How to get the antiferromagnetic structure of NiO in NaCl structure

From the reply of Mr Delamora to my question 

Abed Reg Sat, 29 Nov 2014 13:08:47 -0800

Dear Wien2k users

To do the antiferromagnetic calculation for the bcc  Cr, we use the P cubic
structure with 2 atoms; and for the fcc Ni we use the P cubic structure
with 4 atoms.

If we want to do a antiferromagnetic calculation for NaCl cubic structure
with 2 atoms, what will be the structure in cubic system?

https://www.mail-archive.com/wien%40zeus.theochem.tuwien.ac.at/msg11512.html

delamora Sun, 30 Nov 2014 15:07:19 -0800

This problem is quite interesting;

You have Ni in a FCC arrangement, so you have Ni tetrahedra, so how can you 
place them in an antiferromangnetic order???

It is frustratng!!! Well this is known as geometric frustration, which is a 
very interesting field!!!

On the opposite stance immagine a simple Ni crystal with an antiferromagnetic 
order, there is a simple answer; alternating spins in the axis, like the NaCl 
crystal: Na represents up, Cl dn;

Now, the picture that you sent the crystal has Ni atoms alternating in spin in 
the 111 planes; one plane up, next dn. In each plane the Ni are ordered 
ferromagnetic!!!

This is not the correct structure, but it is good for a approximate calculation.


To reproduce this structure you start by defining the structure as shown in 
your picture;

You make a crystal with 2 atoms, cubic "F" with Na at 0,0,0 and O at 1/2,0,0.

The conventional structure looks like the one that you sent, but the primitive 
one is simpler.

The problem is that when you try to put one Ni plane up and the next dn then 
the Ni at 000 is up and the one at 111 is dn, then you have to double the 
structure in the 111 direction:

You make the cell with a=b=c=4.17A, alfa=beta=gamma=89.999 (not 90, but close)

and put

Ni 000   0,1/2,1/2   1/2,0,1/2    1/2,1/2,0

O  1/2,0,0   0,1/2,0    0,0,1/2    1/2,1/2,1/2

with sgroup it will convert it to rhombohedral which with supercell you can now 
convert it hexagonal and you can expand in the 001 direction (wich in the 
original cell was 111)

https://www.mail-archive.com/wien%40zeus.theochem.tuwien.ac.at/msg11517.html

delamora Sun, 30 Nov 2014 16:00:24 -0800

Here I make the structures step by step

***********************************

Here you have;

    aaa.struct-cub-F

https://www.mail-archive.com/wien%40zeus.theochem.tuwien.ac.at/msg11519/aaa.struct-cub-F

with supercell =>
    aaa.struct-cub-P

https://www.mail-archive.com/wien%40zeus.theochem.tuwien.ac.at/msg11519/aaa.struct-cub-P

change angles
    aaa.struct-89.999

https://www.mail-archive.com/wien%40zeus.theochem.tuwien.ac.at/msg11519/aaa.struct-89.999

with "initialize calc" and "x sgroup" =>
    aaa.struct-rho

https://www.mail-archive.com/wien%40zeus.theochem.tuwien.ac.at/msg11519/aaa.struct-rho

with supercell =>

    aaa.struct-hex

https://www.mail-archive.com/wien%40zeus.theochem.tuwien.ac.at/msg11519/aaa.struct-hex

with supercell =>
    aaa.struct-hex-2

https://www.mail-archive.com/wien%40zeus.theochem.tuwien.ac.at/msg11519/aaa.struct-hex-2

here the Ni at

    c=0, 1/3 and 2/3 are marked as Ni   1

    c=1/6, 3/6 and 5/6 are marked as Ni   2

with "initialize calc" and "x sgroup" =>
    aaa.struct-anti

https://www.mail-archive.com/wien%40zeus.theochem.tuwien.ac.at/msg11519/aaa.struct-anti

Which is the structure that you want.

**************************

In this "aaa.struct-anti" with F4 you see the hexagonal structure where you see 
the Ni-1 planes and Ni-2 planes while with F3 you see the primitive cell.