Breaking of spin degeneracy in antiferromagnetic structure
Posted: Wed Oct 24, 2018 11:31 am
Dears all:
I'm dealing with an antiferromagnetic material where the two spin compositions have an equal status (just like NiO). Owing to this symmetry, the bands structures should be strictly degenerate for the two spin compositions. In the ground state PBE calculation (by QE), this degeneracy is perfectly obtained. Of course some very slight difference is observed, because the two spin Hamiltonians are built independently and in QE you should formally set magnetic atoms to be different species to get antiferromagnetic geometry, but the difference only occurs at a few bands and with a magnitude of 0.1meV.
However, after the G0W0 correction, the "almost perfect" degeneracy between two spin channels are dramatically lifted, and the splitting could be as large as 0.3eV for band 32 here.
# K-point Band Eo E-Eo Sc|Eo Spin_Pol
......
1.00000 30.00000 -0.27732 -0.06357 4.35493 1.00000
1.00000 30.00000 -0.27721 -0.05498 4.35509 -1.00000
1.00000 31.00000 -0.27732 -0.06361 4.35493 1.00000
1.00000 31.00000 -0.27721 -0.05502 4.35510 -1.00000
1.00000 32.00000 0.19200 1.02326 -7.34663 1.00000
1.00000 32.00000 0.19184 0.75809 -7.34662 -1.00000
1.00000 33.00000 1.65217 0.94575 -5.72798 1.00000
1.00000 33.00000 1.65199 0.96537 -5.72772 -1.00000
1.00000 34.00000 1.65217 0.94579 -5.72793 1.00000
1.00000 34.00000 1.65199 0.96541 -5.72768 -1.00000
......
By a detailed checking, It seems that the difference comes from the difference in the matrix element of Kohn-Sham term, for example:
......
<31(up)|HF|31(up)> = -24.10883 0.111E-16 <31(up)|DFT|31(up)> = -19.66989 0.000000
<31(dn)|HF|31(dn)> = -24.10933 -.240E-17 <31(dn)|DFT|31(dn)> = -19.68157 -.189E-15
<32(up)|HF|32(up)> = -13.61064 -.480E-18 <32(up)|DFT|32(up)> = -22.43869 0.000000
<32(dn)|HF|32(dn)> = -13.60964 0.581E-18 <32(dn)|DFT|32(dn)> = -22.05383 0.944E-16
<33(up)|HF|33(up)> = -14.60489 -.262E-18 <33(up)|DFT|33(up)> = -21.66759 0.000000
<33(dn)|HF|33(dn)> = -14.60509 -.156E-18 <33(dn)|DFT|33(dn)> = -21.69521 0.000000
......
where <32(up)|DFT|32(up)> and <32(dn)|DFT|32(dn)> is splitted by ~0.4eV, but in PBE they only differed by ~0.2meV. I want to know what's wrong in my calculations and how this happens. The attachment is related input and output files, and I would be very grateful for any suggestions~~
I'm dealing with an antiferromagnetic material where the two spin compositions have an equal status (just like NiO). Owing to this symmetry, the bands structures should be strictly degenerate for the two spin compositions. In the ground state PBE calculation (by QE), this degeneracy is perfectly obtained. Of course some very slight difference is observed, because the two spin Hamiltonians are built independently and in QE you should formally set magnetic atoms to be different species to get antiferromagnetic geometry, but the difference only occurs at a few bands and with a magnitude of 0.1meV.
However, after the G0W0 correction, the "almost perfect" degeneracy between two spin channels are dramatically lifted, and the splitting could be as large as 0.3eV for band 32 here.
# K-point Band Eo E-Eo Sc|Eo Spin_Pol
......
1.00000 30.00000 -0.27732 -0.06357 4.35493 1.00000
1.00000 30.00000 -0.27721 -0.05498 4.35509 -1.00000
1.00000 31.00000 -0.27732 -0.06361 4.35493 1.00000
1.00000 31.00000 -0.27721 -0.05502 4.35510 -1.00000
1.00000 32.00000 0.19200 1.02326 -7.34663 1.00000
1.00000 32.00000 0.19184 0.75809 -7.34662 -1.00000
1.00000 33.00000 1.65217 0.94575 -5.72798 1.00000
1.00000 33.00000 1.65199 0.96537 -5.72772 -1.00000
1.00000 34.00000 1.65217 0.94579 -5.72793 1.00000
1.00000 34.00000 1.65199 0.96541 -5.72768 -1.00000
......
By a detailed checking, It seems that the difference comes from the difference in the matrix element of Kohn-Sham term, for example:
......
<31(up)|HF|31(up)> = -24.10883 0.111E-16 <31(up)|DFT|31(up)> = -19.66989 0.000000
<31(dn)|HF|31(dn)> = -24.10933 -.240E-17 <31(dn)|DFT|31(dn)> = -19.68157 -.189E-15
<32(up)|HF|32(up)> = -13.61064 -.480E-18 <32(up)|DFT|32(up)> = -22.43869 0.000000
<32(dn)|HF|32(dn)> = -13.60964 0.581E-18 <32(dn)|DFT|32(dn)> = -22.05383 0.944E-16
<33(up)|HF|33(up)> = -14.60489 -.262E-18 <33(up)|DFT|33(up)> = -21.66759 0.000000
<33(dn)|HF|33(dn)> = -14.60509 -.156E-18 <33(dn)|DFT|33(dn)> = -21.69521 0.000000
......
where <32(up)|DFT|32(up)> and <32(dn)|DFT|32(dn)> is splitted by ~0.4eV, but in PBE they only differed by ~0.2meV. I want to know what's wrong in my calculations and how this happens. The attachment is related input and output files, and I would be very grateful for any suggestions~~