[Wien] How to determine the exchange splitting in metals ?
Fecher, Gerhard
fecher at uni-mainz.de
Sun Apr 26 09:21:38 CEST 2020
Actually it is not clear what you want to do, and for what purpose !
... and answer to "Is correct ?" : NO, the exchange splitting is not the energy difference between two maxima of the density of states.
Check the band structure of Fe
you see that there are in the majority case three bands (states) occupied at the Gamma point,
these are from bottom (lowest energy) a1g (s), t2g (dxy, dxz, dyz) , and eg (dz^2, dx^2-y^2)
in the minority case only the a1g and t2g are at Gamma below the Fermi energy.
(the degeneracy is seen from the dispersion in the Sigma direction)
You should easily find out that there is no unique splitting, but it depends on the state,
and as I already mentioned in earlier mail you have different splittings (including not only exchange splitting) depending on the k-points and their symmetry.
The energies of the bands, or better the ranges of the band energies are (roughly, depending on the k-mesh) given in the case.scf2up/dn files.
To find the correct energies at Gamma you van either have a look in the spaghetti files or better use irrep.
(Note their might be changes in the band series if you have a more complicated system,
and then you have to use irrep do find the correct band character)
The case.outputirruo/dn contains all informations, in a shortened way you will find for iron something like
(note that I cut the values after 3 digits)
for the states at Gamma (using irrep, eigval in Ry, all other information skipped):
from up from down
bnd ndg eigval eigval diff * 13.605 my info: band character
4 1 -0.021 .......... =G1+ 0.005 .......... =G1+ ==> 0.22 eV A1g (s)
5 3 0.436 .......... =G5+ 0.57 .......... =G5+ ==> 1.91 eV T2g (dxy, dxz, dyz)
8 2 0.525 .......... =G3+ 0.728 .......... =G3+ ==> 2.75 eV Eg (dz^2, dx^2-y^2)
you see that there is a very different splitting that depends on the character of the state !
(Principally one could calculate the average (1.9eV all, 2.2eV only d, note the degeneracy !),
but I think that this is an oversimplification and might be used for very rough comparison only.)
To use single maxima of the density of states for determination of the splitting does not make any sense,
just plot the density and shift either up or dn DOS by the value you found to see that it doesn't tell anything.
(The idea of Peter would only work if the up/dn densities are identical with only a rigid shift, what is usually never the case.)
Another way may be to try to find the average energy of the bands, as I mentioned before, but this will only give a very rough idea as it includes not only
the exchange but also the crystal field and possible other splittings. Further one has to take care on suitable energy ranges (see case.scf2) and normalization.
The difference in the band energies for majority and minority electrons, however, is still a good measure for the magnetic energy.
You where also asking for " the exchange splitting between the paramagnetic and ferromagnetic states", it is not clear what you mean ?
Do you mean the shift of the states between non-spinpolarized and spinpolarized up, and between non-spinpolarized and spinpolarized dn ?
Again, there is no unique shift of the states but you may compare the energies at Gamma similar to what I did above.
I suggest to read and understand the textbook of J Kübler "Theory of itinerant electron magnetism", he lists the splittings at different
high symmetry points of the Brillouin zone (for different calculaton schemes compared to experiment) for iron and cobalt.
Ciao
Gerhard
DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
"I think the problem, to be quite honest with you,
is that you have never actually known what the question is."
====================================
Dr. Gerhard H. Fecher
Institut of Inorganic and Analytical Chemistry
Johannes Gutenberg - University
55099 Mainz
and
Max Planck Institute for Chemical Physics of Solids
01187 Dresden
________________________________________
Von: Wien [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von Abderrahmane Reggad [abde.reggad at gmail.com]
Gesendet: Freitag, 24. April 2020 16:42
An: A Mailing list for WIEN2k users
Betreff: Re: [Wien] How to determine the exchange splitting in metals ?
Hello again
I have adopted another procedure as follows:
I have extracted the energy values corresping to the maximum values of DOS in the up and down spin from the files case.dos1evup and case.dos1evdn and I have found the following values:
E (max DOS up = 2.40) = - 0.95185 eV
E (maxDOS dn = 2.80) = + 1.95977 eV
and I have calculated the exchange splitting from this formula dE= + 1.95977 - ( - 0.95185) = 2.91162 eV
Is correct ?
On Fri, 24 Apr 2020 at 14:54, Abderrahmane Reggad <abde.reggad at gmail.com<mailto:abde.reggad at gmail.com>> wrote:
Thanks Gerhard for the explanation but I couldn't apply the inforation to get the exchange splitting neither from the DOS nor from the band structure
Now i have some questions about my idea using the DOS picture and I want from both of you to answer me
- is it possible from the files case.outputtup and case.outputtdn to get the energies corresponding to the integrated DOS values for spin up (5.1 e) and spin down (2.9 e) ? in the case o iron Fe
- Is it possible to determine the exchange splitting as follows: dE = E (5.1 e) - E (2.9 e) in abslute value
On Fri, 24 Apr 2020 at 14:52, Abderrahmane Reggad <abde.reggad at gmail.com<mailto:abde.reggad at gmail.com>> wrote:
Thanks Gerhard for the explanation but I couldn't apply the inforation to get the exchange splitting neither from the DOS nor from the band structure
Now i have some questions about my idea using the DOS picture and I want from both of you to answer me
- is it possible from the files case.outputtup and case.outputtdn to get the energies corresponding to the integrated DOS values for spin up (5.1 e) and spin down (2.9 e) ? in the case o iron Fe
- Is it possible to determine the exchange splitting as follows: dE = E (5.1 e) - E (2.9 e) in abslute value
I have joinded the case.outputt files or the paraagnetic and ferromagnetic state of iron Fe
Best regards
On Fri, 24 Apr 2020 at 12:26, Fecher, Gerhard <fecher at uni-mainz.de<mailto:fecher at uni-mainz.de>> wrote:
maybe use irrep to see how much the bands at the Gamma point are splitted between up and down
(single k-point no shift of BZ before calculating lapw1 -up, -dn; but be carefull which states at Gamma you compare)
Note the splitting depends on k, what you easily see from the bands, therfore a comparison of the bands mmight not be very helpful.
the mean or state resolved splittings may also be calculated by the difference in the band energies for up and down states, that is
integral n(E)up * E dE - integral n(E)down * E dE
where the integrals run over all occupied states of the valence bands, or you use only particular states, e.g. all d pr eg, or t2g only.
(Note the sum is the overall band energy, that you may compare to that of the paramagnetic state, if you wish to do for whatever reason)
Ciao
Gerhard
DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
"I think the problem, to be quite honest with you,
is that you have never actually known what the question is."
====================================
Dr. Gerhard H. Fecher
Institut of Inorganic and Analytical Chemistry
Johannes Gutenberg - University
55099 Mainz
and
Max Planck Institute for Chemical Physics of Solids
01187 Dresden
________________________________________
Von: Wien [wien-bounces at zeus.theochem.tuwien.ac.at<mailto:wien-bounces at zeus.theochem.tuwien.ac.at>] im Auftrag von Abderrahmane Reggad [abde.reggad at gmail.com<mailto:abde.reggad at gmail.com>]
Gesendet: Freitag, 24. April 2020 11:30
An: A Mailing list for WIEN2k users
Betreff: Re: [Wien] How to determine the exchange splitting in metals ?
Thanks Pr Plaha for the explanation
Now how to determine it through the band structure
Best regards
On Fri, 24 Apr 2020 at 09:14, Peter Blaha <pblaha at theochem.tuwien.ac.at<mailto:pblaha at theochem.tuwien.ac.at><mailto:pblaha at theochem.tuwien.ac.at<mailto:pblaha at theochem.tuwien.ac.at>>> wrote:
I would do this with the band structure (because this could be
k-dependent), but DOS is also fine.
Just shift up and dn DOS in energy until they overlap as much as
possible. This shift is your exchange splitting.
Am 24.04.2020 um 00:07 schrieb Abderrahmane Reggad:
> Hello wien2k users
>
> I have calculated the DOS of the paramagnetic and ferromagnetic of 3d
> transition metals Ni , Fe and I want to determine the exchange splitting
> between the paramagnetic and ferromagnetic states.
>
> How to do that ?
>
> Best regards
>
> --
> Dr. Abderrahmane Reggad
> Engineering Physics Laboratory
> Faculty of Material Sciences, Ibn Khaldoun University, Tiaret, 14000,
> Algeria
> Tel: +213(0)561861963 - Algeria
>
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--
Peter Blaha
Inst.Materials Chemistry
TU Vienna
Getreidemarkt 9
A-1060 Vienna
Austria
+43-1-5880115671
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Tel: +213(0)561861963 - Algeria
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Dr. Abderrahmane Reggad
Engineering Physics Laboratory
Faculty of Material Sciences, Ibn Khaldoun University, Tiaret, 14000, Algeria
Tel: +213(0)561861963 - Algeria
--
Dr. Abderrahmane Reggad
Engineering Physics Laboratory
Faculty of Material Sciences, Ibn Khaldoun University, Tiaret, 14000, Algeria
Tel: +213(0)561861963 - Algeria
--
Dr. Abderrahmane Reggad
Engineering Physics Laboratory
Faculty of Material Sciences, Ibn Khaldoun University, Tiaret, 14000, Algeria
Tel: +213(0)561861963 - Algeria
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