[QE-users] Technical questions about calculation of exchage coupling constant J in Heisenberg model

[BARRETEAU Cyrille]

Dear Konrad Gruszka

This is a difficult question in fact.
There are to my knowledge three ways to extract Jij  from DFT calculation:

i) Your approach that consist in doing several DFT calculation of various spin (usually collinear) configurations and mapping to Heinsenberg by inverting a series of linear equation.
ii) The explicit approach that uses Liechtenstein formula (not implemented in QE)
iii) The spin-spiral approach (based on the generalized Bloch theorem) that consists in calculation E(q) for various spin sipral vectors q and then fitting the E(q)  to get the Jij.

All these approaches have their advantages and inconveniences but they all rely on the validity of Heisenberg Hamiltonian.

If in your case some magnetic configurations lead to solutions with a strong decrease of the magnetic moment that means that you are no longer in a pure Heisenberg picture.

Either you ignore these configurations or you generalize your Hamiltonian by adding a Landau-like term AM^2+BM^4 for example to reproduce the variation of magnetic amplitude...

There are some publications using this generalized Hamiltonian.

Cyrille

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Cyrille Barreteau
CEA Saclay, IRAMIS, SPEC Bat. 771
91191 Gif sur Yvette Cedex, FRANCE
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+33 1 69 08 38 56 /+33  6 47 53 66 52  (mobile)
email:     cyrille.barreteau at cea.fr
Web:     http://iramis.cea.fr/Pisp/cyrille.barreteau/
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De : users [users-bounces at lists.quantum-espresso.org] de la part de kgruszka [kgruszka at wip.pcz.pl]
Envoyé : mercredi 5 juin 2019 13:52
À : users at lists.quantum-espresso.org
Objet : [QE-users] Technical questions about calculation of exchage coupling constant J in Heisenberg model

Dear users,

Recently I'm trying to do the so called mapping of DFT energies to the Heisenberg spin hamiltonian in order to calculate spin coupling constants J(i, j). To do so,  I need to calculate Total energy for system with specific various spin configurations,  that I should force my system to be in.  Then the procedure is to solve equations obtained in that way in respect to J(i, j). In those eq.  spin i or j can have only 2 values: up (1) and down (-1).
The main question is how to force specific spin configurations?  For simplicity let consider BCC iron.
I define in input supercell for BCC iron with different species (fe1,  fe2 etc and nspin=2) so any site is defined separately  and each different site can have diffetent spin.  Then,  I define starting_magnetisation for each site for eg.  starting_magnetisation(1)=1, starting_magnetisation(2)=-1 etc,  for lets say antiferromagnetic configuration.  The problem is,  that during SCF cycles I can see spin flips,  sometimes spin magnitude is going close to 0 (I conidered not only BCC iron) ruining my starting configuration,  so my system evolves (as it is supposed to) searching for the lowest energy state,  that is not always my enforced state.

Therefore,  as I know that this approach is quite  bad,  could you please suggest the correct way to do this mapping? Searching for local energy minima in metastable spin configurations seems to be some way,  but I hope that there is another, quicker/better/correct way; how to "lock"  my spin configuration?

Also,  is in case of obtaining J(i, j)  noncollinear spin calculation a neccesity? My another doubt is that in case of low spin moment for example = - 0.2 uB can I treat it like spin down configuration in model Hamiltonian,  or do I need exact -1 uB, and what in case of magnitude greater/lower than 1/-1?.

As you can see by my questions I am really confused and I need some basic understanding...

Hope I didn't offended any one by my very basic questions,  but despite my efforts, I did not find an article describing the technicalities of this procedure, only some general considerations.

Regards,

Konrad Gruszka
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