[Wien] SOC value \zeta

Peter Blaha peter.blaha at tuwien.ac.at
Sat Aug 26 18:00:12 CEST 2023 

I'm afraid, you have to hack the code.

In SRC_lapwso  checkout the routines:

hmsec.F (see comments at the top)  and
garadme.f

The latter calculates the radial matrix elements in hexl, but this is a 
4 dim array (hexl(0:lomax,nato,2,9))  and you have to figure out what 
you want.

Regards


Am 21.08.2023 um 20:33 schrieb Samolyuk, German D. via Wien:
> Dear Gerhard,
> 
> Thank your for detailed answer.
> 
> If I understand it correctly the SOC part is introduced to the 
> hamiltonian as
> 
> <phi|\zeta (\sigma l)|phi> (1)
> 
> following the expression for wave function phi (2.4 in the manual)
> |phi_k(r)> = \sum_{L} [A_{L, k}u_L(r) + B_{L, k}{\dot u_L(r)}] Y_L
> 
> the expression (1) is naturally calculated as sum of four contributions 
> and the first one has
> 
> \int dr u_L(r) \zeta u_L'(r). Again if I understand it correctly this 
> integral is calculated in the code and it's the value I'm interested in.
> 
> Best,
> 
> German
> 
> Dr. German D Samolyuk
> Materials Theory Group
> Materials Science & Technology Division
> Oak Ridge National Laboratory
> Post Office Box 2008
> Oak Ridge, TN 37831-6138
> (865) 241-5394
> (865) 241-3650 (FAX)
> ------------------------------------------------------------------------
> *From:* Wien <wien-bounces at zeus.theochem.tuwien.ac.at> on behalf of 
> Fecher, Gerhard <fecher at uni-mainz.de>
> *Sent:* Friday, August 18, 2023 4:13 AM
> *To:* A Mailing list for WIEN2k users <wien at zeus.theochem.tuwien.ac.at>
> *Subject:* [EXTERNAL] Re: [Wien] SOC value \zeta
> Dear German,
> as mentioned by Peter
> https://urldefense.us/v2/url?u=https-3A__www.mail-2Darchive.com_wien-40zeus.theochem.tuwien.ac.at_msg09672.html&d=DwIGaQ&c=v4IIwRuZAmwupIjowmMWUmLasxPEgYsgNI-O7C4ViYc&r=lTD7jQRfMViWEsN8TZ1wLmkMhVe4MCRH76GADmGBpD4&m=OsbEKiRMVyoB6JJ9cR0TBU0G3VtOXEqJhXaWmGQ8ribakT8R1LoQvMUNDI4mByuR&s=UIakgS3uhi68CwcKv4g46tpXC0-ZvZ8f_A2rVPjmMdM&e= <https://urldefense.us/v2/url?u=https-3A__www.mail-2Darchive.com_wien-40zeus.theochem.tuwien.ac.at_msg09672.html&d=DwIGaQ&c=v4IIwRuZAmwupIjowmMWUmLasxPEgYsgNI-O7C4ViYc&r=lTD7jQRfMViWEsN8TZ1wLmkMhVe4MCRH76GADmGBpD4&m=OsbEKiRMVyoB6JJ9cR0TBU0G3VtOXEqJhXaWmGQ8ribakT8R1LoQvMUNDI4mByuR&s=UIakgS3uhi68CwcKv4g46tpXC0-ZvZ8f_A2rVPjmMdM&e=>
> one may use the potential to estimate the spin-orbit coupling strength.
> That is one may find the average of 1/r dV/dr by integration over space,
> taking care that the potential is not spherical (as in a free atom) and 
> thus depends not just on r but also on theta and phi.
> (potential files from lapw0: spherical part: case.vsp and non-spherical 
> part: case.vns., check the mesh and if they contain V or r*V !)
> - Care has to be taken on the singularity at the nucleus (r=0) as 
> mentioned previously, check r_0 !
> - But which space do you take for the integration in case you have 
> different atoms ?
>    the muffin tin spheres or some Bader basins ?
>    This is also the problem when 'estimating' so called site specific 
> magnetic moments,
>    the 'size' of the individual atoms in compounds is not known a priori  !
> 
> To calculate <Psi| H | Psi> you have to understand the wave functions in 
> FPLAPW
> as mentioned by Peter in
> https://urldefense.us/v2/url?u=https-3A__www.mail-2Darchive.com_wien-40zeus.theochem.tuwien.ac.at_msg22739.html&d=DwIGaQ&c=v4IIwRuZAmwupIjowmMWUmLasxPEgYsgNI-O7C4ViYc&r=lTD7jQRfMViWEsN8TZ1wLmkMhVe4MCRH76GADmGBpD4&m=OsbEKiRMVyoB6JJ9cR0TBU0G3VtOXEqJhXaWmGQ8ribakT8R1LoQvMUNDI4mByuR&s=wUyUKaXnqM6OAq2CDj8BVF5eGvoneLd5IH_t4pv1N_E&e= <https://urldefense.us/v2/url?u=https-3A__www.mail-2Darchive.com_wien-40zeus.theochem.tuwien.ac.at_msg22739.html&d=DwIGaQ&c=v4IIwRuZAmwupIjowmMWUmLasxPEgYsgNI-O7C4ViYc&r=lTD7jQRfMViWEsN8TZ1wLmkMhVe4MCRH76GADmGBpD4&m=OsbEKiRMVyoB6JJ9cR0TBU0G3VtOXEqJhXaWmGQ8ribakT8R1LoQvMUNDI4mByuR&s=wUyUKaXnqM6OAq2CDj8BVF5eGvoneLd5IH_t4pv1N_E&e=>
> Note that the wave functions (of the valence electrons) are k-dependent
> This you see from the spin orbit splitting of the bands that depends on 
> the direction in k-space.
> Maybe you also think too much in atomic physics, where the spin orbit 
> splitting does not depend k or any direction.
> 
> 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 Physics
> Johannes Gutenberg - University
> 55099 Mainz
> ________________________________________
> Von: Wien [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von 
> Samolyuk, German D. via Wien [wien at zeus.theochem.tuwien.ac.at]
> Gesendet: Donnerstag, 17. August 2023 17:43
> An: A Mailing list for WIEN2k users
> Cc: Samolyuk, German D.
> Betreff: Re: [Wien] SOC value \zeta
> 
> Gerhard,
> 
> I wanted to know <fi_l|1/r dV/dr|fi_l>, i.e. part added to the 
> hamiltonian resulting in eigenvalues and eigenvectors in case of added 
> SOC and calculated using basis of wf obtained in no SOC case. The 
> <(\sigma * l)> part I can calculate from density matrix output.
> 
> Gavin,
> 
> Thank you, the references help, but I'd rather don't hack the code 🙂.
> 
> Thank you,
> 
> German
> 
> 
> Dr. German D Samolyuk
> Materials Theory Group
> Materials Science & Technology Division
> Oak Ridge National Laboratory
> Post Office Box 2008
> Oak Ridge, TN 37831-6138
> (865) 241-5394
> (865) 241-3650 (FAX)
> ________________________________
> From: Wien <wien-bounces at zeus.theochem.tuwien.ac.at> on behalf of 
> Fecher, Gerhard <fecher at uni-mainz.de>
> Sent: Thursday, August 17, 2023 2:23 AM
> To: A Mailing list for WIEN2k users <wien at zeus.theochem.tuwien.ac.at>
> Subject: [EXTERNAL] Re: [Wien] SOC value \zeta
> 
> I don't understand the question,
> what do you like to know, \zeta (proportional to 1/r dV/dr) for each 
> atom or the orbital moment (m_l) for each atom ?
> 
> The r dependence tells you already that there is no single value for 
> 'zeta = zeta(r)'
> SO is calculated directly from dV/dr which is not printed somewhere, 
> however for a pure Coulomb potential (Z/r) it depends on the ordinal 
> number Z of the atom,
> This explains why the spin orbit interaction is stronger for 'heavier' 
> atoms.
> |1/r dV/dr| becomes large in the vicinity of the nucleus (infinity at 
> r=0) for all atoms.
> This explains why the spin-orbit splitting is large for core level (the 
> larger the closer they are (in average) to the nucleus) and small for 
> semi-core or valence level, as these electrons are in average farer away 
> from the nucleus.
> 
> Check the manual how to have the orbital moments printed.
> 
> 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 Physics
> Johannes Gutenberg - University
> 55099 Mainz
> ________________________________________
> Von: Wien [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von 
> Samolyuk, German D. via Wien [wien at zeus.theochem.tuwien.ac.at]
> Gesendet: Mittwoch, 16. August 2023 23:20
> An: wien at zeus.theochem.tuwien.ac.at
> Cc: Samolyuk, German D.
> Betreff: [Wien] SOC value \zeta
> 
> Dear colleagues,
> 
> I'm running wien2k version WIEN2K_19_LI on linux cluster. The goal is to 
> analyze magnetic anisotropy energy in YCo_5 intermetallic.
> 
> As it was explained in few presentation discussing SOC implementation in 
> wien2K it's added in following form
> 
> \zeta ({\vec \sigma}{\vec l}), where \zeta = 1/(2Mc^2) 1/r^2 dV/dr.
> 
> Question: is it possible to output value \zeta for each atom, orbital 
> moment?
> 
> I cant find it in output files and was not able to find following  
> discussion in archive.
> 
> Thank you,
> 
> German
> 
> Dr. German D Samolyuk
> Materials Theory Group
> Materials Science & Technology Division
> Oak Ridge National Laboratory
> Post Office Box 2008
> Oak Ridge, TN 37831-6138
> (865) 241-5394
> (865) 241-3650 (FAX)
> _______________________________________________
> Wien mailing list
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