamma
bcc 5.27 , , , , , ,
c------------------------------------------------------------
c edelt ewidth reltyp sdftyp magtyp record
0.001 1.0 nrl mjw mag 2nd
c------------------------------------------------------------
c outtyp bzqlty maxitr pmix
update 4 50 0.023
c------------------------------------------------------------
c ntyp
1
c------------------------------------------------------------
c type ncmp rmt field mxl anclr conc
Fe 1 1 0.0 2
26 100
c------------------------------------------------------------
c natm
1
c------------------------------------------------------------
c atmicx atmtyp
0 0 0 Fe
c------------------------------------------------------------
Inputfile
fcc, bcc, hcp, sc, bct, st, etc.
See the manual for details.

9. bcc structure

10. c----------------------Fe------------------------------------
go data/fe
c------------------------------------------------------------
c brvtyp a c/a b/a alpha beta gamma
bcc 5.27 , , , , , ,
c------------------------------------------------------------
c edelt ewidth reltyp sdftyp magtyp record
0.001 1.0 nrl mjw mag 2nd
c------------------------------------------------------------
c outtyp bzqlty maxitr pmix
update 4 50 0.023
c------------------------------------------------------------
c ntyp
1
c------------------------------------------------------------
c type ncmp rmt field mxl anclr conc
Fe 1 1 0.0 2
26 100
c------------------------------------------------------------
c natm
1
c------------------------------------------------------------
c atmicx atmtyp
0 0 0 Fe
c------------------------------------------------------------
Inputfile
Atomic unit
Length : 1 bohr = 0.529 Å
Energy : 1 Ry = 13.6 eV

11. core state
valence state
DOS
E
energy contour C
ewidth
edelt
Im E
Re E
Atomic unit
Length : 1 bohr = 0.529 Å
Energy : 1 Ry = 13.6 eV

12. c----------------------Fe------------------------------------
go data/fe
c------------------------------------------------------------
c brvtyp a c/a b/a alpha beta gamma
bcc 5.27 , , , , , ,
c------------------------------------------------------------
c edelt ewidth reltyp sdftyp magtyp record
0.001 1.0 nrl mjw mag 2nd
c------------------------------------------------------------
c outtyp bzqlty maxitr pmix
update 4 50 0.023
c------------------------------------------------------------
c ntyp
1
c------------------------------------------------------------
c type ncmp rmt field mxl anclr conc
Fe 1 1 0.0 2
26 100
c------------------------------------------------------------
c natm
1
c------------------------------------------------------------
c atmicx atmtyp
0 0 0 Fe
c------------------------------------------------------------
Inputfile
nrl : non-relativistic
sra : relativistic

13. c----------------------Fe------------------------------------
go data/fe
c------------------------------------------------------------
c brvtyp a c/a b/a alpha beta gamma
bcc 5.27 , , , , , ,
c------------------------------------------------------------
c edelt ewidth reltyp sdftyp magtyp record
0.001 1.0 nrl mjw mag 2nd
c------------------------------------------------------------
c outtyp bzqlty maxitr pmix
update 4 50 0.023
c------------------------------------------------------------
c ntyp
1
c------------------------------------------------------------
c type ncmp rmt field mxl anclr conc
Fe 1 1 0.0 2
26 100
c------------------------------------------------------------
c natm
1
c------------------------------------------------------------
c atmicx atmtyp
0 0 0 Fe
c------------------------------------------------------------
Inputfile
mjw, vbh, vwn, gga91, etc.

14. c----------------------Fe------------------------------------
go data/fe
c------------------------------------------------------------
c brvtyp a c/a b/a alpha beta gamma
bcc 5.27 , , , , , ,
c------------------------------------------------------------
c edelt ewidth reltyp sdftyp magtyp record
0.001 1.0 nrl mjw mag 2nd
c------------------------------------------------------------
c outtyp bzqlty maxitr pmix
update 4 50 0.023
c------------------------------------------------------------
c ntyp
1
c------------------------------------------------------------
c type ncmp rmt field mxl anclr conc
Fe 1 1 0.0 2
26 100
c------------------------------------------------------------
c natm
1
c------------------------------------------------------------
c atmicx atmtyp
0 0 0 Fe
c------------------------------------------------------------
Inputfile
mag : magnetic
nmag : non-magnetic

15. c----------------------Fe------------------------------------
go data/fe
c------------------------------------------------------------
c brvtyp a c/a b/a alpha beta gamma
bcc 5.27 , , , , , ,
c------------------------------------------------------------
c edelt ewidth reltyp sdftyp magtyp record
0.001 1.0 nrl mjw mag 2nd
c------------------------------------------------------------
c outtyp bzqlty maxitr pmix
update 4 50 0.023
c------------------------------------------------------------
c ntyp
1
c------------------------------------------------------------
c type ncmp rmt field mxl anclr conc
Fe 1 1 0.0 2
26 100
c------------------------------------------------------------
c natm
1
c------------------------------------------------------------
c atmicx atmtyp
0 0 0 Fe
c------------------------------------------------------------
Inputfile
init : make new potential data
2nd : use the latest data
1st : use the second latest data

16. c----------------------Fe------------------------------------
go data/fe
c------------------------------------------------------------
c brvtyp a c/a b/a alpha beta gamma
bcc 5.27 , , , , , ,
c------------------------------------------------------------
c edelt ewidth reltyp sdftyp magtyp record
0.001 1.0 nrl mjw mag 2nd
c------------------------------------------------------------
c outtyp bzqlty maxitr pmix
update 4 50 0.023
c------------------------------------------------------------
c ntyp
1
c------------------------------------------------------------
c type ncmp rmt field mxl anclr conc
Fe 1 1 0.0 2
26 100
c------------------------------------------------------------
c natm
1
c------------------------------------------------------------
c atmicx atmtyp
0 0 0 Fe
c------------------------------------------------------------
Inputfile
update : save the potential data
quit : do not save the data

17. Optimize the lattice constant
-2522.8185
-2522.8180
-2522.8175
-2522.8170
-2522.8165
-2522.8160
totalenergy(Ry)
5.405.355.305.255.20
lattice constant (bohr)

18. Optimize the lattice constant
-2522.8185
-2522.8180
-2522.8175
-2522.8170
-2522.8165
-2522.8160
totalenergy(Ry)
5.405.355.305.255.20
lattice constant (bohr)
a=5.334
-2522.8185
-2522.8180
-2522.8175
-2522.8170
-2522.8165
-2522.8160
totalenergy(Ry)
5.405.355.305.255.20
lattice constant (bohr)

19. hcp structure
a
b
x
y

20. c----------------------Co------------------------------------
go data/co
c------------------------------------------------------------
c brvtyp a c/a b/a alpha beta gamma
hcp 4.74 , 1.6215 , , , , ,
c------------------------------------------------------------
c edelt ewidth reltyp sdftyp magtyp record
0.001 1.0 nrl mjw mag 2nd
c------------------------------------------------------------
c outtyp bzqlty maxitr pmix
update 4 50 0.023
c------------------------------------------------------------
c ntyp
1
c------------------------------------------------------------
c type ncmp rmt field mxl anclr conc
Co 1 1 0.0 2
27 100
c------------------------------------------------------------
c natm
2
c------------------------------------------------------------
c atmicx atmtyp
0a 0b 0c Co
1/3a 2/3b 1/2c Co
c------------------------------------------------------------
Inputfile(Co)

21. c----------------------Co------------------------------------
go data/co
c------------------------------------------------------------
c brvtyp a c/a b/a alpha beta gamma
hcp 4.74 , 1.6215 , , , , ,
c------------------------------------------------------------
c edelt ewidth reltyp sdftyp magtyp record
0.001 1.0 nrl mjw mag 2nd
c------------------------------------------------------------
c outtyp bzqlty maxitr pmix
update 4 50 0.023
c------------------------------------------------------------
c ntyp
1
c------------------------------------------------------------
c type ncmp rmt field mxl anclr conc
Co 1 1 0.0 2
27 100
c------------------------------------------------------------
c natm
2
c------------------------------------------------------------
c atmicx atmtyp
0x 0y 0z Co
1/2x 0.86602y 1/2z Co
c------------------------------------------------------------
Inputfile(Co)

22. c----------------------Co------------------------------------
go data/co
c------------------------------------------------------------
c brvtyp a c/a b/a alpha beta gamma
hcp 4.74 , 1.6215 , , , , ,
c------------------------------------------------------------
c edelt ewidth reltyp sdftyp magtyp record
0.001 1.0 nrl mjw mag 2nd
c------------------------------------------------------------
c outtyp bzqlty maxitr pmix
update 4 50 0.023
c------------------------------------------------------------
c ntyp
1
c------------------------------------------------------------
c type ncmp rmt field mxl anclr conc
Co 1 1 0.0 2
27 100
c------------------------------------------------------------
c natm
2
c------------------------------------------------------------
c atmicx atmtyp
0 0 0 Co
0.5 0.86602 0.81075 Co
c------------------------------------------------------------
Inputfile(Co)

23. Impurity problem
n Green’s function of the host
n Consider the scattering when one host atom is
replaced by an impurity.
€
˜G = g0 1− thost g0[ ]
−1
€
G = ˜G 1− (timpurity − thost ) ˜G[ ]
−1

24. CPA (coherent potential approximation)
n Consider the t-matrix of the imaginary atom which
describes configuration average of a substitutional
random alloy (coherent t-matrix).
tA
tB
t
~

25. CPA
n Coherent t-matrix satisfy the following relation.
€
˜G = g0 1− ˜tg0[ ]
−1
GA(B)
= ˜G 1− (tA(B) − ˜t) ˜G[ ]
−1
cGA
+ (1− c)GB
= ˜G
c× + (1-c)× =

26. NiFe alloy (fcc)
n Replace Ni atoms by Fe atoms.
Ni Fe

27. NiFe alloy (fcc)
Fe0% Fe20% Fe40%
Fe60% Fe80% Fe100%

28. Theor.
Exp.
Slater-Pauling curve
n Alloys of transition metals,
such as Fe, Co and Ni.
n The magnetic moments are
on the common curve.
n Calculation reproduces the
experimentally observed
behaviors including the
branches.
H. Akai, Hyperfine Interactions 68 (1991) 3
H.P.J. Wijn, Magnetic Properties of Metals (1991)

29. Transition metal impurities in Fe
n 3d
n 4d
n 5d
n local moment (parallel or antiparallel ?)
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
21
22
23
24
25
26
27
28
29
30
Y
Zr
Nb
Mo
Tc
Ru
Rh
Pd
Ag
Cd
39
40
41
42
43
44
45
46
47
48
Lu
Hf
Ta
W
Re
Os
Ir
Pt
Au
Hg
71
72
73
74
75
76
77
78
79
80

30. Transition metal impurities in Fe
H. Akai et al, Prog. Theor. Phys. Suppl. 101 (1990) 11.

31. Transition metal impurities in Fe
Fe V
Ni
<
<

32. Curie temperature of ferromagnets
n Ferromagnetic state
n The magnetic moments align to the same direction.

33. Curie temperature of ferromagnets
n Paramagnetic state
n The directions of the moments are random.
n Atoms with up and down moments align randomly.
(local moment disorder)

34. copy
copy
fmg
n fe.fmg
../data/fe 1
../data/fe_lmd 1 -1
data/fe
potential data for spin up
potential data for spin down
Potential data file of bcc Fe
data/fe_lmd
potential data for spin up
potential data for spin down
New potential data file
potential data for spin up
potential data for spin down
copy
copy

35. Curie temperature of Fe
€
TC =
2
3
ELMD − EFerro( )/kBMean field approximation
Experimental value： ~ 1000 K
Ferromagnetic LMD
1 Ry = 13.6 eV, kB = 8.617 * 10-5 (eV/K)

36. Reference etc.
n Reference
n 計算機ナノマテリアルデザイン入門（笠井秀明・赤井久
純・吉田博編 大阪大学出版会）
n W.Kohn and N. Rostoker, Phys. Rev. 94 (1954) 1111.
n F.S. Ham and B. Segall, Phys. Rev. 124 (1961) 1786.
n H. Akai, J. Phys. Soc. Japan 51 (1982) 468.
n H. Akai, J. Phys.: Cond. Matter 1 (1989) 8045.
n KKR package http://kkr.phys.sci.osaka-u.ac.jp/