WIEN2k(GGA+U)

 ここではWIEN2kを用いた入力ファイルとその結果を掲載していく。
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CentOS 6.4 64-bit
プロセッサ: Intel® Core™ i7-2700K CPU @ 3.50GHz × 8
メモリ: 15.7 GiB
WIEN2k 12
コンパイラ: gfortran
VESTA v.2.1.6
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Ueff values used for the different elements in the LDA+U caluculations of Heusler compounds.
Element: Effective parameter Ueff (U-J), J=0, LDA+U (SIC) [1]
Ti: 1.36 eV
V: 1.34 eV
Cr: 1.59 eV
Mn: 1.69 eV
Fe: 1.80 eV
Co: 1.92 eV
Ueff = U * 0.075 (approximately 7%-8%)
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U = F0 - J : Cowan’s program
Ueff = U * 0.075 (approximately 7%-8%)

d state : F0 = 15.31 + 1.50 * (Z-21)
f state : F0 = 2.38 + 0.93 * (Z-57)

3d: J = 0.81 + 0.08 * (Z-21)
4d: J = 0.59 + 0.056 * (Z-39)
5d: J= 0.60 + 0.053 * (Z-71)

4f: J = 0.90 + 0.036 * (Z-57)
5f: J = 0.66 + 0.035 * (Z-89)

google : Atomic Coulomb exchange parameter 5d transition
[12] http://optics.unige.ch/Publications/ele88.pdf
[13] http://arxiv.org/pdf/1103.5593.pdf
--
U: Coulomb replusion parameter
J: exchange integral parameter
Fe Heusler: Ueff = 4.0 eV ( Eg = 0 case, Ueff = 2.0 eV) [2]
V Heusler: Ueff = 1.5 eV ( Eg =0 case, Ueff = 1.0 eV) [2]
Fe metal: Ueff = 6.2-6.8 eV [26]
Fe oxide: 4.8-7.4 eV [36]
GGA-EV (Eg = -0.06 eV)
mBJ = LDA+U (Fe Heusler: Ueff = 3.0 eV, V Heusler: Ueff = 1.0 eV)
change: V (unoccupied states at X), Fe(occupied and unoccupied states especially at Gamma)
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LSDA
Fe: U = 4.0 eV, J = 0.8 eV [3]
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Fe2VAl (hole dope system) [4]
0.75 mΩcm at 300 K
nh = 4.8 x 1020 cm-3
relaxation time
PBE: 0.9 x 10-14 s
B1-WC: 1.4 x 10-14 s
specific heat
experimental 1.5 ± 0.3 mJ/mol K2
PBE: 0.76 mJ/mol K2
B1-WC: 1.00 mJ/mol K2
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Fe2VAl (electron dope system) [4]
0.65 mΩcm at 300 K corresponding to a doping x = 0.03 (Fe2VAl1-xMx, M=Si, Ge)
ne = 6.0 x 1020 cm-3
relaxation time
PBE: 1.5 x 10-14 s
B1-WC: 3.4 x 10-14 s
specific heat
experimental 1.5 ± 0.3 mJ/mol K2
PBE: 0.76 mJ/mol K2
B1-WC: 1.00 mJ/mol K2
-
the doping x = 0.03 (Fe2VAl1-xMx, M=Si, Ge) [4]
B1-WC: 3.4 x 10-14 s (Eg= 0.6, 0.34, and 0.2 eV)
B1-WC: 3.2 x 10-14 s (Eg= 0 eV)
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Refrences
[1] H. C. Kandpal et al., J. Phys. D: Appl. Phys. 40 (2007) 15074-1523.: http://iopscience.iop.org/0022-3727/40/6/S01
  , H. C. Kandpal et al., Phys. Rev. B 73 (2006) 094422.: http://journals.aps.org/prb/pdf/10.1103/PhysRevB.73.094422
[2] Dat Do et al., Phys. Rev. B 84 (2011) 125104.: http://journals.aps.org/prb/pdf/10.1103/PhysRevB.84.125104
[3] V. N. Antonov et al., Phys. Rev. B 77 (2008) 134444.: http://journals.aps.org/prb/pdf/10.1103/PhysRevB.77.134444
[4] D. I. Bilc et al., Phys. Rev. B 83 (2011) 205204.: http://journals.aps.org/prb/pdf/10.1103/PhysRevB.83.205204
[26] V. I. Anisimov and O. Gunnarson, Phys. Rev. B 43 (1991) 7570.: http://journals.aps.org/prb/pdf/10.1103/PhysRevB.44.943
[36] G. K. H. Madsen and P. Novak, Europhys. Lett. 69 (2005) 777.: http://iopscience.iop.org/0295-5075/69/5/777
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■ Fe2VAl
[1] http://www.apph.tohoku.ac.jp/kiso/files/0803_magne.pdf
[2] http://www.nims.go.jp/cmsc/staff/arai/wien/ldau.html
[3] http://journals.aps.org/prb/pdf/10.1103/PhysRevB.83.205204

□ GGA+U calculation
1. SCF calculation (needs spin polarizationm, other case is very difficult)
  energy seperation between core/valence -8.0 Ry (x lstart)
2. runSCF -> Remove the files -> Yes, delete it
3. runSCF -> orbital pot (LDA+U) -> start SCF cycle -> case.inorb
4. runSCF -> orbital pot (LDA+U) -> start SCF cycle -> case.indm
5. runSCF -> orbital pot (LDA+U) -> start SCF cycle -> case.indm -> 1 cycle

0: AMF (Around the Mean Field)
1: SIC (self-interaction correction)
2: HFM (in addition the Hubbard model in the mean field approximation)

■ AMF case (is same as SIC case)


AMF, 10 cycle, 1000 k, Ueff = U * 0.075



AMF, ? cycle, 1000 k, Ueff = U * 0.03
 
struct file


case.indm
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-9.                      Emin cutoff energy
 2                       number of atoms for which density matrix is calculated
 2  1  2      index of 1st atom, number of L's, L1
 3  1  2      dtto for 2nd atom, repeat NATOM times
 0 0           r-index, (l,s)index 
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case.inorb
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  1  2  0                     nmod, natorb, ipr
PRATT  1.0                    BROYD/PRATT, mixing
  2 1 2                          iatom nlorb, lorb
  3 1 2                          iatom nlorb, lorb
  0                              nsic 0..AMF, 1..SIC, 2..HFM
   0.098 0.00        U J (Ry)   Note: we recommend to use U_eff = U-J and J=0
   0.132 0.00        U J
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■ boltztrap
□ calculation
1. [initialize_calc.]で "x kgen"のボタンを押して、k点数を2〜3万点に増やす
2. runsp_lapw -i 1 -orb
3. case.struct, case.energydn, case.energyup and case.intrans
4. $HOME/boltztrap-*/src/x_trans BoltzTraP -up

□ hole-doped system
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WIEN                      # Format of DOS                                         
0 0 0 0.0                 # iskip (not presently used) idebug setgap shiftgap                         
0.67500 0.0005 0.3  56.   # Fermilevel (Ry), energygrid, energy span around Fermilevel, number of electrons             
CALC                      # CALC (calculate expansion coeff), NOCALC read from file                     
5                         # lpfac, number of latt-points per k-point                                    
BOLTZ                     # run mode (only BOLTZ is supported)                                 
0.15                       # (efcut) energy range of chemical potential                             
800. 50.                  # Tmax, temperature grid                                     
-1                        # energyrange of bands given individual DOS output sig_xxx and dos_xxx (xxx is band number)
HISTO                  #scheme to obtain DOS. HISTO/TETRA: histogram/thetrahedron[4] sampling
14.0 2.0 0.67500 300      #τ-model. tauref(Reference lifetime (femtoseconds)), tauexp(scattering parameter "r": 0 -> acoustic phonons, 2 -> ionized impurities), taurefen(Ry), taureftemp(K)
0                         #number of fixed dopings
4.8E20 -4.8E20          #fixed doping levels in cm3
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□ Electron doping system = Fe2VAl1-xMx (x=0.03), chemical potential 0.23
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WIEN                      # Format of DOS                                         
0 0 0 0.0                 # iskip (not presently used) idebug setgap shiftgap                         
0.67500 0.0005 0.3  56.   # Fermilevel (Ry), energygrid, energy span around Fermilevel, number of electrons             
CALC                      # CALC (calculate expansion coeff), NOCALC read from file                     
5                         # lpfac, number of latt-points per k-point                                    
BOLTZ                     # run mode (only BOLTZ is supported)                                 
0.15                       # (efcut) energy range of chemical potential                             
800. 50.                  # Tmax, temperature grid                                     
-1                        # energyrange of bands given individual DOS output sig_xxx and dos_xxx (xxx is band number)
HISTO                  #scheme to obtain DOS. HISTO/TETRA: histogram/thetrahedron[4] sampling
34.0 2.0 0.67500 300      #τ-model. tauref(Reference lifetime (femtoseconds)), tauexp(scattering parameter "r": 0 -> acoustic phonons, 2 -> ionized impurities), taurefen(Ry), taureftemp(K)
0                         #number of fixed dopings
6.0E20 -6.0E20          #fixed doping levels in cm3
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see Fermi energy = FERMI ENERGY AT in case.output2 or EF in case.dos1
see number of electrons = NE in case.in2

Max absolute seebeck value is 20 microV/K -> 50 microV/K @ 300 K (Eg = 0.2 eV)
Max absolute seebeck value is 20 microV/K -> 14 microV/K @ 300 K (Eg = 0 eV)
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