Breaking of spin degeneracy in antiferromagnetic structure

[xueshanxihua]

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~~

[Daniele Varsano]

Dear Zeyu Jiang,
that look very bad. It seems a problem related with the libxc.
The only variable that could affect this bad behavior is:

Code: Select all

FFTGvecs= 11393        RL    

if it is set to a too low value, as you need a good representation of the density to calculate the PBE <Vxc> , but I do suspect that there is something else here not working properly.

We will try to reproduce the problem and let you know.
Best,
Daniele

[xueshanxihua]

Dear Varsano,

Thank a lot for the quick reply, I would look forward for your results~~

[Davide Sangalli]

Dear Zeyu Jiang,
on the same line.

Can you try to change the subroutine
src/xc_functionals/XC_eval_gga_potential.F
replacing all wf_ng with ng_closed ?

Also you need to replace

Code: Select all

use wave_func,     ONLY:wf_ng

with

Code: Select all

use R_lattice,     ONLY:ng_closed

After that you will need to recompile yambo

Best,
D

[xueshanxihua]

Dear Sangalli,

Thank you very much for this suggestion, I will try it.

[xueshanxihua]

Dear Sanglli,

Following your suggestion, I perform the calculations both with and without this modification, and the results are shown below.

Without:
QP [eV] @ K [1] (iku): 0.00 0.00 0.00
B=25 Eo= -1.21 E= -1.45 E-Eo= -0.23 Re(Z)=0.79 Im(Z)=-.1546E-2 nlXC=-16.21 lXC=-13.43 So= 2.483
B=25 Eo= -1.21 E= -1.45 E-Eo= -0.24 Re(Z)=0.79 Im(Z)=-.1541E-2 nlXC=-16.21 lXC=-13.43 So= 2.483
B=26 Eo= -1.21 E= -1.45 E-Eo= -0.23 Re(Z)=0.79 Im(Z)=-.1542E-2 nlXC=-16.21 lXC=-13.43 So= 2.483
B=26 Eo= -1.21 E= -1.45 E-Eo= -0.24 Re(Z)=0.79 Im(Z)=-.1538E-2 nlXC=-16.21 lXC=-13.43 So= 2.483
B=27 Eo= -1.17 E= -1.43 E-Eo= -0.25 Re(Z)=0.79 Im(Z)=-.1488E-2 nlXC=-16.51 lXC=-13.47 So= 2.719
B=27 Eo= -1.17 E= -1.42 E-Eo= -0.25 Re(Z)=0.79 Im(Z)=-.1488E-2 nlXC=-16.51 lXC=-13.47 So= 2.718
B=28 Eo= -0.73 E= 0.62 E-Eo= 1.36 Re(Z)=0.67 Im(Z)=-.6850E-2 nlXC=-31.05 lXC=-25.47 So= 7.609
B=28 Eo= -0.73 E= 0.65 E-Eo= 1.38 Re(Z)=0.67 Im(Z)=-.6860E-2 nlXC=-31.05 lXC=-25.51 So= 7.609
B=29 Eo= -0.73 E= 0.62 E-Eo= 1.36 Re(Z)=0.67 Im(Z)=-.6821E-2 nlXC=-31.05 lXC=-25.47 So= 7.609
B=29 Eo= -0.73 E= 0.65 E-Eo= 1.38 Re(Z)=0.67 Im(Z)=-.6831E-2 nlXC=-31.05 lXC=-25.51 So= 7.609
B=30 Eo= -0.28 E= 0.07 E-Eo= 0.35 Re(Z)=0.76 Im(Z)=-.1799E-2 nlXC=-23.93 lXC=-19.67 So= 4.728
B=30 Eo= -0.28 E= 0.08 E-Eo= 0.36 Re(Z)=0.76 Im(Z)=-.1799E-2 nlXC=-23.93 lXC=-19.68 So= 4.729
B=31 Eo= -0.28 E= 0.07 E-Eo= 0.35 Re(Z)=0.76 Im(Z)=-.1799E-2 nlXC=-23.93 lXC=-19.67 So= 4.728
B=31 Eo= -0.28 E= 0.08 E-Eo= 0.36 Re(Z)=0.76 Im(Z)=-.1798E-2 nlXC=-23.93 lXC=-19.68 So= 4.729
B=32 Eo= 0.19 E= 1.52 E-Eo= 1.33 Re(Z)=0.68 Im(Z)=-.3338E-2 nlXC=-13.47 lXC=-22.44 So=-7.012
B=32 Eo= 0.19 E= 1.26 E-Eo= 1.07 Re(Z)=0.68 Im(Z)=-.3340E-2 nlXC=-13.47 lXC=-22.05 So=-7.012
B=33 Eo= 1.65 E= 2.96 E-Eo= 1.31 Re(Z)=0.70 Im(Z)=-.7422E-2 nlXC=-14.48 lXC=-21.67 So=-5.307
B=33 Eo= 1.65 E= 2.98 E-Eo= 1.33 Re(Z)=0.70 Im(Z)=-.7429E-2 nlXC=-14.48 lXC=-21.70 So=-5.306
B=34 Eo= 1.65 E= 2.96 E-Eo= 1.31 Re(Z)=0.70 Im(Z)=-.7373E-2 nlXC=-14.48 lXC=-21.67 So=-5.307
B=34 Eo= 1.65 E= 2.98 E-Eo= 1.33 Re(Z)=0.70 Im(Z)=-.7380E-2 nlXC=-14.48 lXC=-21.70 So=-5.306

With:
QP [eV] @ K [1] (iku): 0.00 0.00 0.00
B=25 Eo= -1.21 E= -1.16 E-Eo= 0.06 Re(Z)=0.79 Im(Z)=-.1546E-2 nlXC=-16.21 lXC=-13.80 So= 2.482
B=25 Eo= -1.21 E= -1.29 E-Eo= -0.08 Re(Z)=0.79 Im(Z)=-.1541E-2 nlXC=-16.21 lXC=-13.63 So= 2.482
B=26 Eo= -1.21 E= -1.89 E-Eo= -0.67 Re(Z)=0.79 Im(Z)=-.1542E-2 nlXC=-16.21 lXC=-12.88 So= 2.482
B=26 Eo= -1.21 E= -1.93 E-Eo= -0.71 Re(Z)=0.79 Im(Z)=-.1537E-2 nlXC=-16.21 lXC=-12.82 So= 2.482
B=27 Eo= -1.17 E= -1.72 E-Eo= -0.54 Re(Z)=0.79 Im(Z)=-.1488E-2 nlXC=-16.50 lXC=-13.10 So= 2.718
B=27 Eo= -1.17 E= -1.70 E-Eo= -0.53 Re(Z)=0.79 Im(Z)=-.1487E-2 nlXC=-16.50 lXC=-13.11 So= 2.718
B=28 Eo= -0.73 E= 0.66 E-Eo= 1.39 Re(Z)=0.67 Im(Z)=-.6851E-2 nlXC=-31.04 lXC=-25.52 So= 7.608
B=28 Eo= -0.73 E= 1.12 E-Eo= 1.85 Re(Z)=0.67 Im(Z)=-.6861E-2 nlXC=-31.05 lXC=-26.21 So= 7.608
B=29 Eo= -0.73 E= 0.60 E-Eo= 1.33 Re(Z)=0.67 Im(Z)=-.6821E-2 nlXC=-31.04 lXC=-25.43 So= 7.608
B=29 Eo= -0.73 E= 0.84 E-Eo= 1.58 Re(Z)=0.67 Im(Z)=-.6831E-2 nlXC=-31.05 lXC=-25.80 So= 7.608
B=30 Eo= -0.28 E= -0.34 E-Eo= -0.06 Re(Z)=0.76 Im(Z)=-.1799E-2 nlXC=-23.93 lXC=-19.12 So= 4.728
B=30 Eo= -0.28 E= -0.37 E-Eo= -0.09 Re(Z)=0.76 Im(Z)=-.1798E-2 nlXC=-23.93 lXC=-19.08 So= 4.728
B=31 Eo= -0.28 E= 0.10 E-Eo= 0.38 Re(Z)=0.76 Im(Z)=-.1799E-2 nlXC=-23.93 lXC=-19.71 So= 4.728
B=31 Eo= -0.28 E= -0.04 E-Eo= 0.24 Re(Z)=0.76 Im(Z)=-.1798E-2 nlXC=-23.93 lXC=-19.52 So= 4.728
B=32 Eo= 0.19 E= 1.54 E-Eo= 1.35 Re(Z)=0.68 Im(Z)=-.3338E-2 nlXC=-13.47 lXC=-22.47 So=-7.011
B=32 Eo= 0.19 E= 1.56 E-Eo= 1.37 Re(Z)=0.68 Im(Z)=-.3340E-2 nlXC=-13.47 lXC=-22.49 So=-7.011
B=33 Eo= 1.65 E= 3.04 E-Eo= 1.39 Re(Z)=0.70 Im(Z)=-.7422E-2 nlXC=-14.48 lXC=-21.79 So=-5.306
B=33 Eo= 1.65 E= 3.28 E-Eo= 1.63 Re(Z)=0.70 Im(Z)=-.7429E-2 nlXC=-14.48 lXC=-22.13 So=-5.305
B=34 Eo= 1.65 E= 3.38 E-Eo= 1.73 Re(Z)=0.70 Im(Z)=-.7373E-2 nlXC=-14.48 lXC=-22.28 So=-5.306
B=34 Eo= 1.65 E= 3.62 E-Eo= 1.97 Re(Z)=0.70 Im(Z)=-.7380E-2 nlXC=-14.48 lXC=-22.61 So=-5.305

The largest deviation previously in band_32 is well corrected, however the overall behavior is not improved, this time it occurs in more bands. In both cases, the difference solely comes from "lXC" term, for which all bands have a splitting more or less. I also check the <nks|HF|nks> term given in the output, and its degeneracy is well produced.

*By the way, the absolutely value is different with above, because I use a coarser k-grid for this comparison.

[Daniele Varsano]

Dear Zeyu Jiang,
many thanks, indeed this does not solve the problem.
We will reproduce the error in the next days and see what is going on.

Best,
Daniele