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Dear <span style="font-size: 12pt;">Gerhard,</span></div>
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<span style="font-size: 12pt;"><br>
</span></div>
<div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
<span style="font-size: 12pt;">Thank your for detailed answer.</span></div>
<div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
<span style="font-size: 12pt;"><br>
</span></div>
<div style="" class="elementToProof"><span style=""><font face="Calibri, Arial, Helvetica, sans-serif" style="color: rgb(0, 0, 0);"><span style="font-size: 12pt;">If I
</span>understand<span style="font-size: 12pt;"> it correctly the SOC part is introduced to the hamiltonian as</span></font></span></div>
<div style="" class="elementToProof"><span style=""><font face="Calibri, Arial, Helvetica, sans-serif" style="color: rgb(0, 0, 0);"><span style="font-size: 12pt;"><br>
</span></font></span></div>
<div style="" class="elementToProof"><span style=""><font face="Calibri, Arial, Helvetica, sans-serif" style="color: rgb(0, 0, 0);"><span style="font-size: 12pt;"><phi|\zeta (\sigma l)|phi> (1)</span></font></span></div>
<div style="" class="elementToProof"><span style=""><font face="Calibri, Arial, Helvetica, sans-serif" style="color: rgb(0, 0, 0);"><span style="font-size: 12pt;"><br>
</span></font></span></div>
<div style="" class="elementToProof"><span style=""><font face="Calibri, Arial, Helvetica, sans-serif" style="color: rgb(0, 0, 0);"><span style="font-size: 12pt;">following the
</span>expression<span style="font-size: 12pt;"> for wave function phi (2.4 in the manual)</span></font></span></div>
<div style="" class="elementToProof"><span style=""><font face="Calibri, Arial, Helvetica, sans-serif" style="color: rgb(0, 0, 0);"><span style="font-size: 12pt;">|phi_k(r)> = \sum_{L} [A_{L, k}u_L(r) + B_{L, k}{\dot u_L(r)}] Y_L </span></font></span></div>
<div style="" class="elementToProof"><span style=""><font face="Calibri, Arial, Helvetica, sans-serif" style="color: rgb(0, 0, 0);"><span style="font-size: 12pt;"><br>
</span></font></span></div>
<div style="" class="elementToProof"><font face="Calibri, Arial, Helvetica, sans-serif" style="color: rgb(0, 0, 0);">the expression (1) is naturally calculated as sum of four contributions and the first one has</font></div>
<div style="" class="elementToProof"><font face="Calibri, Arial, Helvetica, sans-serif" style="color: rgb(0, 0, 0);"><br>
</font></div>
<div style="" class="elementToProof"><font face="Calibri, Arial, Helvetica, sans-serif" style="color: rgb(0, 0, 0);">\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.</font></div>
<div style="" class="elementToProof"><font face="Calibri, Arial, Helvetica, sans-serif" style="color: rgb(0, 0, 0);"><br>
</font></div>
<div style="" class="elementToProof"><font face="Calibri, Arial, Helvetica, sans-serif" style="color: rgb(0, 0, 0);">Best,</font></div>
<div style="" class="elementToProof"><font face="Calibri, Arial, Helvetica, sans-serif" style="color: rgb(0, 0, 0);"><br>
</font></div>
<div style="" class="elementToProof"><font face="Calibri, Arial, Helvetica, sans-serif" style="color: rgb(0, 0, 0);">German</font></div>
<div style="" class="elementToProof"><span style=""><font face="Calibri, Arial, Helvetica, sans-serif" style="color: rgb(0, 0, 0);"><span style="font-size: 12pt;"><br>
</span></font></span></div>
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<div class="PlainText">Dr. German D Samolyuk<br>
Materials Theory Group<br>
Materials Science & Technology Division<br>
Oak Ridge National Laboratory<br>
Post Office Box 2008<br>
Oak Ridge, TN 37831-6138<br>
(865) 241-5394<br>
(865) 241-3650 (FAX)<br>
</div>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Wien <wien-bounces@zeus.theochem.tuwien.ac.at> on behalf of Fecher, Gerhard <fecher@uni-mainz.de><br>
<b>Sent:</b> Friday, August 18, 2023 4:13 AM<br>
<b>To:</b> A Mailing list for WIEN2k users <wien@zeus.theochem.tuwien.ac.at><br>
<b>Subject:</b> [EXTERNAL] Re: [Wien] SOC value \zeta</font>
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<div class="PlainText">Dear German,<br>
as mentioned by Peter<br>
<a href="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=</a>
<br>
one may use the potential to estimate the spin-orbit coupling strength.<br>
That is one may find the average of 1/r dV/dr by integration over space, <br>
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.<br>
(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 !)<br>
- Care has to be taken on the singularity at the nucleus (r=0) as mentioned previously, check r_0 !<br>
- But which space do you take for the integration in case you have different atoms ?<br>
the muffin tin spheres or some Bader basins ?<br>
This is also the problem when 'estimating' so called site specific magnetic moments,
<br>
the 'size' of the individual atoms in compounds is not known a priori !<br>
<br>
To calculate <Psi| H | Psi> you have to understand the wave functions in FPLAPW<br>
as mentioned by Peter in<br>
<a href="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=</a>
<br>
Note that the wave functions (of the valence electrons) are k-dependent<br>
This you see from the spin orbit splitting of the bands that depends on the direction in k-space.<br>
Maybe you also think too much in atomic physics, where the spin orbit splitting does not depend k or any direction.<br>
<br>
Ciao<br>
Gerhard<br>
<br>
DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:<br>
"I think the problem, to be quite honest with you,<br>
is that you have never actually known what the question is."<br>
<br>
====================================<br>
Dr. Gerhard H. Fecher<br>
Institut of Physics<br>
Johannes Gutenberg - University<br>
55099 Mainz<br>
________________________________________<br>
Von: Wien [wien-bounces@zeus.theochem.tuwien.ac.at] im Auftrag von Samolyuk, German D. via Wien [wien@zeus.theochem.tuwien.ac.at]<br>
Gesendet: Donnerstag, 17. August 2023 17:43<br>
An: A Mailing list for WIEN2k users<br>
Cc: Samolyuk, German D.<br>
Betreff: Re: [Wien] SOC value \zeta<br>
<br>
Gerhard,<br>
<br>
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.<br>
<br>
Gavin,<br>
<br>
Thank you, the references help, but I'd rather don't hack the code 🙂.<br>
<br>
Thank you,<br>
<br>
German<br>
<br>
<br>
Dr. German D Samolyuk<br>
Materials Theory Group<br>
Materials Science & Technology Division<br>
Oak Ridge National Laboratory<br>
Post Office Box 2008<br>
Oak Ridge, TN 37831-6138<br>
(865) 241-5394<br>
(865) 241-3650 (FAX)<br>
________________________________<br>
From: Wien <wien-bounces@zeus.theochem.tuwien.ac.at> on behalf of Fecher, Gerhard <fecher@uni-mainz.de><br>
Sent: Thursday, August 17, 2023 2:23 AM<br>
To: A Mailing list for WIEN2k users <wien@zeus.theochem.tuwien.ac.at><br>
Subject: [EXTERNAL] Re: [Wien] SOC value \zeta<br>
<br>
I don't understand the question,<br>
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 ?<br>
<br>
The r dependence tells you already that there is no single value for 'zeta = zeta(r)'<br>
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,<br>
This explains why the spin orbit interaction is stronger for 'heavier' atoms.<br>
|1/r dV/dr| becomes large in the vicinity of the nucleus (infinity at r=0) for all atoms.<br>
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.<br>
<br>
Check the manual how to have the orbital moments printed.<br>
<br>
Ciao<br>
Gerhard<br>
<br>
DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:<br>
"I think the problem, to be quite honest with you,<br>
is that you have never actually known what the question is."<br>
<br>
====================================<br>
Dr. Gerhard H. Fecher<br>
Institut of Physics<br>
Johannes Gutenberg - University<br>
55099 Mainz<br>
________________________________________<br>
Von: Wien [wien-bounces@zeus.theochem.tuwien.ac.at] im Auftrag von Samolyuk, German D. via Wien [wien@zeus.theochem.tuwien.ac.at]<br>
Gesendet: Mittwoch, 16. August 2023 23:20<br>
An: wien@zeus.theochem.tuwien.ac.at<br>
Cc: Samolyuk, German D.<br>
Betreff: [Wien] SOC value \zeta<br>
<br>
Dear colleagues,<br>
<br>
I'm running wien2k version WIEN2K_19_LI on linux cluster. The goal is to analyze magnetic anisotropy energy in YCo_5 intermetallic.<br>
<br>
As it was explained in few presentation discussing SOC implementation in wien2K it's added in following form<br>
<br>
\zeta ({\vec \sigma}{\vec l}), where \zeta = 1/(2Mc^2) 1/r^2 dV/dr.<br>
<br>
Question: is it possible to output value \zeta for each atom, orbital moment?<br>
<br>
I cant find it in output files and was not able to find following discussion in archive.<br>
<br>
Thank you,<br>
<br>
German<br>
<br>
Dr. German D Samolyuk<br>
Materials Theory Group<br>
Materials Science & Technology Division<br>
Oak Ridge National Laboratory<br>
Post Office Box 2008<br>
Oak Ridge, TN 37831-6138<br>
(865) 241-5394<br>
(865) 241-3650 (FAX)<br>
_______________________________________________<br>
Wien mailing list<br>
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