[Wien] Units in Stoner criteria

[Gavin Abo]

Not an expert on the subject, but below are my comments.

For /I/*DOS(/E/_F), whether you use

/I/ in eV and DOS(/E/_F) in 1/eV [1,2]

or

/I/ in (eV*spin*f.u.)/states and DOS(/E/_F)in states/(eV*spin*f.u.) [3]

or

another unit variant such aswith energy in Ry [4].  It does not look 
like it matters as long as /I/*DOS(/E/_F) comes out unitless for the 
dimensional analysis and has appropriate values/constants.

Note: For natural units (atomic units of WIEN2k [5]), while they have 
the advantage of simplicity, their can sometimes be a loss of 
information for dimensional analysis [6].  Thus, you may want to use SI 
units [7].

For //U/*/D/(E_/F/) > /(1/v) with D/(E_/F/)/ in atom/volume/energy and 
perhaps U in 1/(atom/energy), if you multiple both sides of the equation 
by v:

//U/*/D/(E_/F/)*v > /(1/v)*v

//U/*/D/(E_/F/)*v > /1

then

//U/*/D/(E_/F/) > /1

with D/(E_/F/)/ now in atom/energy.

[1] https://hal.archives-ouvertes.fr/hal-00785221 , 
https://doi.org/10.1016/j.solidstatesciences.2012.12.003
[2] 
http://susi.theochem.tuwien.ac.at/reg_user/textbooks/WIEN2k_lecture-notes_2011/Schwarz_magnetism.pdf 
(slide 7) , 
https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg05254.html
[3] http://yclept.ucdavis.edu/Publ/tiau-prb-20april.pdf , 
https://doi.org/10.1103/PhysRevB.95.205124
[4] 
https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg05127.html
[5] 
https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg15660.html
[6] https://en.wikipedia.org/wiki/Natural_units
[7] https://en.wikipedia.org/wiki/SI_base_unit
[8] No Stoner parameter in WIEN2k output file: 
http://zeus.theochem.tuwien.ac.at/pipermail/wien/2014-April/020942.html

On 12/7/2017 7:51 PM, Alex wrote:
> Dear all,
>
> I was wondering that what the correct units of Stoner parameter (/I/) 
> and DOS(/E/_F) (density of state at Fermi level) used in the Stoner 
> criteria of magnetism (/I/*DOS(/E/_F) >‌ 1) is?
> Does DOS(/E/_F) should have a unit of (atom/energy) or 
> (atom/volume/energy) ... and then similar change for the unit of /I/?
> Different defined units for them in different literatures cause 
> confusion (for me), or for example when Coulomb repulsion (/U/) is 
> used instead of /I,/ the Stoner criteria change to //U/*/D/(E_/F/) > 
> /(1/v) where v is the unit cell volume/./
> Or for instance inspection of the formulas of 14--27 of below 
> reference [1] convinces me that the unit of volume is missing somewhere.
> /
> /
> [1]. 
> http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.92.9357&rep=rep1&type=pdf/
> /
> /
> /
> In my specific case I consider an simple FCC Ni, and then in 
> non-magnetic phase I calculated the DOS(/E/_F) for one of the Ni atoms 
> such that the integration of the corresponding DOS curve until the 
> Fermi level gives around 10 electron./
> /
> /
> /
> Thanks for you help.
>
> Regards,
> Alex
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://zeus.theochem.tuwien.ac.at/pipermail/wien/attachments/20171208/b15d9914/attachment.html>