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question on MLWF in Noncolinear calculation
Date: 2011/05/06 00:30
Name: jchang   <wony65@gmail.com>

Hi,

I have a question on MLWF.
In calculating MLWF, we assign a certain orbital as a projector.

For example,

in the wannier function example file of calculating MLWF for GaAs without spin-orbit coupling -> 'GaAs.dat' in work folder

<Wannier.Initial.Projectors
proj-s 0.125 0.125 0.125 0.0 0.0 1.0 1.0 0.0 0.0
proj-s -0.375 0.125 0.125 0.0 0.0 1.0 1.0 0.0 0.0
proj-s 0.125 -0.375 0.125 0.0 0.0 1.0 1.0 0.0 0.0
proj-s 0.125 0.125 -0.375 0.0 0.0 1.0 1.0 0.0 0.0
<Wannier.Initial.Projectors

we assign one s orbital on every atom.


If we do the same thing with spin-orbit coupling (Noncolinear calculation), in the file 'GaAs_NC.dat',

<Wannier.Initial.Projectors
proj-s 0.125 0.125 0.125 0.0 0.0 1.0 1.0 0.0 0.0
proj-s -0.375 0.125 0.125 0.0 0.0 1.0 1.0 0.0 0.0
proj-s 0.125 -0.375 0.125 0.0 0.0 1.0 1.0 0.0 0.0
proj-s 0.125 0.125 -0.375 0.0 0.0 1.0 1.0 0.0 0.0
proj-s 0.125 0.125 0.125 0.0 0.0 1.0 1.0 0.0 0.0
proj-s -0.375 0.125 0.125 0.0 0.0 1.0 1.0 0.0 0.0
proj-s 0.125 -0.375 0.125 0.0 0.0 1.0 1.0 0.0 0.0
proj-s 0.125 0.125 -0.375 0.0 0.0 1.0 1.0 0.0 0.0
Wannier.Initial.Projectors>

we assign two s orbital on every atom.


I guess that it is to consider spin-up orbital and spin-down orbital.


Then, can we say which orbital(used as a projector) is spin-up or spin-down?
In other words, among the calculated MLWF, can we say which one is spin-up or spin-down?


Please give me some advices.


Thanks
jiwon





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Re: question on MLWF in Noncolinear calculation ( No.1 )
Date: 2011/05/21 00:36
Name: T.Ozaki

Hi,

In non-collinear calculations, one-particle wave functions are
expressed by a linear combination of spin-up and spin down components,
which makes simple assignment of wave functions to spin-up and spin-down
difficult, while in the GaAs case the one-particle wave functions almost
preserve the character.

With this mind, when you give eight projectors by


<Wannier.Initial.Projectors
proj-s 0.125 0.125 0.125 0.0 0.0 1.0 1.0 0.0 0.0
proj-s -0.375 0.125 0.125 0.0 0.0 1.0 1.0 0.0 0.0
proj-s 0.125 -0.375 0.125 0.0 0.0 1.0 1.0 0.0 0.0
proj-s 0.125 0.125 -0.375 0.0 0.0 1.0 1.0 0.0 0.0
proj-s 0.125 0.125 0.125 0.0 0.0 1.0 1.0 0.0 0.0
proj-s -0.375 0.125 0.125 0.0 0.0 1.0 1.0 0.0 0.0
proj-s 0.125 -0.375 0.125 0.0 0.0 1.0 1.0 0.0 0.0
proj-s 0.125 0.125 -0.375 0.0 0.0 1.0 1.0 0.0 0.0
Wannier.Initial.Projectors>

this implies that you are trying to obtain eight WFs in the energy windows.
So, roughly speaking, it is true that 4 of them are used for the "spin-up"
and the others are for "spin-down".

However, when you treat a system with a non-collinear magnetic structure,
the above is not a proper statement anymore.

Best regards,

TO
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