How can I assign spins to an non-planar Anti-Ferro Magnetic system (CoO in this case)?

Question

I have been working with an anti-ferromagnetic material Cobalt Oxide. And in the image given below the blue spheres are Co ions. The blue spheres form a tetrahedron shape.

And I've assigned the spin configuration as per this image I've taken from an online thesis.

So according to the image, the 3 Co atoms in a plane will be assigned on spin(say up) and the remaining one Co atom is assigned a down spin. I have given the code below (input file):

&CONTROL 
 calculation = "scf"
 prefix = "CoO"
 outdir = "./outdir"
 pseudo_dir = "."
 tprnfor = .true.
 tstress = .true.
 verbosity = "low"

/


&SYSTEM
  ibrav = 0
  A =    4.59861
  nat = 8
  ntyp = 3
  ecutwfc = 60
  ecutrho = 445
  nspin = 2
  starting_magnetization(1)=  1
  starting_magnetization(2)= -1
  occupations = "smearing"
  smearing = "mv"
  degauss = 0.005d0
  
/
&electrons 
    conv_thr = 1d-8
    mixing_beta = 0.7d0
/

CELL_PARAMETERS {alat}
  1.000000000000000   0.000000000000000   0.000000000000000 
  0.000000000000000   1.000000000000000   0.000000000000000 
  0.000000000000000   0.000000000000000   1.000000000000000 
ATOMIC_SPECIES
  Co   58.93300  Co.pbe-spn-kjpaw_psl.0.3.1.UPF
  Co1   58.93300  Co.pbe-spn-kjpaw_psl.0.3.1.UPF
   O1   15.99900   O.pbe-n-kjpaw_psl.1.0.0.UPF
ATOMIC_POSITIONS {crystal}
 Co    0.250000000000000   0.750000000000000   0.750000000000000 
 Co1   0.250000000000000   0.250000000000000   0.250000000000000 
 Co    0.750000000000000   0.750000000000000   0.250000000000000 
 Co    0.750000000000000   0.250000000000000   0.750000000000000 
 O1    0.500000000000000   0.500000000000000   0.500000000000000 
 O1   0.500000000000000   0.000000000000000   0.000000000000000 
 O1    0.000000000000000   0.500000000000000   0.000000000000000 
 O1    0.000000000000000   0.000000000000000   0.500000000000000 

K_POINTS {automatic}
 17 17 17 0 0 0

But the magnetization is non-zero. which is wrong.

 total magnetization       =     6.01 Bohr mag/cell
 absolute magnetization    =    10.32 Bohr mag/cell

It would be nice if someone could shed some light on this .Thanks in advance :)

Answer 1

The problem is that you haven't got a unit cell which can support that magnetic structure. Your cell is a perfectly good representation of the atomic periodicity, but it is not compatible with the desired magnetic periodicity -- remember that the magnetic structure of a material does not need to have the same periodicity as the atomic structure (or, indeed, any periodicity!).

A periodic simulation program needs to work with a simulation cell which, when repeated periodically throughout all space, generates the electronic structure you want, which means it must obey respect both the atomic and magnetic symmetries. Since the relevant planes for the magnetic structure you want are (111) planes, I suggest you re-orient your cell along the (111)-direction. With this new cell, the magnetic structure you seek is simply alternating up and down spins in the out-of-plane direction.