[QE-users] Broken kramers degeneracy in antiferromagnet

[Davide Ceresoli]

Dear Francesco,
I might be wrong, but could it be this case:
https://physics.aps.org/articles/v17/4
?

Best,
D.


On 1/16/24 21:47, Francesco Delodovici wrote:
> Dear users,
> 
> I have a problem computing the electrons band structure of BiFeO3, 
> antiferromagnet (no SOC), R3c space gorup,
> with Hubbard corrections on Fe.
> I define different starting_magnetizations for the two sublattices of spin 
> centers, as described in the Input File Description.
> When I compute the electronic bands I see that the degeneracy of the spin-up and 
> spin-down states is lifted
> only along certain directions.
> Since the time-reversal symmetry is present but the inversion symmetry is broken 
> I would expect the bands to respect
> Kramers degeneracy:   E_up (k) = E_dn (-k) .
> This is not what I find, as you can see from the picture attached.
> The energy difference can be as large as 0.2 eV, so this is not numerical noise.
> 
> I tried different solutions, including using an explicit k-points mesh, use 
> nosym=true, starting from different
> initial magnetizations, but I always obtain the same odd behaviour.
> I also tried FeO3, same procedure, with an automatically generated k-mesh, and 
> the spin-polarized bands are degenerate as they should.
> I paste below the input file of the self consistent calculation, I'm using 
> version 7.0, with PAW pseudopotentials.
> 
> I appreciate any suggestion,
> thank you!
> 
> Francesco Delodovici, CentraleSupelec, Universitè Paris-Saclay.
> 
> 
> ##################################################
> 
>   &control
>      calculation='scf'
>      restart_mode='from_scratch',
>      pseudo_dir = './pseudop/',
>      outdir='./'
>      prefix='BFO'
>      tstress = .TRUE.
>      tprnfor = .TRUE.
>   /
> &system
>      ibrav = 0, celldm(1)=10.660942,
>      nat= 10, ntyp=4,
>      ecutwfc =120.0, ecutrho=600.0
>      occupations='smearing', smearing='gaussian', degauss=0.02
>      nspin = 2,
>      starting_magnetization(2) = -1
>      starting_magnetization(3) = 1
>      lda_plus_u=.true.
>      lda_plus_u_kind = 0
>      Hubbard_U(2) = 4.5
>      Hubbard_U(3) = 4.5
> 
>   /
>   &electrons
>      conv_thr = 1.0e-9
>   /
> 
> ATOMIC_SPECIES
>   Bi 208.98 Bi.upf
>   Fe1 55.85  Fe.upf
>   Fe2 55.85  Fe.upf
>   O  15.999 O.upf
> 
> CELL_PARAMETERS (alat= 10.66094200)
>     0.496963620  -0.286922080   0.819002251
>    -0.000000000   0.573844160   0.819002251
>    -0.496963620  -0.286922080   0.819002251
> 
> ATOMIC_POSITIONS (crystal)
> Bi           -0.0064211942       -0.0064211938       -0.0064211942
> Bi            0.4935787307        0.4935787311        0.4935787307
> Fe1           0.2189690501        0.2189690504        0.2189690501
> Fe2           0.7189689110        0.7189689114        0.7189689110
> O             0.3893335266        0.5347428617        0.9390758847
> O             0.9390758845        0.3893335266        0.5347428617
> O             0.5347428621        0.9390758842        0.3893335268
> O             0.0347428643        0.8893334799        0.4390758846
> O             0.8893334801        0.4390758843        0.0347428647
> O             0.4390758848        0.0347428643        0.8893334799
> 
> K_POINTS (automatic)
> 6 6 6 0 0 0
> 

-- 
+--------------------------------------------------------------+
   Davide Ceresoli
   CNR - Istituto di Scienze e Tecnologie Chimiche (SCITEC)
   c/o University of Milan, via Golgi 19, 20133 Milan, Italy
   Email: davide.ceresoli at cnr.it
   Phone: +39-02-50314276, +39-347-1001570 (mobile)
   Skype: dceresoli
   Website: http://sites.google.com/site/dceresoli/
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