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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. AkaiKKRの実習

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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. AkaiKKRの実習

  1. 1. KKR GREEN’S FUNCTION METHOD MACHIKANEYAMA2000 (AKAIKKR) KKR Hands-On
  2. 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. 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. 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. 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. 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. 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. 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. 9. bcc structure
  10. 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. 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. 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. 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. 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. 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. 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. 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. 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. 19. hcp structure a b x y
  20. 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. 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. 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. 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. 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. 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. 26. NiFe alloy (fcc) n  Replace Ni atoms by Fe atoms. Ni Fe
  27. 27. NiFe alloy (fcc) Fe0% Fe20% Fe40% Fe60% Fe80% Fe100%
  28. 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. 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. 30. Transition metal impurities in Fe H. Akai et al, Prog. Theor. Phys. Suppl. 101 (1990) 11.
  31. 31. Transition metal impurities in Fe Fe V Ni < <
  32. 32. Curie temperature of ferromagnets n  Ferromagnetic state n  The magnetic moments align to the same direction.
  33. 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. 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. 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. 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/

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