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About Fermi level and magnetic moment in MnBi2Te4 Date: 2022/10/17 01:51 Name: ooteki   <ooteki@163.com> Dear All, I'm using openmx to study magnetic topological insulator MnBi2Te4 and encounter a problem about Fermi level and magnetic moment. The calculation takes an hour and then converged. The band structure, plot with bandgnu13, seems correct at first glance but the Fermi level is about 1eV higher than reported results. The other problem is the magnetic moment. Openmx code give me a 2.075 muB, which is about 5 muB as the half-filling of 3d of Mn, and other reported reults. In short, my calculation include SOC, non-collinear, +U, with PBE. If anyone could help me solve this problem! Thank you so much. Best reguards. Oo Teki The input file # # File Name # System.CurrrentDirectory ./ # default=./ System.Name MnBi2Te4 level.of.stdout 1 # default=1 (1-3) level.of.fileout 1 # default=1 (0-2) DATA.PATH ../DFT_DATA19 # # # Definition of Atomic Species # Species.Number 3 <Definition.of.Atomic.Species Mn Mn6.0-s3p2d1 Mn_PBE19 Bi Bi8.0-s3p2d2f1 Bi_PBE19 Te Te9.0-s3p2d2f1 Te_PBE19 Definition.of.Atomic.Species> # # Hubbard U # <Hubbard.U.values # eV Mn 1s 0.0 2s 0.0 3s 0.0 1p 0.0 2p 0.0 1d 3.0 Bi 1s 0.0 2s 0.0 3s 0.0 1p 0.0 2p 0.0 1d 0.0 2d 0.0 1f 0.0 Te 1s 0.0 2s 0.0 3s 0.0 1p 0.0 2p 0.0 1d 0.0 2d 0.0 1f 0.0 Hubbard.U.values> # # Atoms # Atoms.Number 7 Atoms.SpeciesAndCoordinates.Unit FRAC # Ang|AU <Atoms.SpeciesAndCoordinates 1 Bi 0.9224369969999998 0.9224369969999998 0.9224369969999998 7.0 8.0 0.0 0.0 0.0 0.0 0 off 2 Te 0.7966216506666665 0.7966216506666665 0.7966216506666667 8.0 8.0 0.0 0.0 0.0 0.0 0 off 3 Te 0.6320013256666664 0.6320013256666667 0.6320013256666667 8.0 8.0 0.0 0.0 0.0 0.0 0 off 4 Mn 0.4999999999999999 0.4999999999999999 0.5000000000000000 10.0 5.0 0.0 0.0 0.0 0.0 1 off 5 Te 0.3679986743333334 0.3679986743333335 0.3679986743333335 8.0 8.0 0.0 0.0 0.0 0.0 0 off 6 Te 0.2033783493333333 0.2033783493333332 0.2033783493333332 8.0 8.0 0.0 0.0 0.0 0.0 0 off 7 Bi 0.0775630030000000 0.0775630029999999 0.0775630029999999 8.0 7.0 0.0 0.0 0.0 0.0 0 off Atoms.SpeciesAndCoordinates> Atoms.UnitVectors.Unit Ang # Ang|AU <Atoms.UnitVectors 2.1670000553163558 1.2511180652708318 13.6366670432000703 -2.1670000553163558 1.2511180652708318 13.6366670432000703 0.0000000000000000 -2.5022361305416636 13.6366670432000703 Atoms.UnitVectors> # # SCF or Electronic System # scf.XcType GGA-PBE # LDA|LSDA-CA|LSDA-PW|GGA-PBE scf.SpinPolarization NC # On|Off|NC scf.SpinOrbit.Coupling On # On|Off, default=off scf.Constraint.NC.Spin On scf.Hubbard.U on # on|off, default=off scf.DFTU.Type 1 # 1:Simplified(Dudarev)|2:General, default=1) scf.Hubbard.Occupation dual # onsite|full|dual, default=dual scf.ElectronicTemperature 300.0 # default=300 (K) scf.energycutoff 200.0 # default=150 (Ry) scf.maxIter 1000 # default=40 scf.EigenvalueSolver band # DC|GDC|Cluster|Band scf.Kgrid 8 8 8 # means n1 x n2 x n3 scf.Generation.Kpoint regular # regular|MP scf.Mixing.Type rmm-diish # Simple|Rmm-Diis|Gr-Pulay|Kerker|Rmm-Diisk scf.Init.Mixing.Weight 0.30 # default=0.30 scf.Min.Mixing.Weight 0.001 # default=0.001 scf.Max.Mixing.Weight 0.400 # default=0.40 scf.Mixing.History 5 # default=5 scf.Mixing.StartPulay 6 # default=6 scf.Mixing.EveryPulay 6 # default=6 scf.criterion 1.0e-8 # default=1.0e-6 (Hartree) scf.lapack.dste dstevx # dstevx|dstedc|dstegr,default=dstevx HS.fileout on Voronoi.Charge on # default = Off # # SCF Order-N # orderN.HoppingRanges 5.0 # default=5.0 (Ang) orderN.NumHoppings 2 # default=2 # # 1DFFT # 1DFFT.NumGridK 900 # default=900 1DFFT.NumGridR 900 # default=900 1DFFT.EnergyCutoff 3600 # default=3DFFT.EnergyCutoff*3.0 (Ry) # # MD or Geometry Optimization # MD.Type Nomd # Nomd|Constant_Energy_MD|Opt MD.maxIter 1 # default=1 MD.TimeStep 0.5 # default=0.5 (fs) MD.Opt.criterion 1.0e-4 # default=1.0e-4 (Hartree/bohr) # # Band dispersion # Band.dispersion on # on|off, default=off # if <Band.KPath.UnitCell does not exist, # the reciprical lattice vector is employed. Band.Nkpath 4 <Band.kpath 50 0.0 0.0 0.0 0.5 0.5 0.5 G Z 50 0.5 0.5 0.5 0.0 0.5 0.5 Z F 50 0.0 0.5 0.5 0.0 0.0 0.0 F G 50 0.0 0.0 0.0 0.0 0.5 0.0 G L Band.kpath> The output file contains *********************************************************** *********************************************************** Voronoi charges *********************************************************** *********************************************************** Sum of Voronoi charges for up = 56.407999960334 Sum of Voronoi charges for down = 54.332706610559 Sum of Voronoi charges for total = 110.740706570893 Total spin magnetic moment (muB) by Voronoi charges = 2.075293349775 Up spin Down spin Sum Diff Theta(Deg) Phi(Deg) Voronoi Volume (Ang.^3) Atom= 1 7.417269959 7.409244244 14.826514203 0.008025716 179.9987 15.5320 31.672419826 Atom= 2 8.337846312 8.316906385 16.654752697 0.020939927 0.0017 182.6097 29.218879770 Atom= 3 8.285939415 8.277803642 16.563743057 0.008135773 0.0029 177.0524 37.297070708 Atom= 4 8.325883935 6.324794247 14.650678183 2.001089688 0.0016 180.0874 25.451433559 Atom= 5 8.285939419 8.277803006 16.563742425 0.008136413 0.0032 182.8816 37.297070708 Atom= 6 8.337848352 8.316908447 16.654756800 0.020939905 0.0015 177.2930 29.218879770 Atom= 7 7.417272568 7.409246639 14.826519207 0.008025929 179.9994 -38.2216 31.672419826

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Re: About Fermi level and magnetic moment in MnBi2Te4 ( No.1 ) Date: 2022/10/19 15:38 Name: T. Ozaki Hi, > The band structure, plot with bandgnu13, seems correct at first glance but the Fermi level is about 1eV higher than reported results. > The other problem is the magnetic moment. Openmx code give me a 2.075 muB, which is about 5 muB as the half-filling of 3d of Mn, > and other reported reults. Could you tell us the papers you referred? Regards, TO Re: About Fermi level and magnetic moment in MnBi2Te4 ( No.2 ) Date: 2022/10/19 22:37 Name: Oo Teki  <ooteki@163.com> Dear T. Ozaki, I list two papers in the following, 1. Science Advances, 2019, 5(6): eaaw5685 2. Physical review letters, 2019, 122(20): 206401 There are vasp calculated band strucutres in these papers. Furthermore, after I submitted this problem, I performed a calculation on AFM case with openmx. The problem of Fermi level still exists. While the total spin moment for AFM is near zero, so I could not tell whether it's correct or not. I could reproduce these results agree to the papers above with vasp, but I do really need openmx to calculate large system based on MnBi2Te4. Thank you so much! Best regards. Oo Teki Re: About Fermi level and magnetic moment in MnBi2Te4 ( No.3 ) Date: 2022/10/20 15:55 Name: T. Ozaki Hi, Please find the PDF file at http://www.openmx-square.org/forum/img/Band_FM-MnBi2Te4.pdf showing the comparison between the result in Fig. 3(b) in PRL 122, 206401 (2019) and one calculated by OpenMX. It turns out that they are almost equivalent to each other at least near the Fermi level. The magnetic moment calculated by OpenMX is found to be 4.9 muB/unit cell. To get the result by OpenMX, I changed parameters in your input file as shown below: Mn Mn6.0-s3p2d1 Mn_PBE19 Te Te7.0-s3p2d2f1 Te_PBE19 Bi Bi8.0-s3p2d2f1 Bi_PBE19 scf.energycutoff 800.0 The specification of basis functions followed the standard set: http://www.openmx-square.org/openmx_man3.9/node27.html Also, I used the relatively high scf.cutoffenergy because of the shape of unit cell. The issue was already discussed at http://www.openmx-square.org/forum/patio.cgi?mode=view&no=3012 Regards, TO Re: About Fermi level and magnetic moment in MnBi2Te4 ( No.4 ) Date: 2022/10/21 13:04 Name: Oo Teki  <ooteki@163.com> Dear, T. Ozaki Now I can also reproduce all the results. Maybe both errors of spin and Fermi-level come from the miss spelling "Te9.0-s3p2d2f1". Thank you so much! Best regards. Oo Teki

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