KKR GREEN’S FUNCTION METHOD MACHIKANEYAMA2000 (AKAIKKR)
KKR Hands-On
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------------------------------------------------------------
Input file
#----------------------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 #------------------------------------------------------------
Input file
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
Input file
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
Input file
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 >
Input file
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------------------------------------------------------------
Input file go : Perform a band structure calculation dos : Calculate a density of states
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------------------------------------------------------------
Input file fcc, bcc, hcp, sc, bct, st, etc. See the manual for details.
bcc structure
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------------------------------------------------------------
Input file Atomic unit
Length : 1 bohr = 0.529 Å Energy : 1 Ry = 13.6 eV
!"#$%&'('$
)(*$+!$%&'('$
,-.
!
$+$#/0%!"+'"1#%"
#$%&'(
#&#)'
23%!
4$%!
Atomic unit Length : 1 bohr = 0.529 Å Energy : 1 Ry = 13.6 eV
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------------------------------------------------------------
Input file
nrl : non-relativistic sra : relativistic
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------------------------------------------------------------
Input file
mjw, vbh, vwn, gga91, etc.
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------------------------------------------------------------
Input file
mag : magnetic nmag : non-magnetic
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------------------------------------------------------------
Input file
init : make new potential data 2nd : use the latest data 1st : use the second latest data
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------------------------------------------------------------
Input file
update : save the potential data quit : do not save the data
Optimize the lattice constant
-2522.8185
-2522.8180
-2522.8175
-2522.8170
-2522.8165
-2522.8160
tota
l en
ergy (
Ry)
5.405.355.305.255.20
lattice constant (bohr)
Optimize the lattice constant
-2522.8185
-2522.8180
-2522.8175
-2522.8170
-2522.8165
-2522.8160
tota
l en
ergy (
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
tota
l en
ergy (
Ry)
5.405.355.305.255.20
lattice constant (bohr)
hcp structure
a
b
x
y
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------------------------------------------------------------
Input file (Co)
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------------------------------------------------------------
Input file (Co)
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------------------------------------------------------------
Input file (Co)
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− thostg0[ ]−1
€
G = ˜ G 1− (timpurity − thost ) ˜ G [ ]−1
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 ~
CPA
n Coherent t-matrix satisfy the following relation.
€
˜ G = g0 1− ˜ t g0[ ]−1
GA(B) = ˜ G 1− (tA(B) − ˜ t ) ˜ G [ ]−1
cGA + (1− c)GB = ˜ G
c× + (1-c)× =
NiFe alloy (fcc)
n Replace Ni atoms by Fe atoms.
Ni Fe
NiFe alloy (fcc)
Fe0% Fe20% Fe40%
Fe60% Fe80% Fe100%
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)
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
Transition metal impurities in Fe
H. Akai et al, Prog. Theor. Phys. Suppl. 101 (1990) 11.
Transition metal impurities in Fe
Fe V
Ni
<
<
Curie temperature of ferromagnets
n Ferromagnetic state n The magnetic moments align to the same direction.
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)
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
Curie temperature of Fe
€
TC =23ELMD − EFerro( ) /kBMean field approximation
Experimental value: ~ 1000 K
Ferromagnetic LMD
1 Ry = 13.6 eV, kB = 8.617 * 10-5 (eV/K)
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/
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