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

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 :)

• I think that you need to map the atoms in your cell with the corresponding atoms in the figure. You have four atoms in the cell, but they are grouped as three (Co) and one (Co1). – Camps Nov 20 '20 at 15:20