[Wien] SOC value \zeta

Mon Aug 21 20:33:57 CEST 2023

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=
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=
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
Wien at zeus.theochem.tuwien.ac.at
https://urldefense.us/v2/url?u=http-3A__zeus.theochem.tuwien.ac.at_mailman_listinfo_wien&d=DwICAg&c=v4IIwRuZAmwupIjowmMWUmLasxPEgYsgNI-O7C4ViYc&r=lTD7jQRfMViWEsN8TZ1wLmkMhVe4MCRH76GADmGBpD4&m=Z0Ws7mNwi0HecEO8g8Ilg4oT94bzABn54RxNzgE074HCxT7FHLbZO1Ftr_ToxEk7&s=9cB8V56edYTJwbLsOWV0-mnAnnWV4nbLT4wVJ_fdEHk&e=
SEARCH the MAILING-LIST at:  https://urldefense.us/v2/url?u=http-3A__www.mail-2Darchive.com_wien-40zeus.theochem.tuwien.ac.at_index.html&d=DwICAg&c=v4IIwRuZAmwupIjowmMWUmLasxPEgYsgNI-O7C4ViYc&r=lTD7jQRfMViWEsN8TZ1wLmkMhVe4MCRH76GADmGBpD4&m=Z0Ws7mNwi0HecEO8g8Ilg4oT94bzABn54RxNzgE074HCxT7FHLbZO1Ftr_ToxEk7&s=XsODSZtsVrEywDdUZ6HpsCkcXNxFS_VN93qPa5DEL3k&e=
_______________________________________________
Wien mailing list
Wien at zeus.theochem.tuwien.ac.at
https://urldefense.us/v2/url?u=http-3A__zeus.theochem.tuwien.ac.at_mailman_listinfo_wien&d=DwIGaQ&c=v4IIwRuZAmwupIjowmMWUmLasxPEgYsgNI-O7C4ViYc&r=lTD7jQRfMViWEsN8TZ1wLmkMhVe4MCRH76GADmGBpD4&m=OsbEKiRMVyoB6JJ9cR0TBU0G3VtOXEqJhXaWmGQ8ribakT8R1LoQvMUNDI4mByuR&s=px4TOj15RbtQ_U5dQLTLYtbTmi8nZnzbd3ptm-M0DtU&e=
SEARCH the MAILING-LIST at:  https://urldefense.us/v2/url?u=http-3A__www.mail-2Darchive.com_wien-40zeus.theochem.tuwien.ac.at_index.html&d=DwIGaQ&c=v4IIwRuZAmwupIjowmMWUmLasxPEgYsgNI-O7C4ViYc&r=lTD7jQRfMViWEsN8TZ1wLmkMhVe4MCRH76GADmGBpD4&m=OsbEKiRMVyoB6JJ9cR0TBU0G3VtOXEqJhXaWmGQ8ribakT8R1LoQvMUNDI4mByuR&s=h9y3KiwHpKBa9q59-XgJShN2usokPefQd9x2_B8_hvs&e=
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://zeus.theochem.tuwien.ac.at/pipermail/wien/attachments/20230821/617b265e/attachment-0001.htm>