[Pw_forum] Antiferromagnetic coupling between vacancies in a III-V ZB semiconductor

[ilyes hamdi]

Dear QE users,

I try to  calculate the exchange coupling constants J in the Heisenberg model, for a  128 atom Zinc Blend supercell of BN containing two vacancies of Boron.
To do this one should determine the energy of the ferromagnetic (FM) and the antiferromagnetic (AFM) states.
The FM state is simple to simulate since the spins of the 4 N atom surrounding one  vacancy are parallel. However for the AFM state, an ambiguity arises since one have many spin configurations, for exemple: 1) The 4 N atoms surrounding the first  vacancy may have spin up and the other 4 N atoms surrounding the second vacancy have spin down.  2) For the first vacancy, 2 N atoms may have spin up and the other 2 N atoms spin down. For the second vacancy, we use the translation symmetry to get the same  spin configuration as the first vacancy.

For  these AFM states, we obtain a different energy. My question is how to choose the correct AFM state? 
For me, I think the first is the correct one, because one must think as one have  two primitive unit cells containing each one  vacancy. To  get
an AFM coupling, the first N atoms (surrounding the first vacancy) may have spin up and second N spin down.

PS: To simulate the AFM state, I have chosen 4 type of atoms B , N, N1 (surrounding the first vacancy) and N2 (surrounding the second vacancy) with:
starting_magnetization(1) = 0.0
starting_magnetization(2) = 0.0
starting_magnetization(3) =  0.5
starting_magnetization(4) = -0.5


-- 
Dr. Ilyes Hamdi Ass. Prof
Department of electronics and automatics
Institute of Applied sciences and technology
Tunisia
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