Specifying MAGMOM for AFM2 (111) plane of the NiO supercell

[reynaldo.putra]

Hello, I have a question.

I am planning to model a NiO supercell, and I would like to know how important it is to obtain AFM1 and/or AFM2. If it is important to obtain AFM2 because this is what is observed in experiments, how do I specify the proper MAGMOM with respect to the Ni atom positions in the (111) plane? Do I have to check which atoms correspond to which coordinate and label them one by one? Are there any tools to assist with assigning the appropriate spins?

I have a POSCAR:

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Ni O
32 32

How do I set the MAGMOM so that it reflects AFM2 properly? Here is an example of what I have done, but I doubt that this is AFM2:

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MAGMOM = 2.0 -2.0 ... 2.0 -2.0 32*0.0
(16 times repetitions of 2.0 -2.0) 

Thank you for your time!

[marie-therese.huebsch]

Hello,

Yes, for NiO it is important to use the AFM2 ordering, if you want your calculations to agree with the experimentally observed magnetic ground state. In AFM2, the Ni magnetic moments are ferromagnetically aligned within each (111) plane, and adjacent (111) planes have opposite spin. This is distinct from AFM1, where the ferromagnetic planes are (001) planes instead.

Regarding your suggested setup: Your approach of writing MAGMOM = 2.0 -2.0 2.0 -2.0 ... assumes that alternating atoms in your POSCAR belong to alternating (111) planes. This is not the case — in a 2×2×2 cubic supercell, the atoms are ordered by their Cartesian coordinates, not by their (111) plane membership. The alternating pattern results in frustrated (mixed up/down) spins within each (111) plane, which is neither AFM2 nor any well-defined magnetic order.

Based on your POSCAR, here is how you can arrive at the appropriate MAGMOM. For the rock-salt FCC Ni sublattice, atoms in the same (111) plane have the same value of $x + y + z$ (in fractional coordinates of the conventional cell). In your 2×2×2 supercell, the rule becomes:

• For each Ni atom with supercell fractional coordinates \((x, y, z)\), compute \(n = 2(x + y + z)\), which will be an integer.

• If \(n\) is even → spin up; if \(n\) is odd → spin down.

Applying this to your 32 Ni atoms gives the correct AFM2 MAGMOM:

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MAGMOM = -2.0 2.0 2.0 2.0 2.0 -2.0 -2.0 -2.0 2.0 -2.0 -2.0 -2.0 -2.0 2.0 2.0 2.0 2.0 -2.0 -2.0 -2.0 -2.0 2.0 2.0 2.0 -2.0 2.0 2.0 2.0 2.0 -2.0 -2.0 -2.0 32*0.0

This gives 16 spin-up and 16 spin-down Ni atoms, as expected for a balanced AFM2 configuration.

However, unless you specifically need the large supercell (e.g., for defects or phonons), I recommend using the 4-atom rhombohedral primitive cell of the AFM2 magnetic structure instead. See attached image. This is much more efficient computationally:

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NiO AFM2
4.19
  1.0  0.5  0.5
  0.5  1.0  0.5
  0.5  0.5  1.0
Ni O
2 2
Direct
  0.00  0.00  0.00
  0.50  0.50  0.50
  0.25  0.25  0.25
  0.75  0.75  0.75

with:

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MAGMOM = 2 -2 0 0

afm2_combined.png

The two Ni atoms at latex[/latex] and latex[/latex] are in (111) planes with opposite spins. This cell has only 4 atoms instead of 64 and captures the full AFM2 symmetry. You can adjust the lattice parameter in the second line (4.19 Å is approximate).

I hope that helps. Let me know if you need more help. NiO can be quite tricky. See eg the discussion here: https://vasp.at/wiki/Choosing_pseudopot ... ium_volume

Best regards,
Marie-Therese

[reynaldo.putra]

Dear Marie-Therese,

Thank you! I highly appreciate your help with the rules of the spin assignment.

Yes, unfortunately I had to simulate a supercell because I would eventually simulate them on an interface slab.
I have a few questions:

• What are the rules for applying the AFM2 spin to a (110)-oriented NiO slab? I understand that for (111) it is much simpler due to how it is parallel with the surface orientation.

• Regarding to the website you sent which discusses the different lattice parameters of NiO depending on the pseudopotential used, would it still be recommended to use the standard Ni pseudopotential? I am trying to figure out situations where using the Ni_sv_GW pseudopotential would be necessary, other than to improve the lattice parameters.

Thank you!
Reynaldo

[marie-therese.huebsch]

Hi Reynaldo,

I see, for a slab you will need to consider the larger unit cell. In order to assign the magnetic moments for any slab or orientation you can write a script that applies the spin wave. The AFM2 magnetic order is characterized by a propagation vector \(\mathbf{q} = (1/2, 1/2, 1/2)\) in reciprocal lattice units of the conventional FCC cubic cell. This means the spin at any lattice site \(\mathbf{R}_i\) (with fractional coordinates \((x, y, z)\) in the conventional cell) is given by:

\(S_i = S_0 \cdot \cos(2\pi\, \mathbf{q} \cdot \mathbf{R}_i) = S_0 \cdot \cos(\pi(x + y + z)) = S_0 \cdot (-1)^{x+y+z} \)

The last step works because for FCC sites in the conventional cubic cell, \( x+y+z \) is always an integer (the FCC positions like (0,0,0), (1/2,1/2,0), etc. all give integer sums). So \( cos(n\pi) = (-1)n \).

For a 2×2×2 supercell, the supercell fractional coordinates \((x_s, y_s, z_s)\) relate to conventional cell coords by a factor of 2: \( (x,y,z)_{conv} = \) \(2\cdot(x_s, y_s, z_s)\). Thus:

\(S_i = S_0 \cdot (-1)^{2(x_s + y_s + z_s)}\)

This is exactly the formula used above. For a general \(N \times N \times N\) supercell, replace 2 with N.

Physically, \(\mathbf{q} = (1/2, 1/2, 1/2)\) means the spin modulation has a wavelength of \(2d_{111}\) (twice the (111) interplanar spacing), i.e., the spins flip sign between every (111) plane. This is precisely the AFM2 definition: ferromagnetic (111) sheets stacked antiferromagnetically.

Regarding the choice of the pseudopotential, honestly you need to test this for the system and quantity of your interest. There is no way to predict a priory which potential has to be used (only vage gut feeling). The save choice is always the one with most valence electrons but that can be computationally expensive. Also, the effect in NiO on the lattice parameters is caused by the electronic state being either more localized or delocalized. So you should not draw the conclusion that it is only important for lattice parameters. There is extended advice on how to test the choice of the pseudopotential here: https://vasp.at/wiki/Choosing_pseudopotentials

Hope this helps. Let me know if you have a follow up question about specifying MAGMOM. If you have a different question, feel free to open another topic.

Best regards,
Marie-Therese