第5回ccmsハンズオン(ソフトウェア講習会): akaikkrチュートリアル 2....
TRANSCRIPT
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KKR GREEN’S FUNCTION METHOD MACHIKANEYAMA2000 (AKAIKKR)
KKR Hands-On
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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
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#----------------------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
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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
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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
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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
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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
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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.
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bcc structure
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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
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Atomic unit Length : 1 bohr = 0.529 Å Energy : 1 Ry = 13.6 eV
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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
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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.
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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
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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
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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
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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)
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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)
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hcp structure
a
b
x
y
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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)
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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)
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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)
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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
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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 ~
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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)× =
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NiFe alloy (fcc)
n Replace Ni atoms by Fe atoms.
Ni Fe
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NiFe alloy (fcc)
Fe0% Fe20% Fe40%
Fe60% Fe80% Fe100%
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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)
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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
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Transition metal impurities in Fe
H. Akai et al, Prog. Theor. Phys. Suppl. 101 (1990) 11.
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Transition metal impurities in Fe
Fe V
Ni
<
<
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Curie temperature of ferromagnets
n Ferromagnetic state n The magnetic moments align to the same direction.
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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)
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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
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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)
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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/