[QE-users] Broken kramers degeneracy in antiferromagnet

[Francesco Delodovici]

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

 
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