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....

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

Input file go : Perform a band structure calculation dos : Calculate a density of states

Input file fcc, bcc, hcp, sc, bct, st, etc. See the manual for details.

bcc structure

Input file Atomic unit

Length : 1 bohr = 0.529 Å Energy : 1 Ry = 13.6 eV

!"#$%&'('$

)(*$+!$%&'('$

$+$#/0%!"+'"1#%"

#$%&'(

Atomic unit Length : 1 bohr = 0.529 Å Energy : 1 Ry = 13.6 eV

Input file

nrl : non-relativistic sra : relativistic

Input file

mjw, vbh, vwn, gga91, etc.

Input file

mag : magnetic nmag : non-magnetic

Input file

init : make new potential data 2nd : use the latest data 1st : use the second latest data

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

ergy (

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

ergy (

5.405.355.305.255.20

a=5.334

-2522.8185

-2522.8180

-2522.8175

-2522.8170

-2522.8165

-2522.8160

ergy (

5.405.355.305.255.20

hcp structure

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).

tB t ~

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.

NiFe alloy (fcc)

Fe0% Fe20% Fe40%

Fe60% Fe80% Fe100%

Theor.

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

H. Akai et al, Prog. Theor. Phys. Suppl. 101 (1990) 11.

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)

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

New potential data file

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/

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....

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